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Stability and continuity for slotted ALOHA with stationary non-independent input traffic

Published online by Cambridge University Press:  14 July 2016

Vinod Sharma
Vinod Sharma*
Affiliation:
University of California, Los Angeles
*
∗ Present address: Department of Electrical Engineering, Indian Institute of Science, Bangalore 560012, India.
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Abstract

Slotted ALOHA with a finite number of users, each with infinite buffer, is considered. For stationary, metrically transitive, non-independent input, the problem of existence of stationary queue length distributions is solved. Results are obtained for zero and arbitrary (finite a.s.) initial conditions. Continuity, in probability, of queue lengths with respect to input sequence is proved.

Keywords

STOCHASTIC CONTINUITYSTATIONARY DISTRIBUTION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 4 , December 1988 , pp. 797 - 807
Copyright
Copyright © Applied Probability Trust 1988 

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References

[1] Abramson, N. (1970) The ALOHA system — another alternative for computer communications. Proc. 1970 Fall Joint Computer Conference 37, 281–285. AFIPS Press, Montvale, NJ.Google Scholar
[2] Borovkov, A. A. (1976) Stochastic Processes in Queueing Theory. Springer-Verlag, New York.CrossRefGoogle Scholar
[3] Borovkov, A. A. (1984) Asymptotic Methods in Queueing Theory. Wiley, New York.Google Scholar
[4] Fayolle, G., Gelenbe, E. and Labetoulle, J. (1977) Stability and optimal control of the packet switching broadcast channel. J. Assoc. Comput. Mach. 24, 375–386.CrossRefGoogle Scholar
[5] Loynes, R. M. (1962) The stability of a queue with non-independent inter-arrival and service times. Proc. Camb. Phil. Soc. 58, 497–520.CrossRefGoogle Scholar
[6] Saadawi, T. N. and Ephremides, A. (1981) Analysis, stability and optimization of slotted ALOHA with a finite number of buffered users. IEEE Trans. Autom. Control. 26, 680–689.CrossRefGoogle Scholar
[7] Sharma, V. (1988) Stability analysis of slotted ALOHA with time varying input. IEEE Trans. Comm. Google Scholar
[8] Sharma, V. (1987) Existence and stability of stationary distributions of stochastic equations and queueing networks.Google Scholar
[9] Szpankowski, W. (1983) Ergodicity aspects of multidimensional Markov chains with application to computer communication system analysis. Proc. Internat. Seminar Modelling and Performance Evaluation Methodology , France. Google Scholar
[10] Tsybakov, B. S. and Mikhailov, V. A. (1979) Ergodicity of slotted ALOHA system. Probl. Pered. Informat. 15, 75–87.Google Scholar