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

2005, 221–235. Available at: . Supplementary
material on this paper is also available at this website.
Abstract. An algorithm is developed to rapidly compute approximations for all the standard
steady-state performance measures in the basic call-center queuing model M/GI/s/r+GI, which
has a Poisson arrival process, independent and identically distributed (IID) service times with
a general distribution, s Servers, r extra waiting spaces and IID customer abandonment times
with a general distribution. Empirical studies of call centers indicate that the service time and
abandon-time distributions often are not nearly exponential, so that it is important to go beyond
the Markovian M/M/s/r + M special case, but the general service-time and abandon-time
distributions make the realistic model very difficult to analyze directly. The proposed algorithm
is based on an approximation by an appropriate Markovian M/M/s/r + M(n) queueing , where
M(n) denotes state-dependent abandonment rates.
Keywords: Algorithms, Call centers, Queuing theory, Markov analysis, Performance evaluation,
Statistical analysis, Workforce planning
157. Whitt, Ward. Two fluid approximations for multi-server queues with abandonments, Operations
Research Letters, 33, 2005, 363–372.
Available at: .
Abstract. Insight is provided into a previously developed M/M/s/r + M(n) approximation
for the M/GI/s/r + GI queueing model by establishing fluid and diffusion limits for the approximating
model. Fluid approximations for the two models are compared in the many-server
efficiency-driven (overloaded) regime. The two fluid approximations do not coincide, but they
are close.
Keywords: Multi-server queues with abandonment, Queues with state-dependent rates, Heavytraffic
limits, Fluid limits, Diffusion approximations, Call centers
158. Abate, J. and W. Whitt. A unified framework for numerically inverting Laplace transforms,
INFORMS Journal of Computing, 2006. To appear. Available at:
.
Abstract. We introduce and investigate a framework for constructing algorithms to numerically
invert Laplace transforms. Given a Laplace transform ˆ f of a complex-valued function of a
nonnegative real-variable, f, the function f is approximated by a finite linear combination of
the transform values; i.e., we use the inversion formula
f(t) ≈ fn(t) ≡ 1
t
n
ωk ˆ f
k=0
αk
t
, 0 < t < ∞ ,
where the weights ωk and nodes αk are complex numbers, which depend on n, but do not depend
on the transform ˆ f or the time argument t. Many different algorithms can be put into
this framework, because it remains to specify the weights and nodes. We examine three onedimensional
inversion routines in this framework: the Gaver-Stehfest algorithm, a version of the
Fourier-series method with Euler summation, and a version of the Talbot algorithm, which is
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