On the overflow process from a finite Markovian queue
Performance Evaluation
Approximation of the overflow process from a G/M/N/K queueing system
Management Science
The pointwise stationary approximation for M1/M1/s
Management Science
Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects
Manufacturing & Service Operations Management
Heavy-Traffic Limits for the G/H2*/n/m Queue
Mathematics of Operations Research
Dynamic Routing in Large-Scale Service Systems with Heterogeneous Servers
Queueing Systems: Theory and Applications
Approximating multi-skill blocking systems by hyperexponential decomposition
Performance Evaluation
Call-Routing Schemes for Call-Center Outsourcing
Manufacturing & Service Operations Management
Pointwise Stationary Fluid Models for Stochastic Processing Networks
Manufacturing & Service Operations Management
Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems
Manufacturing & Service Operations Management
Queue-and-Idleness-Ratio Controls in Many-Server Service Systems
Mathematics of Operations Research
Responding to Unexpected Overloads in Large-Scale Service Systems
Management Science
Admission control for a multi-server queue with abandonment
Queueing Systems: Theory and Applications
A Fluid Approximation for Service Systems Responding to Unexpected Overloads
Operations Research
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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.