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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 148 (24 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.
Server Staffing to Meet TimeVarying Demand
 Management Science
, 1996
"... We consider a multiserver service system with general nonstationary arrival and servicetime processes in which s(t), the number of servers as a function of time, needs to be selected to meet projected loads. We try to choose s(t) so that the probability of a delay (before beginning service) hits or ..."
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Cited by 58 (22 self)
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We consider a multiserver service system with general nonstationary arrival and servicetime processes in which s(t), the number of servers as a function of time, needs to be selected to meet projected loads. We try to choose s(t) so that the probability of a delay (before beginning service) hits or falls just below a target probability at all times. We develop an approximate procedure based on a timedependent normal distribution, where the mean and variance are determined by infiniteserver approximations. We demonstrate that this approximation is effective by making comparisons with the exact numerical solution of the Markovian M t / M / s t model.
Improving Service by Informing Customers about Anticipated Delays
 Management Science
, 1999
"... This paper studies alternative ways to manage a multiserver system such as a telephone call center. Three alternatives can be described succinctly by: (i) blocking, (ii) reneging and (iii) balking. The first alternative – blocking – is to have no provision for waiting. The second alternative is to ..."
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Cited by 49 (9 self)
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This paper studies alternative ways to manage a multiserver system such as a telephone call center. Three alternatives can be described succinctly by: (i) blocking, (ii) reneging and (iii) balking. The first alternative – blocking – is to have no provision for waiting. The second alternative is to allow waiting, but neither inform customers about anticipated delays nor provide state information to allow arriving customers to predict delays. The second alternative tends to yield higher server utilizations. The first alternative tends to reduce to the second, without the firstcome firstserved service discipline, when customers can easily retry, as with automatic redialers in telephone access. The third alternative is to both allow waiting and inform customers about anticipated delays. The third alternative tends to cause balking when all servers are busy (abandonment upon arrival) instead of reneging (abandonment after waiting). Birthanddeath process models are proposed to describe the performance with each alternative. Algorithms are developed to compute the conditional distributions of the time to receive service and the time to renege given each outcome. Algorithms are also developed to help the service provider predict customer waiting times before beginning service, given estimated servicetime distributions and the elapsed service times of the customers in service. Better predictions may be obtained by classifying customers and thereby obtaining better estimates of their servicetime distributions.
Coping with TimeVarying Demand When Setting Staffing Requirements for a Service System
, 2007
"... We review queueingtheory methods for setting staffing requirements in service systems where customer demand varies in a predictable pattern over the day. Analyzing these systems is not straightforward, because standard queueing theory focuses on the longrun steadystate behavior of stationary mode ..."
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Cited by 40 (16 self)
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We review queueingtheory methods for setting staffing requirements in service systems where customer demand varies in a predictable pattern over the day. Analyzing these systems is not straightforward, because standard queueing theory focuses on the longrun steadystate behavior of stationary models. We show how to adapt stationary queueing models for use in nonstationary environments so that timedependent performance is captured and staffing requirements can be set. Relatively little modification of straightforward stationary analysis applies in systems where service times are short and the targeted quality of service is high. When service times are moderate and the targeted quality of service is still high, timelag refinements can improve traditional stationary independent periodbyperiod and peakhour approximations. Timevarying infiniteserver models help develop refinements, because closedform expressions exist for their timedependent behavior. More difficult cases with very long service times and other complicated features, such as endofday effects, can often be treated by a modifiedofferedload approximation, which is based on an associated infiniteserver model. Numerical algorithms and deterministic fluid models are useful when the system is overloaded for an extensive period of time. Our discussion focuses on telephone call centers, but applications to police patrol, banking, and hospital emergency rooms are also mentioned.
Estimating the parameters of a nonhomogeneous Poisson process with linear rate
 Telecommunication Systems
, 1996
"... Motivated by telecommunication applications, we investigate ways to estimate the parameters of a nonhomogeneous Poisson process with linear rate over a finite interval, based on the number of counts in measurement subintervals. Such a linear arrivalrate function can serve as a component of a piecew ..."
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Cited by 26 (14 self)
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Motivated by telecommunication applications, we investigate ways to estimate the parameters of a nonhomogeneous Poisson process with linear rate over a finite interval, based on the number of counts in measurement subintervals. Such a linear arrivalrate function can serve as a component of a piecewiselinear approximation to a general arrivalrate function. We consider ordinary least squares (OLS), iterative weighted least squares (IWLS) and maximum likelihood (ML), all constrained to yield a nonnegative rate function. We prove that ML coincides with IWLS. As a reference point, we also consider the theoretically optimal weighted least squares (TWLS), which is least squares with weights inversely proportional to the variances (which would not be known with data). Overall, ML performs almost as well as TWLS. We describe computer simulations conducted to evaluate these estimation procedures. None of the procedures differ greatly when the rate function is not near 0 at either end, but when the rate function is near 0 at one end, TWLS and ML are significantly more effective than OLS. The number of measurement subintervals (with fixed total interval) makes surprisingly little difference when the rate function is not near 0 at either end. The variances are higher with only two or three
DYNAMIC STAFFING IN A TELEPHONE CALL CENTER AIMING TO IMMEDIATELY ANSWER ALL CALLS
, 1997
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Quantifying fairness in queueing systems: Principles and applications
 RUTCOR, Rutgers University
, 2004
"... In this paper we discuss fairness in queues, view it in the perspective of social justice at large and survey the recently published research work and publications dealing with the issue of measuring fairness of queues. The emphasis is placed on the underlying principles of the different measuring a ..."
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Cited by 19 (9 self)
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In this paper we discuss fairness in queues, view it in the perspective of social justice at large and survey the recently published research work and publications dealing with the issue of measuring fairness of queues. The emphasis is placed on the underlying principles of the different measuring approaches, on reviewing their methodology and on examining their applicability and intuitive appeal. Some quantitative results are also presented. The paper has three major parts (sections) and a short concluding discussion. In the first part, fairness in queues and its importance are discussed in the broader context of the prevailing conception of social justice at large. A special effort, including illustrative examples, is made to differentiate between fairness of the queue and fairness at large, which derives from favoring the more needy. The second part is dedicated to explaining and discussing the three main properties expected of a fairness measure: conformity to the general concept of social justice, granularity, and intuitive appeal and rationality. The third part reviews the fairness of the queue evaluation and
Uniform acceleration expansions for Markov chains with timevarying rates
 Annals of Applied Probability
, 1997
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Modeling and analysis of flexible queueing systems
"... Abstract: We consider queueing systems with multiple classes of customers and heterogeneous servers where customers have the flexibility of being processed by more than one server and servers possess the capability of processing more than one customer class. We provide a unified framework for the mo ..."
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Cited by 13 (0 self)
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Abstract: We consider queueing systems with multiple classes of customers and heterogeneous servers where customers have the flexibility of being processed by more than one server and servers possess the capability of processing more than one customer class. We provide a unified framework for the modeling and analysis of these systems under arbitrary customer and server flexibility and for a rich set of control policies that includes customer/serverspecific priority schemes for server and customer selection. We use our models to generate several insights into the effect of system configuration and control policies. In particular, we examine the relationship between flexibility, control policies and throughput under varying assumptions for
2003) Modelling supply networks and business cycles as unstable transport phenomena
 New Journal of Physics
"... Physical concepts developed to describe instabilities in traffic flows can be generalized in a way that allows one to understand the wellknown instability of supply chains (the socalled “bullwhip effect”). That is, small variations in the consumption rate can cause large variations in the productio ..."
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Cited by 9 (6 self)
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Physical concepts developed to describe instabilities in traffic flows can be generalized in a way that allows one to understand the wellknown instability of supply chains (the socalled “bullwhip effect”). That is, small variations in the consumption rate can cause large variations in the production rate of companies generating the requested product. Interestingly, the resulting oscillations have characteristic frequencies which are considerably lower than the variations in the consumption rate. This suggests that instabilities of supply chains may be the reason for the existence of business cycles. At the same time, we establish some link to queuing theory and between micro and macroeconomics. 1