Optimal Dynamic Mobility Management for PCS Networks

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Optimal Dynamic Mobility Management for PCS Networks Powered By Docstoc
					 Optimal Dynamic Mobility
Management for PCS Networks

        Li, Kameda, and Li
  IEEE Transactions on Networking
             June 2000

              I. Introduction
• Mobile computing system
  – The integration of mobile communications and
• Personal communication system (PCS)
  – A new mobile computing system
    that enable users to economically transfer
    any form of information between any desired
    locations at any time
  – Cells
  – Base stations
  – Mobile switching center(MSC)                2
• Mobility management
  – How to track the mobile users that move from place to
    place in PCS networks
• Two basic operations in mobility management:
  – Location update
     • The process through which the system tracks the location of
       mobile users that are not in conversations
     • The up-to-date location information of a mobile user is reported
       by the mobile users dynamically
     • A location area may include one or more cells.
  – paging
     • When an incoming call arrives, the system searches for the
       mobile users by sending polling signal to cells in the location
       area.                                                          3
• Cost of location update and paging
  – Wireless bandwidth and processing power
    at the mobile users, base stations, and MSCs
  – A large location area will result in a decrease in the
    cost of location update and an increase in the cost of
    paging, and vice versa.
  – To determine the size of the location area is a critical
    problem for minimizing the total cost of location
    update and paging.

• Location update and paging schemes
  – Static
     • The location area size is fixed
     • Problem:
       excess location updates as a mobile user moves back and
       forth between two location areas
  – Dynamic
     • The location area size is determined dynamically according
       to the changes of mobility and calling patterns of mobile

• Three dynamic location update schemes:
  – Distance-based
     • The location update is performed whenever the distance between the
       current cell for the mobile user and the last cell in which the last update
       was performed is d.
     • The location area is an area in which the central cell is the last cell
       where the last update occurred surrounded by d rings of cells
  – Movement-based                Ö (used in this paper)
     • The location update is performed whenever a mobile user completes d
       movements between cells (the location update movement threshold)
     • The location area is an area in which the central cell is the last cell
       where the last update occurred surrounded by d rings of cells
  – Time-based
     • The location update is performed every t units of time.
     • The size of location area is calculated according the the mobility of the
       mobile user user.
II. Modeling and System Description
• The probability density function of
  cell residence time is pm(t) which has
  Laplace-Stieltjes transform fm(s) and mean 1/lm
• When a mobile user leaves a cell, there is an equal
  probability that any one of the immediate neighboring
  cells is selected as the destination.
• The movement-based location update scheme is
  considered in this paper.
   – A location update occurs when the number of boundary
     crossing since the last location update registration equals a
     threshold d.
   – The center cell is the cell where the last location registration
• Assume that incoming call arrivals to each mobile
  user follow a Poisson process with rate lc
• As soon as a call for a mobile user arrives, the
  network initiates a paging process to locate the
  called mobile user.
• The paging area is the covering area within a
  distance d - 1 from the center cell.

• Two popular cell configurations are studied in this paper:
   – Hexagonal cell configuration
   – Mesh cell configuration
     (Ri = the set of cells in the ith ring)

• The size of each cell is determined based on the number
  of mobile channels available per cell and the channel
  allocation scheme used.
• The location tracking mechanism can be applied to both
  macrocell (several kilometers) and microcell (several
  hundreds of meters) environments.
• The size and shape of cells are indirectly reflected by the
  cell residence time.
   – If the size of cells is small, the mean residence time will be
     relatively small, and vice versa.

• Assume that homogeneous cells (of the same shape and
  the same size) are used.
• The distance is measured in terms of
  the number of rings such that
  the distance between a given center cell
  and the cells belonging to set Ri is i rings.
• The number of cells in ring i,

• Paging schemes:
  – Selective paging (Akyildix et al.)
     • The paging is performed in one of the subarea only
  – All cells in the location area are paged.               Ö   11
          III. Problem Formulation
• A. Cost of Location Update
  – U = the cost for performing a location update
  – a(j) = the probability that there are j boundary crossings
    between call arrivals
  – The expected location update cost per call arrival:

                                         d=1        d=2         d=3
    =U{     1 * [a(d) +…+ a(2d-1)]       1          2,3         3,4,5
          + 2 * [a(2d) +…+ a(3d-1)]      2          4,5         6,7,8
          + 3 * [a(3d) +…+ a(4d-1)]      3          6,7         9,10,11
          +… }                           … from 0   … from 0    … from 0
                                         1: to 1    1: to 2,3   1: to 3,4,5
                                         2: to 2    2: to 4,5   2: to 6,7,8
                                         3: to 3    3: to 6,7   3: to 9,10,11
• 1) Calculation of a(j)
                           • tc = call interval
                           • R0 = cell at the last call
                           • tMi = period staying in
                           • tm = interval between
                             the last call and moving
                             out of R0
                           • tc,i = time between
                             entering Ri and the next

• Let tMi (cell residence time) be an independent
  identically distribution (iid) random variable with
  – a general distribution function Gm(tMi),
  – density function gm(tMi),
  – and the Laplace-Stieltjes Transform:

• Let fc(t) and rm(t) be the density function of tc
  (call interval) and tm, respectively.
• Let E[tc] =1/lc and E[tMi] = 1/ lm
• Assume that the incoming phone call is a Poisson

• From the memoryless property of the exponential
  distribution, tc,i has the same exponential
  distribution as tc
• for tm, from the random observer property
  [Stochastic Process - S. Ross], we have
  – The density function:
    (Eq. 5)
  – The Laplace-Stieltjes
    (Eq. 6)

• The probability a(K) that user p moves across K
  cell’s between two phone calls is derived for
  K = 0 and K ³ 1:                 • where q = lc/lm,
  – For K = 0:                       the call-to-
                                     mobility ratio
                                   • q < 1:
                                         lc < lm
                                         1/lc > 1/lm
                                         tc > tm
                                     tc call arrival time
                                     tm cell residence time
– For K ³ 1:

          Eq. 11   Eq. 9   Eq. 10

• From (7) to (11), we have

• 2) Simplify
  the cost function Cu

• Substituting (13) into (2), we have

                   Eq. 15     Eq. 16

• Substituting (15) and (16) into (14), we have

• B. Cost of Paging
  – Assume that the cost of polling a cell is P
  – The number of cells in a paging area with threshold
    value d:

  – The expected paging cost per call arrival:

• C. Total Cost per Call
  – TC(d)
  – The sum of the cost of location update, Cu, and the
    cost of paging , Cp:

    IV. Minimizing the Total Cost
• The goal of the optimal movement-based location
  update scheme
  – To find the optimal threshold, d,
    that minimize the total cost per call, TC(d)

• Theorem 1:
  – The location update cost, Cu(d), is a decreasing and
    convex function with respect to the threshold d;
    and the paging cost, Cp(d), is an increasing and
    convex function with respect to the threshold d.

– Proof:

• Corollary 2: a direct result from Theorem 1
• Theorem 3:
  – The value of d is a unique solution to (21) if and only
    if the following relation holds.

  – That is,

V. Proposed Algorithm

• Step 1
  – Compares the values of –Cu’(d) and Cp’(d) at d = 1
  – where d > 0,
     Cu’(d) is decreasing and Cp’(d) is increasing
  – If Cu’(1) £ Cp’(1), the optimal threshold ð should be 1
• Step 2
  – Determines the interval [d,d+s] which consists of ð
  – ð should not be too large (e.g. > 20), thus we set ð = 10
• Step 3
  – Determines the the optimal threshold ð in the interval [d,d+1]
    by using binary search
• Step 4
  – Determines the the optimal threshold ð
        VI. Numerical Examination
• Assume that the call residence time follows the Gamma
• Let the Laplace-Stieltjes Transform , fm(s), of the
  Gamma distribution with mean 1/lm and variance n is

• We studies effects of optimal threshold d by various
   – Update cost U, polling cost P, CMR (Call-to-Mobility Ratio)
     q = lc/lm, and variance of the cell residence variance n
• Program in C and run on SPARC-20 workstation

• A. Effects of CMR, Update Cost, and Paging

• B.Effects of Cell Residence Time Variance

          VII.Conclusion Remarks
• This paper studies a dynamic mobility management
  scheme: the movement-based location update scheme.
• An analytical model is applied to formulate the costs of
  location update and paging per call arrival.
• The problem of minimizing the total cost per call arrival
  is expressed as an optimization problem that finds the
  optimal threshold in the movement-based location
  update scheme
• An effective algorithm is proposed.


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