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A Stochastic Model to Capture Space and time Dynamics in Wireless Communication Systems

Published online by Cambridge University Press:  27 July 2009

William A. Massey  and
Ward Whitt
William A. Massey
Affiliation:
AT&T Bell Laboratories, Murray Hill, New Jersey
Ward Whitt
Affiliation:
AT&T Bell Laboratories, Murray Hill, New Jersey
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Abstract

We construct a version of the recently developed Poisson-Arrival-Location Model (PALM) to study communicating mobiles on a highway, giving the distribution of calls in progress and handoffs as a function of time and space. In a PALM arrivals generated by a nonhomogeneous Poisson process move independently through a general state space according to a location stochastic process. If, as an approximation, we ignore capacity constraints, then we can use this model to describe the performance of wireless communication systems. Our basic model here is for traffic on a one-way, single-lane, semi-infinite highway, with movement specified by a deterministic location function. For the highway PALM considered here, key quantities are the call density, the handoff rate, the call-origination-rate density and the call-termination-rate density, which themselves are simply related by two fundamental conservation equations. We show that the basic highway PALM can be applied, together with independent superposition, to treat more complicated models. Our analysis provides connections between teletraffic theory and highway traffic theory.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 4 , October 1994 , pp. 541 - 569
Copyright
Copyright © Cambridge University Press 1994

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References

1.Davis, J., Massey, W.A., & Whitt, W. (to appear). Sensitivity to the service-time distribution in the nonstationary Erlang loss model. Management Science.Google Scholar
2.Eick, S., Massey, W.A., & Whitt, W. (1993). The physics of the Mt/G/∞ queue. Operations Research 41: 731–742.Google Scholar
3.Gazis, D.C. (1974). Traffic science. New York: Wiley.Google Scholar
4.Haberman, R. (1977). Mathematical models: Mechanical vibrations, population dynamics, and traffic flow. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
5.Jackson, J.R. (1963). Job-shop like queueing systems. Management Science 10: 131–142.CrossRefGoogle Scholar
6.Jagerman, D.L. (1975). Nonstationary blocking in telephone traffic. Bell System Technical Journal 54: 625–661.Google Scholar
7.Kelly, F.P. (1991). Loss networks. Annals of Applied Probability 1: 319–378.CrossRefGoogle Scholar
8.Lee, W.C.Y. (1989). Mobile cellular telecommunications systems. New York: McGraw-Hill.Google Scholar
9.Leung, K.K., Massey, W.A., & Whitt, W. (to appear). Traffic models for wireless communications networks. INFOCOM '94, Toronto.Google Scholar
10.Massey, W.A. & Whitt, W. (1993). Networks of infinite server queues with nonstationary Poisson input. Queueing Systems 13: 183–250.Google Scholar
11.Massey, W.A. & Whitt, W. (to appear). An analysis of the modified-offered-load approximation for the nonstationary Erlang loss model. Annals of Applied Probability.Google Scholar
12.Meier-Hellstern, K.S., Alonso, E., & O'Neill, D.R. (1992). The use of SS7 and GSM to support high density personal communication systems. Third WINLAB Workshop on Thrid Generation Wireless Networks.Google Scholar
13.Mitra, D., Gibbens, R.J., & Huang, B.D. (1992). State dependent routing on symmetric loss networks with trunk reservations, I. IEEE Transactions on Communications 40: 477–482.Google Scholar
14.Montenegro, G., Sengoku, M., Yamaguchi, Y., & Abe, T. (1992). Time-dependent analysis of mobile communication traffic in a ring-shaped service area with nonuniform vehicle distribution. IEEE Transactions on Vehicular Technology 41: 243–254.Google Scholar
15.Palm, C. (1988). Intensity variations in telephone traffic. Ericsson Technics 44: 1–189 (in German; English translation by North-Holland, Amsterdam, 1988).Google Scholar
16.Seskar, I., Maric, S.V., Holtzman, J., & Wasserman, J. (1992). Rate of location area updates in cellular systems. Third WINLAB Workshop on Third Generation Wireless Networks.Google Scholar
17.Symon, K.R. (1971). Mechanics, 3rd ed.Addison-Wesley.Google Scholar
18.Sze, S.M. (1981). Physics of semiconductor devices, 2nd ed.New York: John Wiley & Sons.Google Scholar