Overflow networks: Approximations and implications to call center outsourcing

Itai Gurvich*, Ohad Perry

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)996-1009
Number of pages14
JournalOperations Research
Issue number4
StatePublished - Jul 2012

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research


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