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Methods in Diffusion Approximation for Multi-Server Systems: Sandwich, Uniform Attraction and State-Space Collapse

In: Queueing Networks

Author

Listed:
  • Hong Chen

    (University of British Columbia)

  • Heng-Qing Ye

    (Hong Kong Polytechnic University)

Abstract

In this chapter, we demonstrate through simple queueing models some of the methods that have been developed for the diffusion approximation. Specifically, we first show how the sandwich method is used to establish the diffusion approximation for a multi-server queue, and next show how the uniform attraction and the state-space collapse method is used to establish the diffusion approximation fora multi-class queue under a first-in-first-out (FIFO) service discipline. Finally, weuse all of the above methods to establish the diffusion approximation for a system with multi-channel queues to which the jobs are routed based on a join-the-shortestqueue (JSQ) routing control.

Suggested Citation

  • Hong Chen & Heng-Qing Ye, 2011. "Methods in Diffusion Approximation for Multi-Server Systems: Sandwich, Uniform Attraction and State-Space Collapse," International Series in Operations Research & Management Science, in: Richard J. Boucherie & Nico M. Dijk (ed.), Queueing Networks, chapter 11, pages 489-530, Springer.
    • Handle: RePEc:spr:isochp:978-1-4419-6472-4_11
    DOI: 10.1007/978-1-4419-6472-4_11
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