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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].
Statistical Analysis of a Telephone Call Center: A Queueing Science Perspective
, 2004
"... A call center is a service network in which agents provide telephonebased services. Customers that seek these services are delayed in telequeues. This paper 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 242 (37 self)
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A call center is a service network in which agents provide telephonebased services. Customers that seek these services are delayed in telequeues. This paper 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.
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.
Scheduling control for queueing systems with many servers: Asymptotic optimality in heavy traffic
, 2005
"... A multiclass queueing system is considered, with heterogeneous service stations, each consisting of many servers with identical capabilities. An optimal control problem is formulated, where the control corresponds to scheduling and routing, and the cost is a cumulative discounted functional of the s ..."
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Cited by 43 (6 self)
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A multiclass queueing system is considered, with heterogeneous service stations, each consisting of many servers with identical capabilities. An optimal control problem is formulated, where the control corresponds to scheduling and routing, and the cost is a cumulative discounted functional of the system’s state. We examine two versions of the problem: “nonpreemptive,” where service is uninterruptible, and “preemptive, ” where service to a customer can be interrupted and then resumed, possibly at a different station. We study the problem in the asymptotic heavy traffic regime proposed by Halfin and Whitt, in which the arrival rates and the number of servers at each station grow without bound. The two versions of the problem are not, in general, asymptotically equivalent in this regime, with the preemptive version showing an asymptotic behavior that is, in a sense, much simpler. Under appropriate assumptions on the structure of the system we show: (i) The value function for the preemptive problem converges to V, the value of a related diffusion control problem. (ii) The two versions of the problem are asymptotically equivalent, and in particular nonpreemptive policies can be constructed that asymptotically achieve the value V. The construction of these policies is based on a Hamilton–Jacobi–Bellman equation associated with V.
Dynamic scheduling of a multiclass queue in the HalfinWhitt heavy traffic regime
, 2003
"... We consider a Markovian model of a multiclass queueing system in which a single large pool of servers attends to the various customer classes. Customers waiting to be served may abandon the queue, and there is a cost penalty associated with such abandonments. Service rates, abandonment rates and aba ..."
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Cited by 41 (5 self)
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We consider a Markovian model of a multiclass queueing system in which a single large pool of servers attends to the various customer classes. Customers waiting to be served may abandon the queue, and there is a cost penalty associated with such abandonments. Service rates, abandonment rates and abandonment penalties are generally different for the different classes. The problem studied is that of dynamically scheduling the various classes. We consider the HalfinWhitt heavy traffic regime, where the total arrival rate and the number of servers both become large in such a way that the system’s traffic intensity parameter approaches one. An approximating diffusion control problem is described and justified as a purely formal (i.e., non rigorous) heavy traffic limit. The HamiltonJacobiBellman equation associated with the limiting diffusion control problem is shown to have a smooth (classical) solution, and optimal controls are shown to have an extremal or “bangbang ” character. Several useful qualitative insights are derived from the mathematical analysis, including a “square root rule ” for sizing large systems and a sharp contrast between system behavior in the HalfinWhitt regime versus that observed in the “conventional ” heavy traffic regime. The latter phenomenon is illustrated by means of a numerical example having two customer classes.
Scheduling flexible servers with convex delay costs in manyserver service systems
 MANUFACTURING AND SERVICE OPERATIONS MANAGEMENT. FORTHCOMING
, 2007
"... In a recent paper we introduced the queueandidlenessratio (QIR) family of routing rules for manyserver service systems with multiple customer classes and server pools. A newly available server next serves the customer from the head of the queue of the class (from among those he is eligible to se ..."
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Cited by 34 (19 self)
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In a recent paper we introduced the queueandidlenessratio (QIR) family of routing rules for manyserver service systems with multiple customer classes and server pools. A newly available server next serves the customer from the head of the queue of the class (from among those he is eligible to serve) whose queue length most exceeds a specified proportion of the total queue length. Under fairly general conditions, QIR produces an important statespace collapse as the total arrival rate and the numbers of servers increase in a coordinated way. That statespace collapse was previously used to delicately balance service levels for the different customer classes. In this sequel, we show that a special version of QIR stochastically minimizes convex holding costs in a finitehorizon setting when the service rates are restricted to be pooldependent. Under additional regularity conditions, the special version of QIR reduces to a simple policy: Linear costs produce a prioritytype rule, in which the leastcost customers are given low priority. Strictly convex costs (plus other regularity conditions) produce a manyserver analogue of the generalizedcµ (Gcµ) rule, under which a newly available server selects a customer from the class experiencing the greatest marginal cost at that time.
Pricing and design of differentiated services: Approximate analysis and structural insights
 Operations Research
, 2005
"... We consider a Markovian service system that offers two grades of service to a market of heterogenous users: a “guaranteed ” (G) service rate to high priority users, and “besteffort” (BE) type service, in which residual capacity not allocated to Gusers is shared by the low priority users. Users, in ..."
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Cited by 28 (5 self)
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We consider a Markovian service system that offers two grades of service to a market of heterogenous users: a “guaranteed ” (G) service rate to high priority users, and “besteffort” (BE) type service, in which residual capacity not allocated to Gusers is shared by the low priority users. Users, in turn, are sensitive to both price and congestionrelated effects. The service provider’s objective is to optimally design the system so as to extract maximum revenues. This design problem consists of optimally pricing the two service classes, and determining the mechanism by which users are informed of the state of congestion in the system. Since these objectives are difficult to address using exact analysis, we pursue approximations that are tractable and lead to structural insights. Specifically, we first solve a deterministic problem to obtain a “fluidoptimal ” solution which is subsequently evaluated and refined to account for stochastic fluctuations. Using diffusion limits, we derive large capacity approximations that yield the following structural results: (i) pricing rules derived from the deterministic analysis are “almost” optimal; (ii) the optimal operational regime for the system is close to heavytraffic, and; (iii) realtime congestion notification results in increased revenues. Numerical results illustrate the accuracy of the proposed approximations and validate the aforementioned structural insights.
Dynamic Control of NSystems with Many Servers: Asymptotic Optimality of a Static Priority Policy in Heavy Traffic
, 2010
"... ..."
Fair dynamic routing in largescale heterogeneousserver systems
, 2008
"... In a call center, there is a natural tradeoff between minimizing customer wait time and fairly dividing the workload amongst agents of different skill levels. The relevant control is the routing policy; that is, the decision concerning which agent should handle an arriving call when more than one a ..."
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Cited by 24 (5 self)
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In a call center, there is a natural tradeoff between minimizing customer wait time and fairly dividing the workload amongst agents of different skill levels. The relevant control is the routing policy; that is, the decision concerning which agent should handle an arriving call when more than one agent is available. We formulate an optimization problem for a call center with two heterogeneous agent pools, one that handles calls at a faster speed than the other, and a single customer class. The objective is to minimize steadystate expected customer wait time subject to a “fairness” constraint on the workload division. The optimization problem we formulate is difficult to solve exactly. Therefore, we solve the diffusion control problem that arises in the manyserver heavytraffic QED limiting regime. The resulting routing policy is a threshold policy that prioritizes faster agents when the number of customers in the system exceeds some threshold level and otherwise prioritizes slower agents. We prove our proposed threshold routing policy is nearoptimal as the number of agents increases, and the system’s load approaches its maximum processing capacity. We further show simulation results that evidence that our proposed threshold routing policy outperforms a common routing policy used in call centers (that routes to the agent that has been idle the longest) in terms of the steadystate expected customer waiting time for identical desired workload divisions.
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,