期刊
M&SOM-MANUFACTURING & SERVICE OPERATIONS MANAGEMENT
卷 11, 期 2, 页码 237-253出版社
INFORMS
DOI: 10.1287/msom.1070.0211
关键词
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 control
资金
- NSF [DMI-0457095]
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.
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