Stochastic Networks and Queues pp 141-175 | Cite as

# The M/M/∞ Queue

## Abstract

The queue with an infinite number of servers is, with the *M/M/*1queue, a basic model. It plays a crucial role in most of the stochastic models of communication networks. If the *M/M/*1 queue is the basic element of a Jackson network (see Section 4.4.1 page 92), the *M/M/*∞ queue is the basic element of loss networks (see Example 4.2.3 page 88) used to represent communication networks. As it is the case for the *M/M/*1 queue, the stochastic processes describing this queue are not only important in the analysis of queueing systems but also in various areas such as statistical physics or theoretical computer science.

## Keywords

Arrival Rate Stochastic Differential Equation Fluid Limit Standard Brownian Motion Poisson Point Process## Preview

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