Paper Info
Title
A Call-Routing Problem with Service-Level Constraints
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 ? H , are processed at rate Î禄ï戮µ H, and are served first come, first served within class. Aservice-level constraint of the form E[delay] = a orP {delay = Î虏} = limits the delay in queue that these jobs may face. An infinite backlog of type-L jobs awaits processing at rate Î禄L , and there is no service-level constraint on this type of work. A pool ofc 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 simpleM/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( c3) variables and O( c2) constraints.
Year
DOI
Venue
2003
10.1287/opre.51.2.255.12787
Operations Research
Keywords
Field
DocType
call-routing problem,effective routing policy,service-level constraints,type-l job,service-level constraint,type-h work,aservice-level constraint,optimal policy parameter,queueing system,system controller,optimal policy,expected service time,service level
Dynamic programming,Mathematical optimization,Service level,Queue,Server,Markov decision process,Linear programming,Normalizing constant,Operations management,Mathematics,Computation
Journal
Volume
Issue
ISSN
51
2
0030-364X
Citations 
PageRank 
References 
36
2.93
12
Authors
2
Name
Order
Citations
PageRank
Noah Gans161366.60
Yongpin Zhou223329.54