The M/M/∞ Queue

  • Philippe Robert
Part of the Applications of Mathematics book series (SMAP, volume 52)


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.


Arrival Rate Stochastic Differential Equation Fluid Limit Standard Brownian Motion Poisson Point Process 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Philippe Robert
    • 1
  1. 1.Domaine de VoluceauINRIALe ChesnayFrance

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