Overflow Networks: Approximations and Implications to Call Center Outsourcing

Itai Gurvich () and Ohad Perry ()
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Itai Gurvich: Kellogg School of Management, Northwestern University, Evanston, Illinois 60208
Ohad Perry: Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208

Operations Research, 2012, vol. 60, issue 4, 996-1009

Abstract: Motivated by call center cosourcing problems, we consider a service network operated under an overflow mechanism. Calls are first routed to an in-house (or dedicated) service station that has a finite waiting room. If the waiting room is full, the call is overflowed to an outside provider (an overflow station) that might also be serving overflows from other stations. We establish approximations for overflow networks with many servers under a resource-pooling assumption that stipulates, in our context, that the fraction of overflowed calls is nonnegligible. Our two main results are (i) an approximation for the overflow processes via limit theorems and (ii) asymptotic independence between each of the in-house stations and the overflow station. In particular, we show that, as the system becomes large, the dependency between each in-house station and the overflow station becomes negligible. Independence between stations in overflow networks is assumed in the literature on call centers, and we provide a rigorous support for those useful heuristics.

Keywords: overflow networks; cosourcing; heavy-traffic approximations; separation of time scales (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (8)

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