On Pooling in Queueing Networks
Avishai Mandelbaum, Martin I. Reiman
Management Science · 1998 · Volume 44 · Issue 7
Abstract
We view each station in a Jackson network as a queue of tasks, of a particular type, which are to be processed by the associated specialized server. A complete pooling of queues, into a single queue, and servers, into a single server, gives rise to an M / PH /1 queue, where the server is flexible in the sense that it processes all tasks. We assess the value of complete pooling by comparing the steady-state mean sojourn times of these two systems. The main insight from our analysis is that care must be used in pooling. Sometimes pooling helps, sometimes it hurts, and its effect (good or bad) can be unbounded. Also discussed briefly are alternative pooling scenarios, for example complete pooling of only queues which results in an M / PH / S system, or partial pooling which can be devastating enough to turn a stable Jackson network into an unstable Bramson network. We conclude with some possible future research directions.
Keywords
Service Facility Design, Flexible Server, Specialized Server, Service Operations, Efficiency, Stability, Economics of scale
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