Abstract
Traditional applications of queuing theory in the analysis and design of communication networks often use the fact that quasi-reversible queues can be interconnected with Bernoulli routing to form network models whose stationary distribution is of product form. To construct such models it is necessary to assume that the external arrival process is a Poisson process (in continuous time) or an i.i.d. sequence of Poisson random variables (in discrete time). Recently, however, several empirical studies have provided strong evidence that the traffic to be carried by the next generation of communication networks exhibits long-range dependence, implying that it cannot be satisfactorily modeled as a Poisson process.
Our purpose in this paper is to exploit the features that make networks of quasi-reversible queues product form so as to construct a self-contained class of queuing network models whose external arrival processes can be long-range dependent. Throughout the paper, we restrict ourselves to discrete time. The long-range dependent arrival process models we consider can be described as follows: Sessions arrive according to a sequence of i.i.d. Poisson random variables. Each session is active for an independent duration that is positive integer valued with a regularly variying distribution having finite mean and infinite second moment. While it is active, a session brings in work at rate 1. The networks we consider are comprised of monotone quasi-reversible S-queues with Bernoulli routing. The queues handle their arrivals at the session level, i.e., once a session enters service at a queue it continues to receive service at rate 1 until all the work it brings in is completed.
Our main observation is that all the internal traffic processes of such networks are long-range dependent. This result provides a family of interesting new examples of long-range dependent processes, in addition to its potential use in studying performance issues for communication networks.
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Anantharam, V. (1996). Networks of Queues with Long-Range Dependent Traffic Streams. In: Glasserman, P., Sigman, K., Yao, D.D. (eds) Stochastic Networks. Lecture Notes in Statistics, vol 117. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4062-4_12
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DOI: https://doi.org/10.1007/978-1-4612-4062-4_12
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