Minimizing response times and queue lengths in systems of parallel queues

Minimizing response times and queue lengths in systems of parallel queues

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Article ID: iaor20013009
Country: United States
Volume: 36
Issue: 4
Start Page Number: 1185
End Page Number: 1193
Publication Date: Dec 1999
Journal: Journal of Applied Probability
Authors: , ,
Abstract:

We consider the problem of routeing customers to one of two parallel queues. Arrivals are independent of the state of the system but otherwise arbitrary. Assuming that queues have infinite capacities and the service times form a sequence of i.i.d. random variables with increasing likelihood ratio distribution, we prove that the shortest queue (SQ) policy minimizes various cost functionals related to queue lengths and response times. We give a counterexample which shows that this result is not generally true when the service times have increasing hazard rate but are not increasing in the likelihood rate sense. Finally, we show that when capacities are finite the SQ policy stochastically maximizes the departure process and minimizes the loss counting process.

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