CALL CENTERS (CENTRES) - Faculty of Industrial Engineering and ...

135. Gans, Noah and Yong-Pin Zhou. Overflow routing for call-center outsourcing. Working paper,
Wharton School of Business Administration, May 2004.
Abstract. Companies may choose to outsource parts, but not all, of their call-center operations.
In some cases, they classify customers as high or low-value, serving the former with their “in
house” operations and routing the latter to an outsourcer. Typically, they impose service-level
constraints on the time each type of customer waits on hold. We consider this outsourcing problem
from both the client company’s and the outsourcer’s points of view. We pose the client’s
problem as that of maximizing the throughput of low-value calls, subject to a high-value customer
service-level constraint, and the outsourcer’s as one of finding the minimal staffing level
able to fulfill the low-value customers service-level constraint. The paper’s analytical results
characterize effective routing policies at the client, as well as the overflow process of low-value
calls to the outsourcer. Its numerical results help to show how the percentage of low-value calls
that overflows from the client affects the burstiness of the overflow process and, in turn, the
effectiveness of various staffing heuristics at the outsourcer.
136. Jelenković, A., A. Mandelbaum and P. Momčilović. Heavy traffic limits for queues with many deterministic
servers, QUESTA, 47, 2004, 53–69. Available at: .
Abstract. Consider a sequence of stationary GI/D/N queues indexed by N ↑ ∞, with servers’
utilization 1 − β/ √ N, β > 0. For such queues we show that the scaled waiting times √ NWN
converge to the (finite) supremum of a Gaussian random walk with drift −β. This further implies
a corresponding limit for the number of customers in the system, an easily computable nondegenerate
limiting delay probability in terms of Spitzer’s random-walk identities, and √ N rate of
convergence. Our asymptotic regime is important for rational dimensioning of large-scale service
systems, for example telephone- or internet-based, since it achieves, simultaneously, arbitrarily
high service-quality and utilization-efficiency.
Keywords: Multi-server queue, GI/D/N, Deterministic service time, Heavy-traffic, Quality-andefficiency-driven
(QED) or Halfin-Whitt regime, Telephone call or contact centers, Economies of
scale, Gaussian random walk, Spitzer’s identities
137. Jiménez, Tania and Ger Koole. Scaling and comparison of fluid limits of queues applied to call
centers with time-varying parameters, OR Spectrum, 26, 2004, 413–422. Abstract. Transient
overload situations in queues can be approximated by fluid queues. We strengthen earlier results
on the comparison of multi-server tandem systems with their fluid limits. At the same time, we
give conditions under which economies-of-scale hold. We apply the results to call centers.
Keywords: Call centers, Fluid limits, Economies-of-scale, Inhomogeneous Poisson processes
138. Mandelbaum, A. and A.L. Stolyar. Scheduling flexible servers with convex delay costs: Heavytraffic
optimality of the generalized cµ-rule, Operations Research, 52 (6), 2004, 836–855. Available
at:
Abstract. We consider a queueing system with multi-type customers and flexible (multi-skilled)
servers that work in parallel. Let µij denote the service rate of type i customers by server j (the
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