On the average waiting time for regular routing to deterministic queues

On the average waiting time for regular routing to deterministic queues

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Article ID: iaor20061434
Country: United States
Volume: 30
Issue: 2
Start Page Number: 521
End Page Number: 544
Publication Date: May 2005
Journal: Mathematics of Operations Research
Authors: ,
Keywords: GI/G/c queues
Abstract:

We consider a deterministic queueing system in which N = 2 servers of different speeds operate in parallel. Each service in queue i takes the deterministic time Si. Identical customers arrive exactly one per time unit, and it is desirable to route them to the queues so that the average waiting time (we consider as waiting time the time a customer waits in the buffer of a queue, and thus the service time is not included in this) is minimized. We provide an algorithm to compute lower and upper bounds on this quantity. The upper bound is found by showing that there is a periodic policy for which the average waiting time is no greater than the lower bound plus (N/2) − 1. Thus, the bounds coincide when N = 2. For obtaining the lower bound, we give explicit formulae for the average waiting time in case of regular routing to a deterministic queue.

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