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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 295 (16 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].
Call centers with impatient customers: manyserver asymptotics of the M/M/n+G queue
, 2005
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Heavy Traffic Limits for Queues with Many Deterministic Servers
"... Consider a sequence of stationary GI/D/N queues indexed by N with servers' utilization 1 #/ # N , # > 0. For such queues we show that the scaled waiting times NWN converge to the (finite) supremum of a Gaussian random walk with drift #. ..."
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Cited by 53 (5 self)
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Consider a sequence of stationary GI/D/N queues indexed by N with servers' utilization 1 #/ # N , # > 0. For such queues we show that the scaled waiting times NWN converge to the (finite) supremum of a Gaussian random walk with drift #.
Dynamic routing in largescale service systems with heterogeneous servers
, 2005
"... Motivated by modern call centers, we consider largescale service systems with multiple server pools and a single customer class. For such systems, we propose a simple routing rule which asymptotically minimizes the steadystate queue length and virtual waiting time. The proposed routing scheme is ..."
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Cited by 52 (12 self)
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Motivated by modern call centers, we consider largescale service systems with multiple server pools and a single customer class. For such systems, we propose a simple routing rule which asymptotically minimizes the steadystate queue length and virtual waiting time. The proposed routing scheme is FSF which assigns customers to the Fastest Servers First. The asymptotic regime considered is the HalfinWhitt manyserver heavytraffic regime, which we refer to as the Quality and Efficiency Driven (QED) regime; it achieves high levels of both service quality and system efficiency by carefully balancing between the two. Additionally, expressions are provided for system limiting performance measures based on diffusion approximations. Our analysis shows that in the QED regime this heterogeneous server system outperforms its homogeneous server counterpart.
AN INTRODUCTION TO NUMERICAL TRANSFORM INVERSION AND ITS APPLICATION TO PROBABILITY MODELS
, 1999
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Scheduling a multiclass queue with many exponential servers: Asymptotic optimality in heavytraffic
 THE ANNALS OF APPLIED PROBABILITY
, 2004
"... We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal. Our cost is an expected cumulative discounted function, line ..."
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Cited by 42 (14 self)
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We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal. Our cost is an expected cumulative discounted function, linear or nonlinear, of appropriately normalized performance measures. As a special case, the cost per unit time can be a function of the number of customers waiting to be served in each class, the number actually being served, the abandonment rate, the delay experienced by customers, the number of idling servers, as well as certain combinations thereof. We study the system in an asymptotic heavytraffic regime where the number of servers n and the offered load r are simultaneously scaled up and carefully balanced: n ≈ r + β √ r for some scalar β. This yields an operation that enjoys the benefits of both heavy traffic (high server utilization) and light traffic (high service levels.)
Stochastic Modeling Of Traffic Processes
 Frontiers in Queueing: Models, Methods and Problems
, 1996
"... Modern telecommunications networks are being designed to accomodate a heterogenous mix of traffic classes ranging from traditional telephone calls to video and data services. Thus, traffic models are of crucial importance to the engineering and performance analysis of telecommunications system, nota ..."
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Cited by 34 (0 self)
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Modern telecommunications networks are being designed to accomodate a heterogenous mix of traffic classes ranging from traditional telephone calls to video and data services. Thus, traffic models are of crucial importance to the engineering and performance analysis of telecommunications system, notably congestion and overload controls and capacity estimation. This chapter surveys teletraffic models, addressing both theoretical and computational aspects. It first surveys the main classes of teletraffic models commonly used in teletraffic modeling, and then proceeds to survey traffic methods for computing statistics relevant to the engineering a teletraffic network. 1 INTRODUCTION Traffic is the driving force of telecommunications systems, representing customers making phone calls, transferring data files and other electronic information, or more recently, transmitting compressed video frames to a display device. The most common modeling context is queueing; traffic is offered to a qu...
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 29 (19 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
Queues with Many Servers: The Virtual WaitingTime Process in the QED Regime
, 2007
"... We consider a multiserver queue (G/GI/N) in the Quality and EfficiencyDriven (QED) regime. In this regime, which was first formalized by Halfin and Whitt, the number of servers N is not small, servers ’ utilization is 1 − O(1/√N) (EfficiencyDriven) while waiting time is O(1/ N) (QualityDriven). ..."
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Cited by 24 (1 self)
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We consider a multiserver queue (G/GI/N) in the Quality and EfficiencyDriven (QED) regime. In this regime, which was first formalized by Halfin and Whitt, the number of servers N is not small, servers ’ utilization is 1 − O(1/√N) (EfficiencyDriven) while waiting time is O(1/ N) (QualityDriven). This is equivalent to having the number of servers N being approximately equal to R + β R, where R is the offered load and β is a positive constant. For the G/GI/N queue in the QED regime, we analyze the virtual waiting time VN (t), as N increases indefinitely. Assuming that the service time distribution has a finite support, it is shown that, in the limit, the scaled virtual waiting time V̂N (t) = NVN (t)/ES is representable as a supremum over a random weighted tree (S denotes a service time). Informally, it is then argued that, for large N,
Sensitivity to the servicetime distribution in the nonstationary Erlang loss model
 Management Sci
, 1995
"... The stationary Erlang loss model is a classic example of an insensitive queueing system: The steadystate distribution of the number of busy servers depends on the servicetime distribution only through its mean. However, when the arrival process is a nonstationary Poisson process, the insensitivity ..."
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Cited by 22 (10 self)
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The stationary Erlang loss model is a classic example of an insensitive queueing system: The steadystate distribution of the number of busy servers depends on the servicetime distribution only through its mean. However, when the arrival process is a nonstationary Poisson process, the insensitivity property is lost. We develop a simple effective numerical algorithm for the M t/PH/s/0 model with two service phases and a nonhomogeneous Poisson arrival process, and apply it to show that the timedependent blocking probability with nonstationary input can be strongly influenced by the servicetime distribution beyond the mean. With sinusoidal arrival rates, the peak blocking probability typically increases as the servicetime distribution gets less variable. The influence of the servicetime distribution, including this seemingly anomalous behavior, can be understood and predicted from the modifiedofferedload and stationarypeakedness approximations, which exploit exact results for related infiniteserver models. Key Words: nonstationary queues; timedependent arrival rates; nonhomogeneous Markov chains; transient behavior; Erlang loss model; blocking probability; insensitivity; infiniteserver queues; modifiedofferedload approximation.