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

Hong Chen () and Heng-Qing Ye ()
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Hong Chen: University of British Columbia
Heng-Qing Ye: Hong Kong Polytechnic University

Chapter 11 in Queueing Networks, 2011, pp 489-530 from Springer

Abstract: 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.

Keywords: Brownian Motion; Queue Length; Diffusion Approximation; Interarrival Time; Service Discipline (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4419-6472-4_11

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