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Telephone call centers: Tutorial, review, and research prospects
 Mgmt
, 2003
"... Telephone call centers are an integral part of many businesses, and their economic role is significant and growing. They are also fascinating sociotechnical systems in which the behavior of customers and employees is closely intertwined with physical performance measures. In these environments trad ..."
Abstract

Cited by 150 (6 self)
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Telephone call centers are an integral part of many businesses, and their economic role is significant and growing. They are also fascinating sociotechnical systems in which the behavior of customers and employees is closely intertwined with physical performance measures. In these environments traditional operational models are of great value – and at the same time fundamentally limited – in their ability to characterize system performance. We review the state of research on telephone call centers. We begin with a tutorial on how call centers function and proceed to survey academic research devoted to the management of their operations. We then outline important problems that have not been addressed and identify promising directions for future research. Acknowledgments The authors thank Lee Schwarz, Wallace Hopp and the editorial board of M&SOM for initiating this project, as well as the referees for their valuable comments. Thanks are also due to L. Brown, A. Sakov, H. Shen, S. Zeltyn and L. Zhao for their approval of importing pieces of [36, 112].
Logarithmic Asymptotics For SteadyState Tail Probabilities In A SingleServer Queue
, 1993
"... We consider the standard singleserver queue with unlimited waiting space and the firstin firstout service discipline, but without any explicit independence conditions on the interarrival and service times. We find conditions for the steadystate waitingtime distribution to have smalltail asympt ..."
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Cited by 150 (14 self)
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We consider the standard singleserver queue with unlimited waiting space and the firstin firstout service discipline, but without any explicit independence conditions on the interarrival and service times. We find conditions for the steadystate waitingtime distribution to have smalltail asymptotics of the form x  1 logP(W > x)  q * as x for q * > 0. We require only stationarity of the basic sequence of service times minus interarrival times and a Ga .. rtnerEllis condition for the cumulant generating function of the associated partial sums, i.e., n  1 log Ee qS n y(q) as n , plus regularity conditions on the decay rate function y. The asymptotic decay rate q * is the root of the equation y(q) = 0. This result in turn implies a corresponding asymptotic result for the steadystate workload in a queue with general nondecreasing input. This asymptotic result covers the case of multiple independent sources, so that it provides additional theoretical support for a concept of effective bandwidths for admission control in multiclass queues based on asymptotic decay rates.
2002a), “Statistical Analysis of a Telephone Call Center: A Queueing Science Perspective,” technical report, University of Pennsylvania, downloadable at http://iew3.technion.ac.il/serveng/References/references.html
"... A call center is a service network in which agents provide telephonebased services. Customers who seek these services are delayed in telequeues. This article summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking cal ..."
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Cited by 119 (19 self)
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A call center is a service network in which agents provide telephonebased services. Customers who seek these services are delayed in telequeues. This article summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking call center, call by call, over a full year. Taking the perspective of queueing theory, we decompose the service process into three fundamental components: arrivals, customer patience, and service durations. Each component involves different basic mathematical structures and requires a different style of statistical analysis. Some of the key empirical results are sketched, along with descriptions of the varied techniques required. Several statistical techniques are developed for analysis of the basic components. One of these techniques is a test that a point process is a Poisson process. Another involves estimation of the mean function in a nonparametric regression with lognormal errors. A new graphical technique is introduced for nonparametric hazard rate estimation with censored data. Models are developed and implemented for forecasting of Poisson arrival rates. Finally, the article surveys how the characteristics deduced from the statistical analyses form the building blocks for theoretically interesting and practically useful mathematical models for call center operations.
Validity of heavy traffic steadystate approximations in open queueing networks
, 2006
"... We consider a single class open queueing network, also known as a generalized Jackson network (GJN). A classical result in heavytraffic theory asserts that the sequence of normalized queue length processes of the GJN converge weakly to a reflected Brownian motion (RBM) in the orthant, as the traffic ..."
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Cited by 28 (4 self)
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We consider a single class open queueing network, also known as a generalized Jackson network (GJN). A classical result in heavytraffic theory asserts that the sequence of normalized queue length processes of the GJN converge weakly to a reflected Brownian motion (RBM) in the orthant, as the traffic intensity approaches unity. However, barring simple instances, it is still not known whether the stationary distribution of RBM provides a valid approximation for the steadystate of the original network. In this paper we resolve this open problem by proving that the rescaled stationary distribution of the GJN converges to the stationary distribution of the RBM, thus validating a socalled “interchangeoflimits” for this class of networks. Our method of proof involves a combination of Lyapunov function techniques, strong approximations and tail probability bounds that yield tightness of the sequence of stationary distributions of the GJN.
Heavy Traffic Limits for Some Queueing Networks
 Annals of Applied Probability
, 2001
"... Using a slight modification of the framework in Bramson [7] and Williams [52], we prove heavy traffic limit theorems for six families of multiclass queueing networks. The first three families are single station systems operating under firstin firstout (FIFO), generalized headoftheline proportio ..."
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Cited by 18 (1 self)
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Using a slight modification of the framework in Bramson [7] and Williams [52], we prove heavy traffic limit theorems for six families of multiclass queueing networks. The first three families are single station systems operating under firstin firstout (FIFO), generalized headoftheline proportional processor sharing (GHLPPS) and static buffer priority (SBP) service disciplines. The next two families are reentrant lines operating under firstbufferfirstserve (FBFS) and lastbufferfirstserve (LBFS) service disciplines; the last family consists of certain 2station, 5class networks operating under an SBP service discipline. Some of these heavy traffic limits have appeared earlier in the literature; our new proofs demonstrate the significant simplifications that can be achieved in the present setting.
A survey on Discriminatory Processor Sharing.
 Queueing Systems
, 2006
"... The Discriminatory Processor Sharing (DPS) model is a multiclass generalization of the egalitarian Processor Sharing model. In the DPS model all jobs present in the system are served simultaneously at rates controlled by a vector of weights {gk> 0; k = 1,..., K}. If there are Nk jobs of class k pre ..."
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Cited by 14 (5 self)
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The Discriminatory Processor Sharing (DPS) model is a multiclass generalization of the egalitarian Processor Sharing model. In the DPS model all jobs present in the system are served simultaneously at rates controlled by a vector of weights {gk> 0; k = 1,..., K}. If there are Nk jobs of class k present in the system, k = 1,..., K, each classk job is served at rate gk/�K j=1 gjNj. The present article provides an overview of the analytical results for the DPS model. In particular, we focus on response times and numbers of jobs in the system.
Calculation Of The Gi/g/1 WaitingTime Distribution And Its Cumulants From Pollaczek's Formulas
"... The steadystate waiting time in a stable GI/G/1 queue is equivalent to the maximum of a general random walk with negative drift. Thus, the distribution of the steadystate waiting time in the GI/G/1 queue is characterized by Spitzer's (1956) formula. However, earlier, Pollaczek (1952) derived an eq ..."
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Cited by 9 (5 self)
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The steadystate waiting time in a stable GI/G/1 queue is equivalent to the maximum of a general random walk with negative drift. Thus, the distribution of the steadystate waiting time in the GI/G/1 queue is characterized by Spitzer's (1956) formula. However, earlier, Pollaczek (1952) derived an equivalent contourintegral expression for the Laplace transform of the GI/G/1 steadystate waiting time. Since Spitzer's formula is easier to understand probabilistically, it is better known today, but it is not so easy to apply directly except in special cases. In contrast, we show that it is easy to compute the GI/G/1 waitingtime distribution and its cumulants (and thus its moments) from Pollaczek's formulas. For the waitingtime tail probabilities, we use numerical transform inversion, numerically integrating the Pollaczek contour integral to obtain the transform values. For the cumulants and the probability of having to wait, we directly integrate the Pollazcek contour integrals numerically. The resulting algorithm is evidently the first for a GI/G/1 queue in which neither the transform of the interarrivaltime distribution nor the transform of the servicetime transform distribution need be rational. The algorithm can even be applied to longtail distributions, i.e., distributions with some infinite moments. To treat these distributions, we approximate them by suitable exponentiallydamped versions of these distributions. Overall, the algorithm is remarkably simple compared to alternative algorithms requiring more structure.
Telephone call centers: A tutorial and literature review
 Computer Access and Internet Use, (Working Paper at http:// www2000.ogsm.vanderbilt.edu/papers/race/science.html). Bridging the Racial Divide on the Internet, Science
, 2003
"... Telephone call centers are an integral part of many businesses, and their economic role is significant and growing. They are also fascinating sociotechnical systems in which the behavior of customers and employees is closely intertwined with physical performance measures. In these environments trad ..."
Abstract

Cited by 9 (3 self)
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Telephone call centers are an integral part of many businesses, and their economic role is significant and growing. They are also fascinating sociotechnical systems in which the behavior of customers and employees is closely intertwined with physical performance measures. In these environments traditional operational models are of great value – and at the same time fundamentally limited – in their ability to characterize system performance. We characterize the state of research on telephone call centers. We begin with a tutorial on how call centers function and proceed to survey academic research devoted to the management of their operations. We then outline important problems that have not been addressed and identify promising directions for future research.
Limits and approximations for the busyperiod distribution in singleserver queues
 Prob. Engr. Inf. Sci. 9
, 1995
"... This paper is an extension of Abate and Whitt (1988b), in which we studied the M/M/1 busyperiod distribution and proposed approximations for busyperiod distributions in more general singleserver queues. Here we provide additional theoretical and empirical support for two approximations proposed in ..."
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Cited by 8 (5 self)
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This paper is an extension of Abate and Whitt (1988b), in which we studied the M/M/1 busyperiod distribution and proposed approximations for busyperiod distributions in more general singleserver queues. Here we provide additional theoretical and empirical support for two approximations proposed in Abate and Whitt (1988b), the natural generalization of the asymptotic normal approximation in (4.3) there and the inverse Gaussian approximation in (6.6), (8.3) and (8.4) there. These approximations yield convenient closedform expressions depending on only a few parameters, and they help reveal the general structure of the busyperiod distribution. The busyperiod distribution is known to be important for determining system behavior.
Stability and Asymptotic Optimality of Generalized MaxWeight Policies
, 2007
"... It is shown that stability of the celebrated MaxWeight or back pressure policies is a consequence of the following interpretation: either policy is myopic with respect to a surrogate value function of a very special form, in which the “marginal disutility ” at a buffer vanishes for vanishingly small ..."
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Cited by 7 (2 self)
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It is shown that stability of the celebrated MaxWeight or back pressure policies is a consequence of the following interpretation: either policy is myopic with respect to a surrogate value function of a very special form, in which the “marginal disutility ” at a buffer vanishes for vanishingly small buffer population. This observation motivates the hMaxWeight policy, defined for a wide class of functions h. These policies that share many of the attractive properties of the MaxWeight policy: (i) The policy does not require arrival rate data. (ii) The hmyopic policy is stabilizing when h is a perturbation of a monotone linear function, or a monotone Lyapunov function for the fluid model. (iii) A perturbation of the relative value function for a workload relaxation gives rise to a myopic policy that is approximately averagecost optimal in heavy traffic, with logarithmic regret. The first results are obtained for a completely general stochastic network model. Asymptotic optimality is established for the general scheduling model with a single bottleneck.