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Dynamic Cache Consistency Schemes for Wireless Cellular Networks

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					IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 1, JANUARY 2006                                                                         1




                Dynamic Cache Consistency Schemes for
                     Wireless Cellular Networks
                                  Zhijun Wang, Mohan Kumar, Sajal K Das, and Huaping Shen



   Abstract— Caching frequently accessed data objects at the                      Asynchronous Stateful (AS) scheme [9], a server maintains
local buffer of a mobile user (MU) has been found to be                           a state that records all retrieved data objects for each MU
very effective in improving information availability in mobile                    cache. Thus, when an MU wakes up from a disconnected
wireless environments. Several mechanisms have been proposed
in the literature to address the challenging problem of cache                     state, cache consistency is maintained by referring to the
consistency in cellular wireless networks. However, these mech-                   corresponding cache state in the server. Our recently proposed
anisms are limited to single cell systems. In this paper, we                      Scalable Asynchronous Cache Consistency Scheme (SACCS)
develop a novel Dynamic Scalable Asynchronous Cache Consis-                       [12][13] is a hybrid approach which exploits server’s partial
tency Scheme (DSACCS) that can adaptively maintain mobile                         knowledge of MU caches and maintains flag bits in the server
data objects globally or locally depending on the minimum
consistency maintenance cost in multi-cell systems. The cost                      as well as in the MU caches.
function is derived by taking into account each data object’s                        The preceding approaches have focused on the cache con-
update frequency, MUs’ access pattern and roaming frequency,                      sistency in single-cell mobile environments. It turns out that
number of cells and number of MUs in the system. Extensive                        a cache consistency scheme designed for a single cell is not
simulation studies demonstrate that DSACCS outperforms three
existing cache strategies extended to multi-cell environments. The                directly applicable to multi-cell systems. Hence, there is a need
three cache consistency strategies are homogeneous invalidation                   for effective cache consistency schemes that achieve optimized
reports (IRs), inhomogeneous IR without roaming check, and                        cache performance in multi-cell systems.
inhomogeneous IR with roaming check. Finally, an improvisation                       In this paper, we propose three types of cache consistency
of DSACCS, called DSACCS-G, is proposed for grouping cells
in order to facilitate effective cache consistency maintenance in                 invalidation reports (IRs) for multi-cell systems using SACCS
multi-cell systems.                                                               and AS schemes: (i) homogeneous IR, (ii) inhomogeneous
                                                                                  IR without roaming check, and (iii) inhomogeneous IR with
   Index Terms— Cache consistency, invalidation reports, mobil-
ity, mobile wireless networks.                                                    roaming check. Simulation results show that the homogeneous
                                                                                  IR strategies are more efficient for slow updating data ob-
                                                                                  jects, fast roaming MUs and small systems. Whereas, the
                           I. I NTRODUCTION                                       inhomogeneous strategies are more efficient for fast updating
   Caching frequently accessed data objects at the local buffer                   data objects, slow roaming MUs and large systems. Based on
of a mobile user (MU) can significantly improve the perfor-                        these observations, we derive two consistency maintenance
mance of mobile wireless networks. However, cache consis-                         cost functions associated with roaming of MUs for globally
tency maintenance in such environments is a challenging task                      and locally maintained data objects. A globally maintained
due to frequent disconnections and mobility of MUs.                               data object implies that its IR is broadcast to every cell in the
   Several cache consistency maintenance schemes have been                        system.
proposed in the literature for mobile wireless environments                          Based on these two cost functions, we design and evaluate a
[1] [4] [5] [7] [8] [9] [10] [11] [12] [13] [15]. The goals of                    Dynamic Scalable Asynchronous Cache Consistency Scheme
these schemes are to ensure valid data objects in the cache to                    (DSACCS) for wireless cellular networks. In DSACCS, the
enhance their availability and minimize overhead due to con-                      IR of a data object is broadcast globally or locally depending
sistency maintenance. Based on the underlying methodologies,                      on which has the minimum consistency maintenance cost. For
these schemes can be classified into three categories: stateless,                  efficient broadcast of IRs, some cells are grouped into a logical
stateful and hybrid. In stateless approaches [1] [4] [7] [8] [10]                 cell. A variation of DSACCS for such grouped cells is called
[11] [15], a server has no knowledge of MU caches. Even                           DSACCS-G. Simulation results show that the performance of
though these schemes employ simple database management,                           DSACCS and DSACCS-G is superior to three extended cache
they have poor ability to support disconnections and mobility                     strategies, for varying number of MUs and data objects in the
of MUs. On the other hand, in statef ul approaches such as                        system.
   Manuscript received July 12, 2003; revised DATE; accepted January 31,             The rest of the paper is organized as follows. Section II
2005. The associate editor coordinating the review of this letter and approving   briefly describes AS and SACCS. In Section III, the three
it for publication was K. Leung.                                                  types of cache consistency maintenance strategies for roaming
   Zhijun Wang is with the Department of Computing, The Hong Kong
Polytechnic University, Hong Kong (e-mail: cszjwang@comp.polyu.edu.hk).           MUs are introduced and applied to SACCS and AS. The three
   Mohan Kumar, Sajal Das, and Huaping Shen are with the Center for               strategies are evaluated for various multi-cell environments in
Research in Wireless Mobility and Networking (CReWMaN), Department                Section IV. In Section V, a DSACCS is designed to achieve
of Computer Science and Engineering, The University of Texas at Arlington,
Arlington, TX 76019, USA (e-mail: kumar, das, hpshen@cse.uta.edu).                optimized cache performance in multi-cell environments based
   Digital Object Identifier 10.1109/TWC.2006.xxxxx.                               on the two cost functions. A scheme combining DSACCS with
                                                              1536-1276/06$20.00 c 2006 IEEE
2                                                           IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 1, JANUARY 2006



cell grouping is also evaluated. Finally, conclusions are offered                               Orignal
                                                                                                Server
in Section VI.
                                                                                                                          Wired Network
                                                                                                              1   0




               II. R EVIEW OF AS AND SACCS                                                                                                         Orignal
                                                                                                          MSC                                       Server
   We briefly describe AS and SACCS in this section. As men-                           1
tioned earlier, both schemes focus on the cache consistency in
                                                                                                                                       Mobile Switching Center
a single cell environment.                                                                                                     1   0




                                                                                                                                            (MSC)
                                                                                            2             3
A. Asynchronous Stateful (AS) Scheme
                                                                                           A
   AS [9] is one of the few stateful cache consistency mainte-                                                        4
                                                                                                                               5                Server Cache
nance schemes in which a server maintains a state that records                                        B
                                                                                Mobile User (MU)
all retrieved data objects for each MU cache. Whenever a                                                                                         MU Cache

server receives an update from the original server for each                     Base Station (BS)
recorded data object, it immediately broadcasts that object’s
IR. After an MU wakes up, it forwards the first query along            Fig. 1.    Wireless cellular network architecture.
with the sleep time to the server to check the cache status.
After receiving such a query, the server counts all the updated
data objects cached by that particular MU during its sleep               III. P ROPOSED C ACHE C ONSISTENCY M AINTENANCE
time. The IDs of these objects are sent through an invalidation                     S CHEMES FOR M OBILE U SERS
check message to the MU to ensure the cache consistency.
                                                                         In this section, we introduce the wireless cellular architec-
                                                                      ture followed by three cache consistency maintenance strate-
B. Scalable    Asynchronous      Cache     Consistency    Scheme      gies for roaming MUs, and apply them to SACCS and AS.
(SACCS)                                                               These strategies were first proposed by us in [14], and applied
   SACCS [12] [13] is a hybrid cache consistency maintenance          to Timestamp (TS) [1] and SACCS schemes. However, we
scheme that is scalable and efficient. It uses (i) flag bits at the     omit the discussions on TS because it has much larger average
server cache and MU cache, (ii) an identifier (ID) in MU cache         access delay as shown in [12] [13] [14].
for each entry after its invalidation, and (iii) an uncertain state
in MU cache.
                                                                      A. Wireless Cellular Network Architecture
   Each data object in a server is associated with a retrieving
flag bit. When an object is retrieved by an MU, its flag                   Fig. 1 shows a wireless cellular network architecture con-
bit is set implying that a valid copy may be available in             sisting of a wired backbone network, multiple mobile switch-
the MU cache. When the data object is updated, the server             ing centers (MSCs), base stations (BSs) and mobile users
immediately broadcasts its IR and resets the retrieving flag           (MUs). An MSC is connected to the wired network and
bit, implying that there is no valid copy in any MU cache.            controls multiple BSs through wired links. A BS serves
Hence, subsequent updates do not entail broadcast of IR until         multiple MUs in a cell through wireless links (channels). Each
the flag bit is reset. At the time of the IR broadcast, an MU is       MSC has a cache, called server cache, to store all accessed
either in an awake, i.e., connected with base station (BS), or        data objects and maintains cache consistency at MU caches
in a sleep state. If an MU is in the awake state, it deletes the      through BSs.
valid copy and sets the entry into ID-only state (i.e., the data         We use roaming to indicate the movement of an MU from
object is deleted, but an ID is kept) after it receives the IR.       cell to cell. There are two types of MU roaming. In intra-
On the other hand, if an MU is in the sleep state, it misses          roaming, an MU roams between cells that are all controlled
the IR and upon wake up, it sets all valid cache entries to           by the same MSC. As shown in Figure 1, the movement of
an uncertain state. An uncertain entry must be refreshed              an MU, say A, from Cell 2 to Cell 3 is an example of intra-
(by downloading a valid data object or setting to valid entry         roaming. In inter-roaming, on the other hand, an MU roams
through a confirmation message) or checked before its usage.           between cells belonging to different MSCs. The movement of
Thus the cache consistency is guaranteed in error-free wireless       the MU, B from Cell 4 to Cell 3 is an example of inter-
communication environments.                                           roaming.
   In an error-prone environment, SACCS can also be applied              In our design, we assume a read-only system (e.g., world
by setting a time-to-live (TTL) for each cached entry [13]. An        wide web), where the MUs can read data objects that are
MU automatically sets an entry into uncertain state when the          updated only at the original servers. Whenever a data object
TTL for that entry expires. If a data object is updated before        is updated, its information (IR or updated object) is forwarded
its TTL expiration, the IR may be lost to the MU and there            to an MSC through cache consistency maintenance protocols
is the probability of a stale hit at the MU. As shown in [13],        [6] [16] in the wired networks. In this paper, we focus on
SACCS provides a weak cache consistency for MU caches                 the cache consistency between a server cache and MU caches
with an insignificant stale cache hit probability in error-prone       through wireless links. Cache consistency between MSCs and
environments.                                                         original servers is beyond the scope of the work.
WANG et al.: DYNAMIC CACHE CONSISTENCY SCHEMES FOR WIRELESS CELLULAR NETWORKS                                                         3



   A roaming MU is in one of two states: awake or sleep. In          data objects into the uncertain state. The cache consistency is
the sleep state, no extra action is needed in either SACCS or        guaranteed because an uncertain entry must be refreshed or
AS. In SACCS, an MU sets all of its valid cache entries to           checked before its usage.
uncertain state upon wake up. In AS, when a roaming MU                  In IM-AS, an MSC maintains a cache state for each MU.
wakes up, its first query is automatically sent to an MSC             The IRs of cached data objects in an MU are broadcast to the
through the current BS. Then the MSC retrieves or resets the         MU current resident cell. A forced wakeup event is also used
cache state corresponding to the current BS, thus maintaining        for a roaming MU. In other words, after an MU arrives at a
cache consistency. For a roaming MU in the awake state, the          new cell, its first query and roaming time must be forwarded
cache consistency maintenance is different from that in single-      through its new BS to an MSC. The roaming time is
cell systems. We propose three types of cache consistency            defined as the time when an MU switches the communication
strategies for roaming MUs that are awake in the following           channel from its previous cell to the new cell. After the MSC
subsections.                                                         receives the first query message, it resets the corresponding
                                                                     state to its new cell for an intra-roaming MU, or retrieves the
B. Homogeneous IR Strategy                                           corresponding state from the previous MSC and sets it to the
                                                                     new cell for an inter-roaming MU. Then the MSC sends an
   In this strategy, all BSs in the system broadcast the same IR
                                                                     invalidation-check message to the MU that contains all cached
to MUs. When an MU roams among these cells, there is no
                                                                     data objects updated during the interval between roaming and
difference between a roaming and a static MU with regard to
                                                                     current time. This is because an MU may miss IR broadcast
cache consistency maintenance. Consequently, the impact of
                                                                     during roaming. After the MU receives an invalidation-check
mobility on the performance of an MU cache is minimized.
                                                                     message, it drops all invalid data entries, thus maintaining
Therefore, such strategies are efficient for fast roaming MUs.
                                                                     cache consistency.
However, the total IR traffic for each cell is increased as
                                                                        One advantage of this kind of strategy is that it minimizes
the number of cells increases. This is because any IR of a
                                                                     IR traffic. But the additional uplinks are introduced by forced
retrieved data object must be broadcast to every cell even if
                                                                     wakeup events. The strategy is superior to others for a system
it is only queried in one cell. The homogenous IR strategy
                                                                     with slow roaming MUs and fast updating data objects. It also
is not scalable for large number of cells as demonstrated in
                                                                     exhibits better scalability than the homogeneous strategy.
Section IV. The corresponding schemes of SACCS and AS
will be called HM-SACCS and HM-AS, where “HM” stands                 D. Inhomogeneous IR with Roaming Check Strategy
for “homogeneous”.
   In HM-SACCS, only a single retrieving flag bit is needed              The IR traffic varies in different cells, similar to that in the
for each data entry in an MSC cache. When a data object              inhomogeneous IR without roaming check. The variations of
is queried, its corresponding flag bit is set. Whenever a data        SACCS and AS will be called CK-SACCS and CK-AS, where
object with a set flag bit is updated, its IR is broadcast to         “CK” stands for “check”.
                                                                        In CK-SACCS, after an MU arrives at a new cell, it
every cell, and the flag bit is reset. For a system with multiple
                                                                     immediately sends its roaming time and an ID list (that
MSCs, when an MSC needs to set the retrieving flag bit for
                                                                     includes all valid cache data object IDs) to an MSC. The
a cache entry, it must send message to all other MSCs to set
                                                                     MSC in turn sends an invalidation-check message containing
the flag bit for the same entry. This guarantees every cell in
                                                                     all data objects (cached in the MU) that were updated during
the system broadcasts the same IR.
   In HM-AS, the MSC maintains a cache state that records            the roaming time. The MU drops all invalidated cache entries.
all queried data objects for each MU. When a recorded data           Then the MSC sets the corresponding retrieving flag bit for
object is updated, the MSC broadcasts its IR to every cell,          each valid entry in the new cell. After the flag bit is set, any
then the cache consistency is maintained as in a single cell.        future IRs for these valid entries will be broadcast in that cell
For a system with multiple MSCs, an IR from one MSC is               to maintain cache consistency.
                                                                        In CK-AS, a roaming MU immediately sends a roaming
first broadcast to all other MSCs and from there to the cells
                                                                     check message to an MSC. The message includes its roaming
in the system.
                                                                     time and previous MSC identifier. After the MSC receives the
                                                                     roaming check message, it resets the corresponding cache state
C. Inhomogeneous IR without Roaming Check Strategy                   to the new cell for an intra-roaming MU, or retrieves the cache
   In this strategy, the broadcast IR varies in different cells.     state from the previous MSC and sets it to the new cell for
A wakeup event is forced by a roaming MU. The variations             an inter-roaming MU. If any data object is updated between
of SACCS and AS are called IM-SACCS and IM-AS, respec-               the roaming time and the current time, an invalidation-check
tively, where “IM” stands for “inhomogeneous”.                       message is sent to the MU to invalidate the updated cache
   In IM-SACCS, a data object in an MSC cache has multiple           entries. Consequently, the future IRs for these valid entries
retrieving flag bits, each corresponding to a particular cell. If     are broadcast to the new cell.
the data object is retrieved in one cell, the corresponding flag         The cost for this strategy is an additional uplink for each
bit is set. When a data object is updated, the MSC informs           roaming. But the valid entries of an MU cache can be used
the BSs under it. A BS in turn broadcasts the IR if the              immediately, resulting in the reduced access delay for valid
corresponding flag bit is set for that cell. All flag bits are reset   cache data objects. Finally, the IR traffic is also minimized.
after the data object is updated. A wakeup event is forced for          The features of the above three cache consistency strategies
each roaming MU in the sense that the MU sets all its valid          are summarized in Table I.
4                                                             IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 1, JANUARY 2006


                                                                  TABLE I
                                    F EATURES OF T HREE C ACHE C ONSISTENCY M AINTENANCE S TRATEGIES

          Strategy                 Action on Roaming            Broadcast       Fast       Roaming       Fast   Updating     Scalability
                                                                IR              MU                       Data Object
          Homogeneous              no action                    all cells       efficient                 not efficient           poor
          Inhomogeneous without    force a wakeup event         one cell        not efficient             efficient              good
          roaming check
          Inhomogeneous     with   immediately send a roam-     one cell        not efficient             efficient              good
          roaming check            ing check message



    IV. P ERFORMANCE E VALUATION OF T HREE S TRATEGIES
                                                                                                              9
   The performance of the three proposed strategies are eval-
uated in [14] by varying the parameters in terms of the                                              8                  10
average MU sojourn time, the number of MUs in a cell,                                      19                 2              11
the number of data objects and cache size. The results show                                          7                  3
that the homogeneous IR strategies are more efficient for fast
roaming MUs and small systems, while the inhomogeneous                                     18                  1             12
IR strategies are more efficient for slow roaming MUs and                                          6                     4
large systems. Due to space limitation, these results are not
presented here. In this section, we study the impacts of other                             17                 5               13
two parameters: data object update frequency and the number
                                                                                                 16                     14
of cells in the system.
   In the simulations, an MU query process is assumed to                                                     15
follow a Poisson process. The access probability for each data
object follows a Zipf-like distribution [3]. The update time
interval is a Poisson distribution. The sleep-wakeup process           Fig. 2. Multi-cell configurations: Configuration 1 includes Cells 1 and 2,
is modeled as a two-state Markov chain with MUs alternating            Configuration 2 is composed of Cells 1-7, and Configuration 3 includes all
                                                                       cells 1-19.
between sleep and awake states. All requests during a sleep
state are ignored. The MU roaming process is also assumed
to be Poisson with an average sojourn time, Tr . When an MU                 MU
arrives in a new cell, the data object queries that were sent to            bp : size of a data object (bytes)
                                                                            •
the previous BS are resent to the current BS. After receiving             • bu : uplink message size (bytes)
such requests, the current BS sends a message to the previous             • bd : downlink control message size (bytes)
BS indicating that the retrieved data objects by the roamed               We consider two metrics for measuring the system perfor-
MU are not necessary to be broadcast. The previous BS, in              mance: average access delay (D) and uplink per query (UPQ).
turn, removes those data objects from the broadcast queue if           The delay is counted as 0 if the accessed data object is valid
they are not retrieved by other MUs in the cell.                       in the MU cache. Otherwise, it is counted as the time interval
   Assume that each cell has an uplink channel with band-              between the query response and the query initiation. An uplink
width Wu bps (bits per second) and a downlink channel                  is counted when a query is retrieved from the BS through an
with bandwidth Wd bps. There are two queues for downlink               uplink channel. U P Q is defined as the number of total uplinks
channel, one having a higher priority than the other. Each             that include missing queries, uncertain queries, and roaming
queue is scheduled on a first in first out (FIFO) basis. The             check messages divided by the number of queries in a system.
IR messages are buffered in the higher priority queue, and all         Hence, for CK-SACCS and CK-AS schemes, U P Q may be
other messages are buffered in the lower priority queue and            larger than 1 due to an additional roaming check uplink for
is scheduled only if the higher priority queue is empty. All           each roaming.
uplink messages in a cell are buffered in a queue scheduled               Fig. 2 shows three configurations in a multi-cell environ-
on FIFO basis. The following parameters are defined in our              ment. Configuration 1 (shaded Cells 1 and 2) is a simple two-
simulations:                                                           cell system. An MU from one cell can roam into another.
     •   N : number of data objects in the system                      Configuration 2 (Cells 1-7) is a tier one cellular system such
     •   M : number of MUs in the system                               that an MU from cell 1 can roam into each of the neighboring
     •   C: MU cache size (bytes)                                      cells with a probability (1/6). An MU from one of Cells
     •   B: number of BSs                                              2 - 7 may roam into Cell 1 with a probability 1/6 and
     •   λ: average query arrival rate for an MU                       another neighboring cell with a probability 5/12. Configuration
     •   Tu : average update time interval for a data object (sec)     3 (Cells 1-19) is a tier two system. Each of inner cells 1
     •   Ts : time period of a sleep-wakeup cycle for an MU (sec)      through 7 has 6 neighbors. An MU from an inner cell has
     •   s: ratio of sleep time to the sleep-wakeup period for an      equal probability (1/6) of roaming into any of its neighboring
WANG et al.: DYNAMIC CACHE CONSISTENCY SCHEMES FOR WIRELESS CELLULAR NETWORKS                                                                                     5



cells. A cell, which is not an inner cell, is called an outer cell.                                                                  11
                                                                                                               HM−SACCS                            HM−AS
                                                                                         4                     IM−SACCS
An even numbered outer cell has four neighboring cells. An                                                     CK−SACCS
                                                                                                                                                   IM−AS
                                                                                                                                                   CK−AS
                                                                                                                                     10
MU from such a cell has 1/6 probability of roaming into one of
its two inner neighboring cells and 1/3 probability of roaming                         3.5
                                                                                                                                      9
into one of its two outer neighboring cells. On the other
hand, an odd numbered outer cell has three neighboring cells                             3                                            8




                                                                         D (Seconds)
originally. For each such cell we make another odd numbered
                                                                                                                                      7
outer cell as its logical neighbor (indicated by arrows in Figure                      2.5
2) so that each odd numbered cell also has four neighbors. An                                                                         6
MU from such a cell has 1/6 probability of roaming into its                              2
inner neighboring cell, 1/3 into each of its even numbered                                                                            5
outer neighboring cells and 1/6 into the logical neighboring                           1.5
cell. This roaming probability balances the number of MUs                                                                             4

in each cell . For studying the impact of data object update
                                                                                         1                                            3
frequency (Case 1), only Configuration 2 is used, and for                                  1    2        4                 8            1   2   4              8
                                                                                                   T (x200 Seconds)
studying impacts of the number of cells (Case 2), all three                                         u

                                                                                                                               (a)
configurations are used.
   In the two cases, we set Wu = 4 Kbps, Wd = 50 Kbps,                                  1.1
                                                                                                                                                   HM−SACCS
bu = 20 bytes, bd = 20 bytes, N = 10, 000 and C =                                                                                                  IM−SACCS
                                                                                                                                                   CK−SACCS
1 M bytes. Note that the uplink roaming check message size                             1.05                                                        HM−AS
                                                                                                                                                   IM−AS
                                                                                                                                                   CK−AS
for an MU using the CK-SACCS is set as the number of                                     1
valid cache data objects times 4 bytes. The third generation
(3G) wireless cellular system such as General Packet Radio                             0.95
System (GPRS) can support up to 144 Kbps bandwidth in
                                                                         UPQ




a cell for high mobility traffic. We consider a system of                                0.9

public data applications without security consideration, such
                                                                                       0.85
as news, traffic information, etc. Other security based traffic
(e.g., email, ftp, etc.) can not be shared by MUs and must use                          0.8
a secure communication model. Hence we choose 50 Kbps
for public data communication traffic in our simulations.                               0.75

   We consider a database with 10 types of data objects. The
                                                                                        0.7
data objects’ update rate, size and percentage of the total                                1            2                 4                                   8

database are shown in Table II. In Case 1, the effects of                                                             Tu (x200 Seconds)
                                                                                                                              (b)
data object update frequency are studied, and hence the update
frequency of all data objects are set to be the same. The             Fig. 3. Performance of six schemes vs average data update interval (Tu ):
                                                                      a) average access delay (D); b) average uplink per query (U P Q).
average data object size for the Web system is about 25
Kbytes in wired networks [2]. We choose a database with
smaller average data object size, based on the observation
that the users accessing wireless networks usually pay more           events, we assume that each MU is always in awake state. Six
attention to the dynamic data objects of smaller size.                schemes based on the three proposed strategies are evaluated.
   Each MU may be different from others. The parameters λ,            We also consider a very basic scheme, where an MU has no
s, and Ts for each MU can take values from the corresponding          cache in its local buffer and every data access needs to be
given sets. Each value has equal probability to be chosen for         retrieved from the BS, and no IR is broadcast in the system.
an MU. The value set for λ is (1/20, 1/35, 1/50, 1/65, 1/80),            Fig. 3 shows the relationship between Tu and the system
for s is (0.15, 0.3, 0.45, 0.60, 0.75), for Ts is (500, 1000,         performance in terms of D and U P Q for six schemes. In
1500, 2000, 2500) in sec, and for Tr is (100, 400, 1600, 6400,        the basic scheme, D is independent of Tu since each data
25600) in sec. In Case 1, we assume all MUs are always in the         access is retrieved from the BS and no IR is broadcast. D
awake state. In this case, sleep-wake up events do not affect         for this scheme (not shown in the figure) is about 31 secs
the performance. The most popular data object in the Zipf-            which is much larger than the other schemes. This indicates
like distribution for each MU is shifted by a random number           that caching data objects at the MU local buffer is an effective
between 0 and 99, and its coefficient is set to 0.9. For SACCS         method to improve system performance.
based scheme, similar to the single-cell case [13], each IR is           In all these schemes, both D and UPQ decrease as the
broadcast twice to reduce the stale hit probability.                  update interval increases. The performance of SACCS based
                                                                      schemes is always better than that of AS based schemes for
                                                                      Tu in the range from 200 to 1600 secs. The SACCS based
A. Case 1: Impact of Data Object Update Frequency                     schemes have more than 50% performance gain in terms of D
  In this case, M = 350, i.e., 50 MUs per cell, and Tu of             over AS based schemes, thus demonstrating their superiority
each data object is assumed to be the same. In order to isolate       in multi-cell environments.
the impact on the performance caused by the sleep-wakeup                 Among SACCS based schemes, IM-SACCS exhibits the
6                                                            IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 1, JANUARY 2006


                                                                  TABLE II
                                                  T EN T YPES OF DATA O BJECT IN DATABASE

                        Data Type             1        2      3     4                  5            6            7        8            9         10
                      Size (Bytes)           500      1K     2K     3K         4K                  5K        6K          7K         8K           9K
                Update interval(Tu ) (Sec)   60       120   240    480      960                    1920      3840        7680      15360        30720
                     Percentage (%)           5        5     10     10           20                 20         10        10            5         5



best performance on D at the cost of slightly more UPQ                                       3
                                                                                                    HM−SACCS
                                                                                                                                           6
                                                                                                                                                HM−AS
than HM-SACCS, for Tu < 800 secs. When Tu > 800 secs,                                               IM−SACCS
                                                                                                    CK−SACCS                           5.95
                                                                                                                                                IM−AS
                                                                                                                                                CK−AS

HM-SACCS has the best performance on both D and UPQ.                                                                                     5.9
The data objects with smaller Tu update fast, leading to an
increase in additional IR traffic in HM-SACCS. On the other                                 2.5
                                                                                                                                       5.85

hand, fast updating data objects in the cache become invalid                                                                             5.8




                                                                             D (Seconds)
quickly. Thus, in IM-SACCS, the cache hit ratio is reduced
                                                                                                                                       5.75
for fast updating data objects and results in fewer additional
confirmation messages due to the roaming. Hence, IM-SACCS                                                                                 5.7

has better performance for fast updating data objects. For data                              2
                                                                                                                                       5.65
objects with large Tu , the additional confirmation traffic is
                                                                                                                                         5.6
over the additional IR traffic and makes HM-SACCS superior
to IM-SACCS. Similar patterns for AS based schemes are                                                                                 5.55

also observed. For small Tu < 800 secs, HM-AS has the best                                 1.5                                           5.5
performance. However, IM-AS and CK-AS are superior to                                         2          7
                                                                                                             B
                                                                                                                              19            2     7                19

HM-AS in terms of D when Tr > 800 secs.                                                                                            (a)

   In summary, the inhomogeneous strategies are more ef-                                     1
ficient for fast updating data objects, while homogeneous
strategies are better for slow updating data objects.                                      0.98


                                                                                           0.96

B. Case 2: Impact of the Number of Cells
                                                                                           0.94
                                                                                                                                                        HM−SACCS
   The relationship between the performance and the number                                                                                              IM−SACCS
                                                                                                                                                        CK−SACCS
                                                                                           0.92
of cells in the system is studied here. As shown in Fig. 4,                                                                                             HM−AS
                                                                            UPQ




                                                                                                                                                        IM−AS
                                                                                                                                                        CK−AS
three multi-cell configurations are simulated. The number of                                 0.9
MUs for each cell is set to 100 initially. Thus, Configurations
                                                                                           0.88
1, 2 and 3 have 200, 700 and 1900 MUs respectively.
   From Figs. 4 (a) and (b), we observe that the performance                               0.86
of both SACCS and AS based schemes are similar, although
                                                                                           0.84
SACCS based schemes perform better than AS based schemes.
In Configuration 1, homogeneous IR strategies have the best                                 0.82
                                                                                               2                     7                                             19
performance. In the other two configurations, inhomogeneous                                                                         B

IR strategies show better performance. D for the homogeneous                                                                       (b)
IR strategies increases much faster than the inhomogeneous IR
strategies as the number of cells increases. U P Q is almost a           Fig. 4. Performance of six schemes vs number of cells (B): a) average
                                                                         uplink per query (U P Q); b) average uplink per query (U P Q).
constant for all strategies in all three multi-cell environments.
In the homogeneous IR strategies, every cell broadcasts the
same IRs that are for any retrieved data objects among these
cells. As the number of cells increases, the additional IR traffic        on these two functions, a Dynamic SACCS, called DSACCS,
increases leading to a longer D. However, there is no such               is proposed to optimize the system performance.
effect on inhomogeneous IR strategies. The results indicate
that the homogeneous IR strategies are not as scalable as                A. Consistency Maintenance Cost Functions
inhomogeneous IR strategies due to increased IR traffic.
                                                                            Through the performance evaluation of our proposed strate-
                                                                         gies, we conclude that the homogeneous IR strategies are more
    V. DYNAMIC S CALABLE A SYNCHRONOUS C ACHE                            efficient for slow updating data objects, fast roaming MUs
              C ONSISTENCY S CHEME                                       and small systems. On the other hand, the inhomogeneous
  In this section, we first derive two consistency maintenance            IR strategies are more efficient for fast updating data objects,
cost functions that define the cost associated with roaming of            slow roaming MUs and large systems. Hence, a good scheme
MUs for globally and locally maintained data objects. Based              should inherit positive features from both.
WANG et al.: DYNAMIC CACHE CONSISTENCY SCHEMES FOR WIRELESS CELLULAR NETWORKS                                                           7



    In a multi-cell system, the consistency of a data object           MU Procedure:
is said to be globally (locally) maintained if its IR must               IF (Send uplink query for di )
(may not) be broadcast to every cell in the system. For a                    IF (Find an entry for di in the cache)    {Get rfi and cmi }
                                                                              ELSE       {Set rfi and cmi as 0}
globally maintained data object, broadcasting IR to every cell                Send uplink query associated with rfi and cmi
results in additional IR traffic for these cells in which the                  IF (Find an entry for di in the cache)
data object is not retrieved. For a locally maintained data                      Reset rfi = 0 and cmi = 0
object, after an MU roams into another cell, the valid cache             IF(Cache a new entry i)       {Set rfi = 0 and cmi = 0}
entry is set to uncertain state even if the data object is still         IF (Refresh entry i)            {gfi = gi and rfi =0}
                                                                         IF (Get an IR of entry i)      {Invalid entry i and set rfi =0}
valid, thus leading to additional confirmation messages when              IF (Wake up from sleep)
the data object is accessed. Based on these observations,                   Reset roaming flag bit for each cache entry to 0
we derive two consistency maintenance cost functions that                IF (Arrive in a new cell)
define the costs associated with roaming of MUs for globally                  Set roaming flag bit as 1 for each valid entry
and locally maintained data objects. The cost for a globally                Set valid entry with global flag bit as 0 to be uncertain entry
(locally) maintained data object is the number of additional
IR (confirmation) messages for the object. Let us first define            MSC Procedure:
some parameters:                                                        IF (Receive an update for di )
                                                                                      g                g        l
    • αi : update arrival rate of ith data object, di
                                                                            Count Ri then forward Ri and Ri to each other MSC
                                                                                          g       l
                                                                            Calculate Ri and Ri for the whole system
    • λij : access arrival rate of di for jth MU, mj
        c
                                                                            IF (No retrieving flag bit is set in the system)
    • λik : access arrival rate of di at cell k                                   Update the cached di
    • sj : ratio of sleep time to the sleep-wakeup period of mj             ELSE
        g                                               g                           g         g              g       g
    • hij : hit ratio of globally maintained di (say di ) for mj                 Ci = β1 Ci + (1 − β1 )Ri and Ri = 0
                                                                                    l        l             l       l
        l                                             l
    • hij : hit ratio of locally maintained di (say di ) for mj
                                                                                 Ci = β2 Ci + (1 − β2 )Ri and Ri = 0
         g                                                                       IF(gi == 1) {Broadcast IR to every cell}
    • Ci : consistency maintenance cost associated with roam-
                                                                                 ELSE
      ing of MUs for dg per update period
                          i                                                            Broadcast IR to cells with set retrieving flag bits
         l
    • Ci : consistency maintenance cost associated with roam-                    Reset the retrieving flag bits for each cell
                                                                                        g       l
      ing of MUs for dl per update period                                        IF(Ci < Ci ) {gi = 1}
                          i
                                                                                 ELSE                {gi = 0 }
    In our model, the data object update and MU’s query,                IF (Receive a query for di )
roaming and sleep wake-up processes are assumed to be                       Set the retrieving flag bit for the corresponding cell
              g                                                                   l     l
Poisson. Ci is the number of additional IR messages for each                and Ri =Ri + cmi
update of di . During an update interval, if di is retrieved in             IF(rfi == 1 and query is uncertain query)
                                                                                                                                 l
the system, the IR is broadcast to every cell. In this case, if                  IF(The uncertain entry is still valid)       {Ri ++}
                                                                            Broadcast a valid or confirmed di as well as gi
di is not retrieved in a cell, the IR messages broadcast in that
                             g
cell are counted into Ci , giving (1), where B is the number
                                                                     Fig. 5.   Pseudo Codes for MSC and MU
of cells. The factor 2 is due to the broadcast of each IR twice.
The first term in Equation (1) is the number of IR messages for
dg in an update interval. The IR messages of dg are broadcast
  i                                                i
to every cell when di is retrieved in the system. The effective      and the hit ratio. The hit ratio is related to the data query
                                B    c
retrieving rate for di is       k=1 λik . The second term is the
                                                                     pattern, data update rate and cache size. The reduced hit ratio
                                  l
number of IR messages for di in an update interval, the IR           for a locally maintained data object in an MU cache depends
messages are only broadcast to cells in which di is retrieved.       on the MU’s roaming and query pattern.
    The difference between hg and hl is caused by the
                                  ij        ij
roaming of mj . For dl in the cache of mj , the valid entry
                           i                                         B. Description of DSACCS
for di is set to uncertain state after each roaming, therefore
                                  l                                     Based on the above two cost functions, DSACCS is pro-
the hit ratio of di is reduced. Ci is the summation of additional
                                                                     posed to minimize the data consistency maintenance cost in
confirmation messages from all MUs in the system during an
                                                                     a system. These costs for each data object are computed
update interval of di , the average of which is 1/αi . During this
                                                                     at the MSC, to determine whether it is globally or locally
period, mj has an average of (1−si )λij /αi accesses on di ,
                                                                     maintained.
thus the additional confirmation messages due to reduced hit
                                                                        Regardless of whether di is globally or locally maintained,
ratio is (hg − hl )(1 − si )λij /αi . Note that each confirmation
            ij     ij                                                  g
                                                                 l   Ci is measured as the average number of cells in which
incurs one uplink and one downlink message. Therefore, Ci
                                                                     di is not retrieved during an update interval. Whenever di
is given by
                                                                     is updated, the number of cells in which di is not retrieved
                                                                                             g                                  l
                                                                     is counted, and then Ci is recalculated by the MSC. Ci is
                 M
                                                 1                   the average number of additional confirmations from all MUs
           l
          Ci =         2(hg − hl )(1 − si )λij
                          ij   ij                             (2)    during an update interval. For dl , an additional confirmation
                 j=1
                                                 αi                                                   i
                                                                     may be introduced only when the uncertain entry is accessed.
  Equations (1) and (2) define two cost functions associated          In this case, an uncertain uplink message must be sent to
with roaming of MUs for maintenance of data objects globally         the MSC which can record all additional confirmations in
and locally. They are determined by B, M , data update rate          the system. For dg , an MU can identify the saved additional
                                                                                       i
8                                                                   IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 1, JANUARY 2006



                                 ∞               t B                                        B               ∞                           t
                                                                  B
                g                                                       λc τ                                                                           c
               Ci = 2B               αi e−αi t           λc e −
                                                          ik
                                                                  k=1    ik    dτ dt − 2                        αi e−αi t                   λc e−λik τ dτ dt
                                                                                                                                             ik
                             0                   0 k=1                                      k=1     0                               0
                         B
                               2αi          2Bαi
                     =                −                                                                                                                                        (1)
                             αi + λc
                                   ik
                                              B
                                        αi + k=1 λc
                                                  ik
                         k=1




confirmations and store at the local buffer. When di is accessed
through the uplink query, the additional confirmations are                                                              4
passed to the MSC.                                                                                              3                           9
                                                                                                                                                 University
   To measure two costs for each data object, some parameters                                                                                    Campus
                                                                                                1                      5                                    10
are introduced for each cache entry in the MSC and MUs. In                                                                                                           15
                                                                                                                2           1   0



                                                                                                                                                   8
                                    g  l   g    l
an MSC, five parameters (gi , Ci , Ci , Ri , Ri ) are associated
                                                                                                                                                                 1   0




                                                                                                                       6                               11                 16
with each cache entry i. Here gi is a global flag bit indicating
                                                                                                                                             7                       14
a globally (value 1) or locally (value 0) maintained di . The
                g         l                                       g
parameters Ri and Ri are the current measured values of Ci                                          1   0




                                                                                                            MSC                                             12
        l
and Ci . In an MU cache, the entry i has three additional                                                                                                        13
parameters (gfi , rfi , cmi ), where gfi is a global flag bit, rfi                                           BS
is a roaming flag bit (explained later) and cmi records the                        Fig. 6.   A multi-cell system.
number of saved additional confirmations for dg associated
                                                     i
with roaming. A global flag bit is also associated with each
downlink valid data and confirmation broadcast messages.                                                    l                   l
                                                                                  through increasing Ri by 1. Hence, Ri for dl is exactlyi
Two values of rfi and cmi are attached to each uplink query                                         g        g
                                                                                  measured but Ri for di may be different from the real value
message of di .                                                                   during update period of di . However, the average value (Ci )   g

   The cache management pseudo codes of MUs and MSCs                              is close to its real average value.
are shown in Fig. 5. In an MU cache, gfi is used to identify                          In an MSC, the retrieving flag bits for each cache entry are
a globally or locally maintained data object. When an MU                          managed in the same way as in IM-SACCS. When the MSC
roams into a new cell, a valid entry i is set to uncertain if gfi                 receives an update for di , if the retrieving flag bit is not set
= 0. The valid entry i is unchanged if gfi = 1. Whenever an                       for any cell in the system, the MSC just updates the cached
MU caches or refreshes entry i, the value of gfi is set to the                    di . Otherwise, the MSC first checks gi . If gi is set, the IR of
same as the global flag bit in the broadcast message.                              di is broadcast to every cell, else the IR is only broadcast to
   For dl , valid entry i is set to uncertain state after each
           i                                                                      the cells in which the retrieving flag bits are set. Now Ri is l
roaming. If di is not updated and refreshed, and the MU                           counted as the number of cells in which the retrieving flag bits
has no sleep-wake up event after roaming, the access of di                                              g        l                          g
                                                                                  are not set. Then Ci and Ci are updated as follows: Ci = β1
results in an additional confirmation due to roaming. We use                         g               g          l      l              l
                                                                                  Ci + (1 − β1 )Ri and Ci = β2 Ci + (1 − β2 ) Ri . Here β1 and
rfi to identify that the additional confirmations for di . rfi and                                                                                  g
                                                                                  β2 are two smoothing coefficients in the range 0 and 1. If Ci
cmi of entry i are initially set to 0 when di is cached. These                          l
                                                                                  < Ci , gi is set to 1 (i.e., globally maintained), otherwise it is
two values are passed to the MSC when the MU retrieves di                                                                    g         l
                                                                                  set to 0. Then the retrieving flag bits, Ri and Ri , are reset to
through the uplink query. When an MU roams into a new cell,                       0. When the MSC receives a query for di , it sets the retrieving
rfi is set to 1 if entry i is valid. Moreover, rfi is reset to 0 if               flag bit for the corresponding cell, adds cmi which is attached
any of the following events occurs: (1) the MU wakes up, (2)                                                             l
                                                                                  to the uplink query message into Ri . If it is uncertain query
the MU receives an IR, a confirmation or a valid data object                       and rfi = 1, and the uncertain di is still valid, an additional
for entry i, and (3) the MU accesses di .                                                                          l
                                                                                  confirmation is added into Ri . When a valid data object or
   For dg , an additional confirmation is saved if it is accessed
          i                                                                       confirmation message is broadcast, the global flag bit with the
as a valid entry in the cache when rfi = 1. This valid entry                      same value as the global flag bit in the cache entry of the
would be uncertain if di were locally maintained. rfi = 1                         MSC is associated. If there are multiple MSCs in the system,
                                                                                                                           g        l
indicates that the MU has no sleep-wakeup event, does not                         for each update of di , the values of Ri and Ri in each MSC
receive an IR, refresh nor access di after the last roaming.                      must be forwarded to all other MSCs so that every MSC has
Hence, a saved confirmation is counted for dg . Thus the MU
                                                i
                                                                                                    g          l
                                                                                  the values of Ri and Ri for the whole system.
increases cmi by 1 and resets rfi = 0. After the entry becomes                        DSACCS can be dynamically applied to different systems
an uncertain or ID-only, the next access of di is retrieved from                  with some advanced features. Fig. 6 shows a multi-cell system,
the MSC. In this case, the value of cmi is passed to the MSC                      in which all 16 cells are controlled under two MSCs. Shaded
                                                                l
and then reset to 0. The MSC in turn adds the cmi into Ri .                       Cells 1-3, 5-8, and 12-13 are controlled by one MSC while all
          l
   For di , an additional confirmation may be counted when                         the other cells are controlled by another. Suppose a university
an uncertain entry with rfi = 1 is accessed. In this case, an                     campus is located at Cells 7-11. Students in the university
uncertain query associated with rfi is sent to the MSC, and                       frequently roam within the campus and rarely roam out. On
if di is still valid, the MSC records an additional confirmation                   the other hand, students usually access some common data
WANG et al.: DYNAMIC CACHE CONSISTENCY SCHEMES FOR WIRELESS CELLULAR NETWORKS                                                             9



objects, which may not be of interest to MUs outside the
                                                                                      12       HM−SACCS
campus. In this scenario, some data objects may be highly                                      IM−SACCS
accessed in the campus cells but rarely in other cells, thus the                               CK−SACCS
                                                                                               DSACCS
additional confirmations for these data objects are caused by                          10
roaming within campus. We can form a cell group including all
campus cells, and allow some data objects to be maintained as




                                                                        D (Seconds)
                                                                                       8
group data objects. For a group data object, its IR is broadcast
to every cell in the group if it is retrieved in any cell within the
group. The valid entry for a group data object is unchanged                            6
when an MU roams among the grouped cells. This is an
efficient mechanism because: (1) it minimizes the mobility
                                                                                       4
impacts on the MU’s roaming within the grouped cells, and
(2) all additional IRs from the grouped cells are only broadcast
among themselves, without affecting the other cells.                                   2
   Now let us describe an improvisation of DSACCS, called
DSACCS-G, in which the cells are grouped. In DSACCS, the                               100         110    120            130            140
                                                                                                          M/B
access popularity of a data object in a cell can be measured
through the retrieving flag bit for that cell. When some data                                              (a)

objects are observed to be very popular in some cells but not                              1
popular in other cells, a cell group can be set by grouping                                                              HM−SACCS
                                                                                                                         IM−SACCS
these cells into a logical cell. After the group is formed, some                                                         CK−SACCS
                                                                                      0.95                               DSACCS
data objects can be maintained as group data objects. The IR
of a group data object is broadcast to all grouped cells if it is
retrieved in any cell of the group. When an MU roams among                             0.9
the grouped cells, the entry states for group data objects in
the cache are unchanged.
                                                                        UPQ




                                                                                      0.85
   To manage group data objects, a group flag bit (fi ) is
introduced for entry i in the caches of MSCs and MUs. fi
= 1 (or 0) implies that di is (or not) a group data object. Four                       0.8
parameters (Ei , Li , ei , li ) are set for entry i in the MSC. Here
Ei and ei are the average and current measured additional                             0.75
IRs of di per update interval in the grouped cells (i.e., the
number of cells in the group in which the data object is not
retrieved during an update interval). Li and li are respectively                       0.7
                                                                                         100        110   120            130            140
the average and current number of additional confirmations                                                 M/B

during an update interval due to MU’s roaming among the                                                    (b)

grouped cells. Two extra parameters (ri , cri ) are associated
with each entry in the cache of an MU, where ri is used                Fig. 7. Performance of four SACCS-based schemes vs number of MUs per
                                                                       cell (M/B): a) average access delay (D); b) uplink per query (U P Q).
to identify the additional confirmations for the MU roaming
among the grouped cells. ri set to 1 for valid entry i when the
MU roams from one grouped cell to another. rmi stores the              communications. Hence we do not count the cost for MSCs’
number of additional confirmations of di . The management               communications here. In both cases, the smooth coefficients
of these extra parameters is the same as the management of             β1 and β2 are set to 0.5.
parameters introduced in DSACCS.
   In DSACCS-G, after di is updated, the MSC first checks               Case 3 : Impact of the Number of MUs per Cell
                                                                   g
if di is globally or locally maintained by comparing Ci                   In this case, we use a 19-cell system similar to Configu-
         l
with Ci . If di is globally maintained, there is no difference         ration 3 shown in Figure 2, and set N = 10,000 and Zipf
between DSACCS and DSACCS-G. However, if di is locally                 coefficient is set to 0.95. All the other parameters for the MUs
maintained, the MSC sets it as a group data object if Ei < Li ,        and the database are set to the same as in Case 2.
otherwise di is locally maintained.                                       Figs. 7 (a) and (b) show the performance of three extended
                                                                       SACCS schemes and DSACCS. We can see that DSACCS
                                                                       has the best performance in terms of delay (D) for varying
C. Performance Evaluation                                              number of MUs per cell. When the number of MUs per cell
  Two simulation cases are presented in this subsection.               reaches 140, DSACCS gains about 10% compared with the
Case 3 studies the performance of DSACCS by varying                    other three schemes. HM-SACCS has better performance
the number of MUs per cell. Case 4 evaluates DSACCS                    for small number of MUs per cell. Both CK-SACCS and
and DSACCS-G under various database sizes. Due to the                  IM-SACCS are superior to HM-SACCS when the number
wired connectivity between MSCs, the communication delay               of MUs per cell is over 130. HM-SACCS has the minimum
is insignificant compared with low bandwidth wireless                   UPQ while CK-SACCS has the maximum UPQ. DSACCS
10                                                               IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 1, JANUARY 2006



                                                                           40 Kbps and for Cells 7-11, it is set to 80 Kbps. The uplink
                        HM−SACCS
               12
                        IM−SACCS                                           channel are set to 4 Kbps for Cells 1-6 and 12-16 and, 6 Kbps
                        CK−SACCS                                           for Cells 7-11. The most popular data object for students is
                        DSACCS
               10
                        DSACCS−G                                           randomly picked from 0-199, and for the first type of MUs
                                                                           is randomly picked from 500-599. The cache size is set as 1
                                                                           M bytes for each MU and the ID-only entry is set to 200. Ten
 D (Seconds)




                8                                                          types of data objects are set in the database as shown in Table
                                                                           II except the set for Tu (in sec), which is (100, 200, 400, 800,
                6
                                                                           1600, 3200, 6400, 12800, 25600, 51200).
                                                                              Figs. 8 (a) and (b) show the performance of five schemes.
                                                                           From the figures, we infer that DSACCS-G has always the
                4                                                          shortest delay D. DSACCS performs better than other three
                                                                           schemes but worse than DSACCS-G. When N approaches
                2                                                          30,000, the D for DSACCS-G is about 5% less than that for
                                                                           DSACCS, and 10% - 30 % less than those for IM-SACCS,
                1           2                       4                 6    CK-SACCS, and HM-SACCS. The better performance of
                                    N (x5000)
                                                                           DSACCS-G is due to the saved additional confirmations of
                                        (a)
                                                                           group data objects while the IRs of group data objects retrieved
                    1                                                      in the grouped cells are only broadcast to themselves, resulting
                        HM−SACCS
                        IM−SACCS
                                                                           in very few additional IR traffic. For the three extended
                        CK−SACCS
                        DSACCS
                                                                           schemes, in a small N , HM-SACCS has the shortest D and
               0.95
                        DSACCS−G                                           CK-SACCS has the largest one. But for large N , CK-SACCS
                                                                           has the shortest D. HM-SACCS has the smallest U P Q among
                0.9                                                        the five schemes. But U P Q for DSACCS and DSACCS-G is
                                                                           very close to that of HM-SACCS for all values of N . Similar
                                                                           to Case 3, CK-SACCS always has the highest U P Q.
 UPQ




               0.85
                                                                              The above results show that DSACCS and DSACCS-G in-
                                                                           herit the positive features from both homogenous and inhomo-
                0.8                                                        geneous strategies, thus minimizing the additional consistency
                                                                           maintenance cost for roaming MUs.
               0.75

                                                                                                VI. C ONCLUSIONS
                0.7
                   1            2              4                      6       In this paper, we first extended three types of cache con-
                                      N (x5000)                            sistency maintenance strategies: 1) homogeneous IR; 2) inho-
                                              (b)                          mogeneous IR without roaming check; and 3) inhomogeneous
                                                                           IR with roaming check for multi-cell wireless networks. The
                                                                           simulation results revealed that the homogeneous IR strategies
Fig. 8. Performance of five SACCS-based schemes vs number of data objects   perform better for slow updating data objects, fast roaming
in the system (N ): a) average delay (D); b) uplink per query (U P Q).
                                                                           MUs and small systems, whereas the inhomogeneous IR
                                                                           strategies are more efficient for fast updating data objects, slow
has a little bit larger UPQ than HM-SACCS for all ranges                   roaming MUs and large systems.
of MUs per cell. The consistency maintenance cost of each                     Two consistency maintenance cost functions are derived
data object is minimized in DSACCS, thus resulting in better               to determine the cost of maintaining data objects locally
performance. These results indicate that DSACCS inherits                   and globally. Based on these two cost functions, a Dynamic
both positive features from homogenous and inhomogeneous                   Scalable Cache Consistency Scheme (DSACCS) is proposed
strategies, and makes it more scalable and efficient.                       for wireless cellular networks. In DSACCS, the IR of a data
                                                                           object is broadcast globally or locally depending on the min-
Case 4 : Impact of the Number of Database size                             imum consistency maintenance cost. Simulation results show
   In this case, DSACCS and DSACCS-G are evaluated in a                    that DSACCS outperforms three cache strategies extended to
system as shown in Figure 6. Two types of MUs are set in the               multi-cell environments. In addition, a variation of DSACCS,
simulation. There are 1100 of the first type MUs (initially 100             called DSACCS-G, is developed for grouping cells in order to
per cell) located in cells 1-6 and 12-16. There are 1000 MUs               facilitate effective cache consistency maintenance in multi-cell
(200 per cell) of the second type (students) in cells 7-11.                systems.
   The parameters for the first type of MUs are set the same                   Cache replacement and power efficiency are two issues
as that of Case 2. For students, the only different parameter              that we are currently investigating for improving system
from the first type of MUs is the set values of Tr (in sec), a              performance in terms of average access delay and power
student randomly picks up a Tr from the set (100,400,1600).                consumption.
The downlink bandwidth for Cells 1-6 and 12-16 is set to
WANG et al.: DYNAMIC CACHE CONSISTENCY SCHEMES FOR WIRELESS CELLULAR NETWORKS                                                                                11



Acknolwdgement                                                                                            Mohan Kumar obtained his PhD (1992) and MTech
We are grateful to the anonymous referees for helpful                                                     (1985) degrees from the Indian Institute of Science
                                                                                                          and the BE (1982) from Bangalore University in
suggestions that improved the quality of the paper. This                                                  India. Kumar is a Professor in Computer Science
work is supported by a grant from Texas Advanced Research                                                 and Engineering at the University of Texas at Arling-
Program (TXARP) Grant Number: 14-771032.                                                                  ton. His current research interests are in pervasive
                                                                                                          computing, wireless networks and mobility, active
                                                                                                          networks, mobile agents, and distributed computing.
                             R EFERENCES                                                                  Recently, he has developed or co-developed algo-
                                                                                                          rithms for active-network based routing and multi-
 [1] D. Barbara and T. Imielinksi, “Sleeper and workaholics: caching scheme                               casting in wireless networks and caching prefetching
     in mobile environments,” in Proc. ACM SIGMOD Conference on Man-            in mobile distributed computing. He has published over 110 articles in
     agement of Data, pp. 1-12, 1994.                                           refereed journals and conference proceedings and supervised Masters and
 [2] P. Barford and M. Crovella, “Generating representative Web workloads       doctoral theses in the areas of pervasive computing, caching/prefetching,
     for network and server models and server performance evaluation,” in       active networks, wireless networks and mobility, and scheduling in distributed
     Proc. ACM SIGMETRICS Conference, Atlanta, 1998.                            systems. He is a co-founder of the IEEE International Conference on pervasive
 [3] L. Breslau, P. Cao, J. Fan, G. Phillips, and S. Shenker, “Web caching      computing and communications (PerCom), and he was the general chair for
     and Zipf-like distributions: evidence and implications,” in Proc. IEEE     PerCom 2005. Kumar is a founding editor of the Pervasive and Mobile
     INFOCOM, pp. 126-134, 1999                                                 Computing Journal; he is on the editorial board of The Computer Journal;
 [4] G. Cao, “A scalable low-latency cache invalidation strategy for mobile     has guest edited special issues of several leading international journals. He
     environments,” inIEEE Trans. Knowledge and Data Engineering, vol.          is a senior member of the IEEE. Prior to joining The University of Texas
     15, no. 5, pp. 1251-1265, 2003 (a preliminary version appeared in ACM      at Arlington in 2001, he held faculty positions at the Curtin University of
     MOBICOM 2000).                                                             Technology, Perth, Australia (1992-2000), The Indian Institute of Science
 [5] G. Cao, “On improving the performance of cache invalidation in mobile      (1986-1992), and Bangalore University (1985-1986).
     environments,” ACM/Kluwer Mobile Network and Application, vol. 7,
     no. 4, pp. 291-303, 2002
 [6] J. Gwertzman and M. Seltzer, “World-Wide Web cache consistency,” in
     Proc. USENIX Symposium on Internet Technologies and Systems, Dec.
     1997.                                                                                                Dr. Sajal K. Das is a Professor of Computer Science
 [7] Q. Hu and D. K. Lee, “Cache algorithms based on adaptive invalidation                                and Engineering and also the Founding Director
     reports for mobile environments,” Cluster Computing, pp. 39-50, 1998.                                of the Center for Research in Wireless Mobility
 [8] J. Jing, A. Elmagarmid, A. Heal, and R. Alonso. “Bit-sequences: an                                   and Networking (CReWMaN) at the University of
     adaptive cache invalidation method in mobile client/server environ-                                  Texas at Arlington (UTA). His current research in-
     ments,” Mobile Networks and Applications, pp. 115-127, 1997.                                         terests include resource and mobility management in
 [9] A. Kahol, S. Khurana, S. K. S. Gupta, and P. K. Srimani, “A scheme to                                wireless and sensor networks, mobile and pervasive
     manage cache consistency in a distributed mobile wireless environment,”                              computing, wireless multimedia and QoS provision-
     IEEE Trans. Parallel Distrib. Syst., vol. 12, no. 7, pp. 686-700, 2001.                              ing, mobile Internet protocols, distributed processing
[10] G. Y. Liu and G. Q. McGuire Jr., “A mobility-aware dynamic database                                  and grid computing. He has published over 350
     caching scheme for wireless mobile computing and communications,”                                    research papers, directed numerous funded projects,
     Distributed and Parallel Databases, pp. 271-288, 1996.                     and holds five US patents in wireless mobile networks. He received the
[11] K. Tan, J. Cai, and B. Ooi, “An evaluation of cache invalidation schemes   Best Paper Awards in ACM MobiCom’99, ICOIN’01, ACM MSWIM’00, and
     in wireless environments,” IEEE Trans. Parallel Distrib. Syst., vol. 12,   ACM/IEEE PADS’97. He is also a recipient of UTA’s Outstanding Faculty
     no. 8, pp. 789-897, 2001.                                                  Research Award in Computer Science in 2001 and 2003, and UTA’s College
[12] Z. Wang, S. Das, H. Che, and M. Kumar, “SACCS: scalable asyn-              of Engineering Excellence in Research Award in 2003. He is the coauthor of a
     chronous cache consistency scheme for mobile environments,” in Proc.       book Smart Environments: Technology, Protocols and Applications, published
     IEEE ICDCS: International Workshop on Mobile and Wireless Networks         in 2004 by John Wiley.
     (MWN), pp. 797-802, 2003.                                                     Dr. Das is the Editor-in-Chief of the journal Pervasive and Mobile Com-
[13] Z. Wang, S. K Das, H. Che, and M. Kumar, “A scalable asynchronous          puting, and serves on the Editorial Boards of four international journals
     cache consistency scheme (SACCS) for mobile environments,” IEEE            including IEEE Transactions on Mobile Computing and ACM/Kluwer Wireless
     Trans. Parallel Distrib. Syst., vol. 15, no. 11, pp. 983-995, 2004.        Networks. He has served as General Chair of IEEE WoWMoM’05, IWDC’04,
[14] Z. Wang, M. Kumar, S. K Das, and H. Shen, “Investigation of cache          IEEE PerCom’04, CIT’03 and IEEE MASCOTS’02; General Vice Chair of
     maintenance schemes for multi-cell environments,” in Proc. Interna-        IEEE PerCom’03, ACM MobiCom’00 and HiPC’00-01; Program Chair of
     tional Conference on Mobile Data Management (MDM), pp. 29-44,              IWDC’02, WoWMoM’98-99; TPC Vice Chair of CIT’05, ICPADS’02; and
     2003.                                                                      as TPC member of numerous IEEE and ACM conferences. He is the Vice
[15] K. L. Wu, P. S. Yu, and M. S. Chen, “Energy-efficient caching for           Chair of IEEE Technical Committees (TCPP and TCCC), and on the Advisory
     wireless mobile computing,” in Proc. 20th International Conference on      Boards of several cutting-edge companies.
     Data Engineering, pp. 336-345, 1996.                                          Prior to 1999, Dr. Das was a professor of computer science at University
[16] H. Yu, L. Breslau, and S. Shenker, “A scalable Web cache consistency       of North Texas, where he twice (in 1991 and 1997) received the Student
     architecture,” in Proc. ACM SIGCOMM, pp. 163-174, 1999.                    Association’s Honor Professor Award for best teaching and scholarly research.
                                                                                He received B.Tech. degree in 1983 from Calcutta University, M.S. degree in
                                                                                1984 from Indian Institute of Science, Bangalore, and PhD degree in 1988
                                                                                from the University of Central Florida, Orlando, all in Computer Science.

                         Zhijun Wang received his Ph.D. degree in Com-                                    Huaping Shen received his B.S. and M.S. degrees
                         puter Science and Engineering from The University                                in computer science from Fudan University, China,
                         of Texas at Arlington, 2005. He is an assistant pro-                             in 1998 and 2001, respectively. He is currently a
                         fessor of the Department of Computing, The Hong                                  Ph.D. candidate in the Department of Computer Sci-
                         Kong Polytechnic University. His current research                                ence and Engineering at the University of Texas at
                         interests include data management in mobile net-                                 Arlington. His research interests include data man-
                         works and peer-to-peer networks, mobile computing                                agement in mobile networks, mobile and pervasive
                         and high speed networks.                                                         computing, peer-to-peer networks, and distributed
                                                                                                          game systems.

				
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Description: Difference between the mobile phone services into one hexagonal sub-areas, each district set up a base station. Forming a shape resembles "honeycomb" structure, which is called to this mobile communication cellular mobile communication. Cellular networks can be divided into analog cellular networks and digital cellular networks, mainly different from the transmission information.