A new technique for analyzing large traffic systems.

*(English)*Zbl 0596.60093Author’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) |