Scheduling flexible servers with convex delay costs in many-server service systems

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Scheduling flexible servers with convex delay costs in many-server service systems (2007)

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by Itay Gurvich , Ward Whitt

Venue:	MANUFACTURING AND SERVICE OPERATIONS MANAGEMENT. FORTHCOMING
Citations:	34 - 19 self

BibTeX

@INPROCEEDINGS{Gurvich07schedulingflexible,
    author = {Itay Gurvich and Ward Whitt},
    title = {Scheduling flexible servers with convex delay costs in many-server service systems},
    booktitle = { MANUFACTURING AND SERVICE OPERATIONS MANAGEMENT. FORTHCOMING},
    year = {2007},
    publisher = {}
}

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Abstract

In a recent paper we introduced the queue-and-idleness-ratio (QIR) family of routing rules for many-server service systems with multiple customer classes and server pools. A newly available server next serves the customer from the head of the queue of the class (from among those he is eligible to serve) whose queue length most exceeds a specified proportion of the total queue length. Under fairly general conditions, QIR produces an important state-space collapse as the total arrival rate and the numbers of servers increase in a coordinated way. That state-space collapse was previously used to delicately balance service levels for the different customer classes. In this sequel, we show that a special version of QIR stochastically minimizes convex holding costs in a finite-horizon setting when the service rates are restricted to be pool-dependent. Under additional regularity conditions, the special version of QIR reduces to a simple policy: Linear costs produce a priority-type rule, in which the least-cost customers are given low priority. Strictly convex costs (plus other regularity conditions) produce a many-server analogue of the generalized-cµ (Gcµ) rule, under which a newly available server selects a customer from the class experiencing the greatest marginal cost at that time.

Keyphrases

many-server service system flexible server manufacturing service oper convex delay cost management forthcoming special version available server qir reduces total queue length server pool specified proportion priority-type rule different customer class service rate low priority many-server analogue multiple customer class least-cost customer additional regularity condition important state-space collapse recent paper convex cost marginal cost regularity condition state-space collapse coordinated way linear cost general condition queue length finite-horizon setting service level total arrival rate simple policy

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