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A new technique for analyzing large traffic systems. (English) Zbl 0596.60093
Author’s abstract: This paper presents a new technique for analyzing the frequency of a very large class of rare events in large traffic systems. The method is based on the theory of large deviations. If n is a large parameter, typically the number of potential traffic sources, then \[ E(time\quad between\quad events)=\exp (nI+o(n)) \] where I is the solution to an associated variational problem. We present a new analysis of a previously solved system as well as an analysis of a previously intractable system. As by-products of our analysis, we obtain estimates of the transient behavior of the system, and show how they may be used in analyzing some flow control schemes.
Reviewer: E.A.van Doorn

MSC:
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
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