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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 123 (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.
Dynamic Scheduling of a TwoClass Queue with Setups
, 1994
"... We analyze two scheduling problems for a queueing system with a single server and two customer classes. Each class has its own renewal arrival process, general service time distribution, and holding cost rate. In the first problem, a setup cost is incurred when the server switches from one class to ..."
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Cited by 28 (2 self)
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We analyze two scheduling problems for a queueing system with a single server and two customer classes. Each class has its own renewal arrival process, general service time distribution, and holding cost rate. In the first problem, a setup cost is incurred when the server switches from one class to the other, and the objective is to minimize the longrun expected average cost of holding customers and incurring setups. The setup cost is replaced by a setup time in the second problem, where the objective is to minimize the average holding cost. By assuming that a recently derived heavy traffic principle holds not only for the exhaustive policy but for nonexhaustive policies, we approximate (under standard heavy traffic conditions) the dynamic scheduling problems by diffusion control problems. The diffusion control problem for the setup cost problem is solved exactly, and asymptotics are used to analyze the corresponding setup time problem. Computational results show that the proposed scheduling policies are within several percent of optimal over a broad range of problem parameters. We consider two dynamic scheduling problems for a singleserver queueing system with two classes of customers. In both problems, each class possesses its own renewal arrival process, general service time distribution, and holding cost rate, and the server incurs a setup when switching from one class to the other. In the setup cost
On pooling in queueing networks
 Management Sci
, 1998
"... We view each station in a Jackson network as a queue of tasks, of a particular type, which are to be processed by the associated specialized server. A complete pooling of queues, into a single queue, and servers, into a single server, gives rise to an M/PH/1 queue, where the server is flexible in th ..."
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Cited by 24 (0 self)
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We view each station in a Jackson network as a queue of tasks, of a particular type, which are to be processed by the associated specialized server. A complete pooling of queues, into a single queue, and servers, into a single server, gives rise to an M/PH/1 queue, where the server is flexible in the sense that it processes all tasks. We assess the value of complete pooling by comparing the steadystate mean sojourn times of these two systems. The main insight from our analysis is that care must be used in pooling. Sometimes pooling helps, sometimes it hurts, and its effect (good or bad) can be unbounded. Also discussed briefly are alternative pooling scenarios, for example complete pooling of only queues which results in an M/PH/S system, or partial pooling which can be devastating enough to turn a stable Jackson network into an unstable Bramson network. We conclude with some possible future research directions.
DEPARTURES FROM A QUEUE WITH MANY BUSY SERVERS
, 1984
"... To analyze networks of queues, it is important to be able to analyze departure processes from single queues. For the Mf M/s and M/G/«i models, the stationary departure process is simple (Poisson), but in general the stationary departure process is quite complicated. As a basis for approximations, th ..."
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Cited by 8 (6 self)
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To analyze networks of queues, it is important to be able to analyze departure processes from single queues. For the Mf M/s and M/G/«i models, the stationary departure process is simple (Poisson), but in general the stationary departure process is quite complicated. As a basis for approximations, this paper shows that the stationary departure process is approximately Poisson when there are many busy slow servers in a large class of stationary G/GI/s congestion models having.; servers, infinite waiting room, the firstcome firstserved discipline, and mutually independent and identically distributed service times that are independent of a stationary arrival process. Limit theorems are proved for the departure process in a G/GI/s system in which the number of servers and the offered load (arrival rate divided by the service rate) both increase. The asymptotic behavior of the departure process depends on the way the arrival rate changes. If the arrival rate is held fixed, so that the offered load increases by slowing down the service rate, then the departure process converges to a Poisson process. For this result, the servicetime distribution is assumed to be phasetype. Other limiting behavior occurs if the arrival rate approaches zero or infinity. Convergence is established in each case by applying previous heavytraffic limit theorems.
Models and algorithms for transient queueing congestion at airports. Management Science 41:12791295
 Ph.D. dissertation, Sloan School of Management, Massacusetts Institute of Technology
, 1995
"... This paper studies the relationship between the hubandspoke design in air transportation and the phenomenon of landing congestion in a transient environment. We model the weather, the principal source of uncertainty, as a Markov or semiMarkov process, and we treat arrivals as timevarying but de ..."
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Cited by 2 (1 self)
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This paper studies the relationship between the hubandspoke design in air transportation and the phenomenon of landing congestion in a transient environment. We model the weather, the principal source of uncertainty, as a Markov or semiMarkov process, and we treat arrivals as timevarying but deterministic. We develop a recursive algorithm for predicting transient queueing delays. To test our model, we conduct a case study using traffic and capacity data for DallasFort Worth International Airport. Our results show that the model's estimates are reasonable, though substantial data difficulties make thorough validation difficult. We explore in depth two policy questions: schedule interference between the two principal carriers, and the likely effects of demand smoothing policies on queueing delays. 1
VarD(t)
"... ABSTRACT. We consider the asymptotic variance of the departure counting process D(t) of the GI/G/1 queue; D(t) denotes the number of departures up to time t. We focus on the case that the system load ϱ equals 1, and prove that the asymptotic variance rate satisfies lim t→∞ ..."
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ABSTRACT. We consider the asymptotic variance of the departure counting process D(t) of the GI/G/1 queue; D(t) denotes the number of departures up to time t. We focus on the case that the system load ϱ equals 1, and prove that the asymptotic variance rate satisfies lim t→∞