Diffusion Approximation Methods for General Queueing Networks

The following sections are included:

• Introduction

• Diffusion approximation for a single queue

  • Queues and the numerical discretisation of the diffusion equation

  • An approach based on the central limit theorem

  • The instantaneous return process [10, 11]

  • Application to the GI/G/1 queue: stationary solution

  • Application to a closed two-server system with general service time distributions

  • The discretisation problem

• Diffusion approximations for general networks of queues with one customer class

  • Application to packet-switching computer-communication networks

  • The approach of Kobayashi and Reiser to the approximation of queueing networks

• Approximate behaviour of a single queue in a network with multiple customer classes

  • Computation of the approximate interarrival statistics for each queue

  • Diffusion approximation to the queue length process

• Conclusion

• References