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Characteristics of mobile communication traffic considering the vehicle movement in a band-shaped service area by Kabasawa_ T.; Sengoku_ M

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Characteristics of mobile communication traffic considering the vehicle movement in a band-shaped service area by Kabasawa_ T.; Sengoku_ M Powered By Docstoc
					                                                                  ence on Circuits and Systems '96




               ics of Mobile Communicat Traffic Con
      the VehicleM                      ed Service Ar

Tatsuva Kabasawa* and Masakazu Sengoku**
*T.Kabasawa is with Nagaoka College of Technology,888 Nishikatakai, Nagaoka-shi, 940 Japan.
Tel: +81-29-34-9242 Fax: +81-258-36-6183
E-Mail: tkaba@nagaoka-ct.ac.jp
**M. Sengoku is with the Faculty               neering, Niigata University, Niigata-shi, 950-21 Japan.


Abstract                                                          the cell is more than other ones. In such cases, traffic
   In cellular mobile communication                               performance has been analyzed on the assumptions that
area is dividedinto a number of cell                                         ityof calls in the cell
channels. It is necessary to consider                                        ider that the density of
movement for analyzing traffic performance of such                especially when the traffic offered to a cell is
cellular mobile communication                                     from other ones. This paper presents the method of
presents a theoretical performance                                evaluating the distribution of calls in the cell and the
shaped service area when the traffic                               characteristics of      mobile communication traffic.
cell is bigger than other cells.                                  Furthermore, the characteristics are analyzed
characteristics of mobile communication t d i c                    length of specific cell is different from other cells.
analyzedwhen the length of the cell is different from
other ells. Thorough the comparison                      cal       2. Analytical Model and Assumptions
results and simulaQonresults,             dty of theoretical            Figure 1 shows the band-shaped                  service area
results has beenshown.                                             considered forthe analysis model. Eachcell is numbered,
                                                                   suchas   *   *    *#j-l,#j,#j+l,    *   +   *   .Thelengthofthe
1. Introduction
              ent-day cellular mobile communication
systems, a service area i
                                                                             # 1-1              #I                     # 1+1


mhction (1). Service areas for such systems are tw
                                                                                                 0                 +
dmensional.      However,      the      analysis   of    th


motion of the vehicles in
                         are quite complicated since


precisely. To simplify the anal
                                                                     - -- --    4,               Ll                      4     ,   -



to be band-shaped like a hi
                                                                                    Fig.1 Band-shaped servicearea.
of vehicle movement is onedimensional. In the band-
shaped service area, the M i c offered to the specific
sell is bigger than other cells if the number of vehicles in

330                                                       T4-PC6.1                             0-7803-3702-6/96/$5.00@1996 IEEE
cell #j is L, and other ones are b. The M i c offered         constructed to calculate the probability P,,,. Figure 2
tothe cell # is a, and the traffic offered to other
            j                                                 shows the state transition     diagram forthe cell #j.
                                                                                                                   In
cells is a*. Followings are assumed for the analysis of                   ,
                                                              Fig. 2, h is originated call arrival rate and /L is call
traffic performance of the banhshaped service a e in
                                               ra             termination rate. hj is the hancbff probability from the
Fig. 1.                                                       cell #j to the cell #j+
                                                                                    1.
  1) Call    interarrival      time    obeys a Poisson
     distribution.                                            4. Density of calls
  2) The position where a call is generated in a cell              The probability of hancbff from the cell #j is
     obeys an uniform distribution.                           expressed as bellow (2).
  3) Call    holding         time obeys an exponential
     distribution.
  4) Call handoff interval beys a Poisson distribution.
  5 ) All vehicles move at the same velocity in the same      where V is the velocity of vehicle and )
                                                                                                     &
                                                                                                     d           is the
     direction to which the cell number increases.                                                     Figure 3 shows an
                                                              density of calls at the endof the cell #j.
  6) Fixed channel           assignment is employed and       originated call and a handoff call in the cell #j.Let the
     calls originatedwhen all channels arebusy are            position of the call be x. The probability that the
     lost (lost call system).
In assumption 4) hancbff consists of surrendering the
channel used in the previous cell and reassigning a new
channel when the vehicle crosses the cell boundary.


3. State Transition Diagram
   In order to analyze the M i c performance o the
                                              f
cell #j in Fig. 1, the probability P,,r that the number of         Fig. 3 Originated call and hadoff call.
simultaneous      connections in the cell #j         is r
(Osr s 8 . H ~ E , s is the number of assigned
channels to each cell.                                        originated call exists at x1is expressed by the sum of
                                                                               ht
                                                              the probability t a the call originated in the
                                                              rauge,O s x s X , , moves to xl. Let the probability be
                                                              p,(x). Since the call holding time obeys an exponential
                                                              distribution, it is given by Fiq. (2).
                     ru+hJ        ( r + l ) u+hJ


            Fig. 2 State transition diagram.

                                                              where   & is     the average      holdng time. Let the
                                                              density of originated calls be g(x). $(x) is given by
    The state transition dagram for the number of
                                                              normalizing p,(x) as bellow.
simultaneous connections in the cell #j need to be




                                                        T4-PC6.2                                                     331
                                                            q,-1 =   0,
   Let the densityof handoffcalls in the cell% bea(x).




                                                            connections is r in the cell #j.
   Let the probability that originated and hanhff calls
exist at x be pJ(x).pJ(x)is expressedas bellow.




where h is the originated call amval rate in the
cell and nJ., is the number of hanhff        calls from


                                                  ving by
                                                                    Fig. 4 Distribution of offered traffic.


                                                                 The analysis is made for the case where the offered
                                                            traffic changes in a step funchon as shown in Fig 4.
                                                            The    density of   call in the cell # is
                                                                                                  j     presented by Eq
5. Analytical        Results                                                    umedthat the densityof calls in the
   Using t                             pressed b            cells before #j-1 obeys uniform distribution becauseof
(l),the state eqahons for the number of simultaneous        the simplicity of analysis. From this assumption, the
                                                            n          f   handoff calls from the the cell 3-1 is
                                                            expressed as bellow (2).




332                                                   T4-PC6.3
                                                             of the cell #j increases.


                                                             6. Conclusion
where rm0 is the average number of simultaneous                   This paper presented the teletraffic performauce
                                is
conuections in the cell #j-1. rm0 giving by solving the      evaluation     for the baud-shaped       service area in a
state equations of the cell #j-1 similar to Eqs. (8a) and    cellular mobile communication system when the offered
(W.                                                          W i c to the specific cell is bigger than other cells.
   Substituting Ekp(7) and(10) for the state equations,
                                                             Furthermore,      the       characteristics    of    mobile
the W i c      performance is giving by solving the          communication MIC been analyzed when the cell
                                                                             has
equations.                                                   length of the specific cell is diffenmt from other cells.
                                                             The teleWic performance is analyzed by deriving the
                                                             density of calls in the cell. Since the theoretical and
                                                             simulation      results agree comparatively well, the
- 6
;R
v
                                                             validity of the theoretical results is shown. The
                                                             analysis results can be used for designing the switching
                                                             system in an actual system.            In this paper,    the
                                                             characteristics has been        analyzed about only one
                                                             cell to which the       @IC     off&     is differat from
                                                             other cells. The teletrafftc pedormance         o other cells
                                                                                                             f
      0
          0          20             40           60          is    influenced by the specific cell. Pdormance
                          Velocity (km/h)                    evaluation     for other cell3 is a           future research
                                                             problem.
          Fig. 5   Teletrafic performance.
                                                             References
                                                             (1) M. Shinji. Mobile Communication.Tokyo Maruzen.
   Figure 5 shows the teletraffic performance, where         1992
the velocity of vehicle is taken as the axis of       the    (2) T. Kabasawa. T. Watanahe, M. Sengoku, Y.
abscissa and the blocking probability is taken as the        Yamaguchi, S. Shinoda and T. Abe. ‘Transient
ordinate with L, as a parameter. The cell length except      characteristics of mobile communication WIC a
                                                                                                        in
the cell #j    = lkm, mean holding time h, = 90s and         band-sbaped service area” IEICE Trans. Fundamentals
number of channels S =8. Simulation results forthe           vol. E76-A. N0.6 pp. 961-966. June 1993
number of cells =lOis also shownin the figure. Since the
theoretical and simulation results agree comparatively
well, the analysis result is validated       As the cell
length L, increases, the blocking probability increases.
It can be interpreted as follows. As the cell length the
cell #j increases, the average time that calls stay in the
cell #j is increases.Thercfore, the blocking probability




                                                      T4-PC6.4                                                        333

				
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