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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.
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 15 (5 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]
Two fluid approximations for multiserver queues with abandonments
 Operations Research Letters
, 2004
"... 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 manyserver efficiencydriven (overloaded) regime. Th ..."
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Cited by 10 (6 self)
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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 manyserver efficiencydriven (overloaded) regime. The two fluid approximations do not coincide, but they are close.
Call centers with delay information: Models and insights
 Manufacturing Service Oper. Management
, 2011
"... In this paper, we analyze a call center with impatient customers. We study how informing customers about their anticipated delays affects performance. Customers react by balking upon hearing the delay announcement, and may subsequently renege, particularly if the realized waiting time exceeds the de ..."
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Cited by 4 (1 self)
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In this paper, we analyze a call center with impatient customers. We study how informing customers about their anticipated delays affects performance. Customers react by balking upon hearing the delay announcement, and may subsequently renege, particularly if the realized waiting time exceeds the delay that has originally been announced to them. The balking and reneging from such a system are a function of the delay announcement. Modeling the call center as an M/M/s+M queue with endogenized customer reactions to announcements, we analytically characterize performance measures for this model. The analysis allows us to explore the role announcing different percentiles of the waiting time distribution, i.e., announcement coverage, plays on subsequent performance in terms of balking and reneging. Through a numerical study we explore when informing customers about delays is beneficial, and what the optimal coverage should be in these announcements. It is shown how managers of a call center with delay announcements can control the tradeoff between balking and reneging, through their choice of announcements to be made.
A fluid approximation for the Gt/GI/st + GI queue
, 2010
"... We introduce and analyze a deterministic fluid model that serves as an approximation for the Gt/GI/st + GI manyserver queueing model, which has a general timevarying arrival process (the Gt), a general servicetime distribution (the first GI), a timedependent number of servers (the st) and allows ..."
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Cited by 3 (3 self)
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We introduce and analyze a deterministic fluid model that serves as an approximation for the Gt/GI/st + GI manyserver queueing model, which has a general timevarying arrival process (the Gt), a general servicetime distribution (the first GI), a timedependent number of servers (the st) and allows abandonment from queue according to a general abandonmenttime distribution (the +GI). This fluid model approximates the associated queueing system when the arrival rate and number of servers are both large. We characterize performance in the fluid model over alternating intervals in which the system is overloaded and underloaded (including critically loaded). For each t ≥ 0 and y ≥ 0, we determine the amount of fluid that is in service (in queue) at time t and has been so for time at most y. We obtain the service content density by applying the Banach contraction fixed point theorem. We also determine the timevarying potential waiting time, i.e., the virtual waiting time of a quantum of fluid arriving at a specified time, assuming that it will not abandon. The potential waiting time is determined by an ordinary differential equation. We show that a timevarying service capacity can be chosen to stabilize delays at any fixed target. Key words: queues with timevarying arrivals; nonstationary queues; manyserver queues; deterministic fluid model; fluid approximation; queues with abandonment; nonMarkovian queues.
A Fluid Model for a LargeScale Service System Experiencing Periods of Overloading
, 2010
"... Motivated by healthcare systems and customer contact centers, we introduce and analyze a deterministic fluid model that can be used to show how queue lengths and waiting times depend on model parameters in a largescale service system that experiences periods of overloading. The main feature of the ..."
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Cited by 1 (1 self)
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Motivated by healthcare systems and customer contact centers, we introduce and analyze a deterministic fluid model that can be used to show how queue lengths and waiting times depend on model parameters in a largescale service system that experiences periods of overloading. The main feature of the model is timevarying arrival rate and staffing, but the model also includes the realistic feature of customer abandonment with a nonexponential patience distribution. Our key assumptionsare(i)thatthescaleislarge(therearemanyservers)and(ii) thatthesystemalternates between overloaded intervals and underloaded intervals. We develop algorithms to describe the timedependent performance. For example, we determine, at each time, the content in queue that has beensofor at most a specifiedduration, as afunction of thetwo parameters: time andduration. Wealsodeterminethetimevaryingpotential waitingtime, i.e., thevirtualwaitingtimeofanarrival at a specified time, assuming that it will not abandon. We conduct simulations to confirm that the algorithm and the approximation are effective. Keywords: Largescaleservicesystems; queueswithtimevaryingarrivals; nonstationaryqueues; manyserver queues; deterministic fluid model; fluid approximation; queues with abandonment; nonMarkovian queues. 1
The Gt/GI/st + GI ManyServer Fluid Queue
, 2012
"... This paper introduces a deterministic fluid model that approximates the manyserver Gt/GI/st + GI queueing model, and determines the timedependent performance functions. The fluid model has timevarying arrival rate and service capacity, abandonment from queue, and nonexponential service and patie ..."
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This paper introduces a deterministic fluid model that approximates the manyserver Gt/GI/st + GI queueing model, and determines the timedependent performance functions. The fluid model has timevarying arrival rate and service capacity, abandonment from queue, and nonexponential service and patience distributions. Two key assumptions are that: (i) the system alternates between overloaded and underloaded intervals, and (ii) the functions specifying the fluid model are suitably smooth. An algorithm is developed to calculate all performance functions. It involves the iterative solution of a fixedpoint equation for the timevarying rate that fluid enters service and the solution of an ordinary differential equation for the timevarying headofline waiting time, during each overloaded interval. Simulations are conducted to confirm that the algorithm and the approximation are effective.
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, 2007
"... In this paper, we studied multiserver queue with Poisson arrivals, general service time distribution, and deterministic reneging times. This work was motivated by the timeout mechanism used in managing application servers in transaction processing environments. In such systems, a customer who stays ..."
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In this paper, we studied multiserver queue with Poisson arrivals, general service time distribution, and deterministic reneging times. This work was motivated by the timeout mechanism used in managing application servers in transaction processing environments. In such systems, a customer who stays in the queue longer than the timeout period is lost. We proposed a scaling approach, and a fast and accurate approximation for the expected waiting time in the queue.
MULTISERVER QUEUEING SYSTEMS WITH RETRIALS AND LOSSES
, 2006
"... Abstract. The paper studies multiserver retrial queueing systems with n servers. Arrival process is a quite general point process. An arriving customer occupies one of free servers. If upon arrival all servers are busy, then the customer waits for his service in orbit, and after random time retries ..."
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Abstract. The paper studies multiserver retrial queueing systems with n servers. Arrival process is a quite general point process. An arriving customer occupies one of free servers. If upon arrival all servers are busy, then the customer waits for his service in orbit, and after random time retries more and more to occupy a server. The orbit has one waiting space only, and arriving customer, who finds all servers busy and the waiting space occupied, losses from the system. Time intervals between possible retrials are assumed to have arbitrary distribution (the retrial scheme is exactly explained in the paper). The paper provides analysis of this system. Specifically the paper studies optimal number of servers to decrease the loss proportion to a given value. The representation obtained for loss proportion enables us to solve the problem numerically. The algorithm for numerical solution includes effective simulation, which meets the challenge of rare events problem in simulation. Contents