Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems
- 1 April 2009
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Manufacturing & Service Operations Management
- Vol. 11 (2), 237-253
- https://doi.org/10.1287/msom.1070.0211
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 serves the customer from the head of the queue of the class (from among those the server 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-c\mu (Gc\mu ) rule, under which a newly available server selects a customer from the class experiencing the greatest marginal cost at that time.queues, many-server queues, heavy-traffic limits for queues, service systems, cost minimization in many-server queues, skill-based routing, generalized-c\mu rule, queue-and-idleness-ratio controlKeywords
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