A Call-Routing Problem with Service-Level Constraints

Noah Gans () and Yong-Pin Zhou ()
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Noah Gans: OPIM Department, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6366
Yong-Pin Zhou: Department of Management Science, School of Business Administration, University of Washington, Seattle, Washington 98195-3200

Operations Research, 2003, vol. 51, issue 2, 255-271

Abstract: We consider a queueing system, commonly found in inbound telephone call centers, that processes two types of work. Type-H jobs arrive at rate (lambda) H , are processed at rate (mu) H , and are served first come, first served within class. A service-level constraint of the form E[delay] (le) (alpha) or P {delay (le) (beta)} (ge) limits the delay in queue that these jobs may face. An infinite backlog of type-L jobs awaits processing at rate (mu) H , and there is no service-level constraint on this type of work. A pool of c identical servers processes all jobs, and a system controller must maximize the rate at which type-L jobs are processed, subject to the service-level constraint placed on the type-H work.We formulate the problem as a constrained, average-cost Markov decision process and determine the structure of effective routing policies. When the expected service times of the two classes are the same, these policies are globally optimal, and the computation time required to find the optimal policy is about that required to calculate the normalizing constant for a simple M/M/c system. When the expected service times of the two classes differ, the policies are optimal within the class of priority policies, and the determination of optimal policy parameters can be determined through the solution of a linear program with O( c 3 ) variables and O( c 2 ) constraints.

Keywords: Dynamic programming; infinite state Markov: average cost; constrained MDP; Queues; optimization: control of multiclass; Markovian systems (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (31)

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