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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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