Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems, Manufacturing & Service Operations Management (M&SOM)
In a recent paper we introduced the fixed-queue-ratio (FQR) 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, FQR 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 FQR 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 FQR 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 (GC) rule, under which a newly available server selects a customer from the class experiencing the greatest marginal cost at that time.
Itai Gurvich, Ward Whitt
Gurvich, Itai, and Ward Whitt. 2009. Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems. Manufacturing & Service Operations Management (M&SOM). 11(2): 237-253.LINK