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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 ..."
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Cited by 286 (14 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].
The FourierSeries Method For Inverting Transforms Of Probability Distributions
, 1991
"... This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method are remar ..."
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Cited by 212 (53 self)
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This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method are remarkably easy to use, requiring programs of less than fifty lines. The Fourierseries method can be interpreted as numerically integrating a standard inversion integral by means of the trapezoidal rule. The same formula is obtained by using the Fourier series of an associated periodic function constructed by aliasing; this explains the name of the method. This Fourier analysis applies to the inversion problem because the Fourier coefficients are just values of the transform. The mathematical centerpiece of the Fourierseries method is the Poisson summation formula, which identifies the discretization error associated with the trapezoidal rule and thus helps bound it. The greatest difficulty is approximately calculating the infinite series obtained from the inversion integral. Within this framework, lattice cdf's can be calculated from generating functions by finite sums without truncation. For other cdf's, an appropriate truncation of the infinite series can be determined from the transform based on estimates or bounds. For Laplace transforms, the numerical integration can be made to produce a nearly alternating series, so that the convergence can be accelerated by techniques such as Euler summation. Alternatively, the cdf can be perturbed slightly by convolution smoothing or windowing to produce a truncation error bound independent of the original cdf. Although error bounds can be determined, an effective approach is to use two different methods without elaborate error analysis. For this...
Numerical inversion of probability generating functions
 Oper. Res. Letters
, 1992
"... Random quantities of interest in operations research models can often be determined conveniently in the form of transforms. Hence, numerical transform inversion can be an effective way to obtain desired numerical values of cumulative distribution functions, probability density functions and probabil ..."
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Cited by 62 (19 self)
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Random quantities of interest in operations research models can often be determined conveniently in the form of transforms. Hence, numerical transform inversion can be an effective way to obtain desired numerical values of cumulative distribution functions, probability density functions and probability mass functions. However, numerical transform inversion has not been widely used. This lack of use seems to be due, at least in part, to good simple numerical inversion algorithms not being well known. To help remedy this situation, in this paper we present a version of the Fourierseries method for numerically inverting probability generating functions. We obtain a simple algorithm with a convenient error bound from the discrete Poisson summation formula. The same general approach applies to other transforms. Key Words: numerical inversion of transforms, computational probability, generating functions, Fourierseries method, Poisson summation formula, discrete Fourier transform.
AN INTRODUCTION TO NUMERICAL TRANSFORM INVERSION AND ITS APPLICATION TO PROBABILITY MODELS
, 1999
"... ..."
Simulation run lengths to estimate blocking probabilities
 ACM Transactions on Modelling and Computer Simulation
, 1996
"... We derive formulas approximating the asymptotic variance of four estimators for the steadystate blocking probability in a multiserver loss system, exploiting diffusion process limits. These formulas can be used to predict simulation run lengths required to obtain desired statistical precision befor ..."
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Cited by 32 (22 self)
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We derive formulas approximating the asymptotic variance of four estimators for the steadystate blocking probability in a multiserver loss system, exploiting diffusion process limits. These formulas can be used to predict simulation run lengths required to obtain desired statistical precision before the simulation has been run, which can aid in the design of simulation experiments. They also indicate that one estimator can be much better than another, depending on the loading. An indirect estimator based on estimating the mean occupancy is significantly more (less) efficient than a direct estimator for heavy (light) loads. A major concern is the way computational effort scales with system size. For all the estimators, the asymptotic variance tends to be inversely proportional to the system size, so that the computational effort (regarded as proportional to the product of the asymptotic variance and the arrival rate) does not grow as system size increases. Indeed, holding the blocking probability fixed, the computational effort with a good estimator decreases to 0 as the system size increases. The asymptotic variance formulas also reveal the impact of the arrivalprocess and servicetime variability on the statistical precision. We validate these formulas by comparing them to exact numerical
Service Engineering in Action: The Palm/ErlangA Queue, with Applications to Call Centers
 Advances in Services Innovations
, 2005
"... Our note 1 is dedicated to the Palm/ErlangA Queue. This is the simplest practiceworthy queueing model, that accounts for customers ’ impatience while waiting. The model is gaining importance in support of the staffing of call centers, which is a central step in their ServiceEngineering. We discuss ..."
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Cited by 23 (8 self)
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Our note 1 is dedicated to the Palm/ErlangA Queue. This is the simplest practiceworthy queueing model, that accounts for customers ’ impatience while waiting. The model is gaining importance in support of the staffing of call centers, which is a central step in their ServiceEngineering. We discuss computations of performance measures, both theoretical and softwarebased (via the 4CallCenter software). Then several examples of Palm/ErlangA applications are presented, mostly motivated by and based on real call center data. Acknowledgements. The research of both authors was supported by ISF (Israeli Science Foundation) grants 388/99, 126/02 and 1046/04, by the Niderzaksen Fund and by the Technion funds for the promotion of research and sponsored research. 1 Parts of the text are adapted from [8], [15], [17] and [22]
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 ..."
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Cited by 20 (4 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.
Exponential Approximation of MultiSkill Call Centers Architecture
 In Proceedings of QNETs 2000
"... We model a multiskill call center as a network of queues: Calls are considered as customers requesting service, agents as servers. A customer that finds all servers busy at a queue may be routed to another queue (if any) or is lost (otherwise). In order to evaluate the losses of such a network, we ..."
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Cited by 20 (4 self)
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We model a multiskill call center as a network of queues: Calls are considered as customers requesting service, agents as servers. A customer that finds all servers busy at a queue may be routed to another queue (if any) or is lost (otherwise). In order to evaluate the losses of such a network, we approximate each queue as an M/M/r loss system. Based on simulations, we illustrate the efficiency of the exponential approximation, and its application to the design of a call center architecture.
Queueing models for computer communications system analysis
 IEEE Transactions on Communications. No
, 1977
"... AbstractModeling and performance prediction are becoming increasingly important issues in the design and operation of computer communications systems. Complexities in their configuration and sophistications in resource sharing found in today’s computer communications demand our intensive ffort to ..."
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Cited by 16 (0 self)
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AbstractModeling and performance prediction are becoming increasingly important issues in the design and operation of computer communications systems. Complexities in their configuration and sophistications in resource sharing found in today’s computer communications demand our intensive ffort to enhance the modeling capability. The present paper is intended to review the state of affairs of analytic methods, queueing analysis techniques in particular, which are essential to modeling of computer communication systems. First we review basic properties of exponential queueing systems, and then give an overview of recent progress made in the areas of queueing network models and discretetime queueing systems. A unified treatment of buffer storage overflow problems will be discussed as an application example, in whichwe call attention to the analogy between buffer behavior and waiting time in the GI/G/l queue. Another application deals with the analysis of various multiplexing techniques and net