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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 280 (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].
Dimensioning Large Call Centers
 OPERATIONS RESEARCH
, 2000
"... We develop a framework for asymptotic optimization of a queueing system. The motivation is the staffing problem of call centers with 100's of agents (or more). Such a call center is modeled as an M/M/N queue, where the number of agents N is large. Within our framework, we determine the asymptot ..."
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Cited by 108 (15 self)
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We develop a framework for asymptotic optimization of a queueing system. The motivation is the staffing problem of call centers with 100's of agents (or more). Such a call center is modeled as an M/M/N queue, where the number of agents N is large. Within our framework, we determine the asymptotically optimal staffing level N that trades off agents' costs with service quality: the higher the latter, the more expensive is the former. As an alternative to this optimization, we also develop a constraint satisfaction approach where one chooses the least N that adheres to a given constraint on waiting cost. Either way, the analysis gives rise to three regimes of operation: qualitydriven, where the focus is on service quality; efficiencydriven, which emphasizes agents' costs; and a rationalized regime that balances, and in fact unifies, the other two. Numerical experiments reveal remarkable accuracy of our asymptotic approximations: over a wide range of parameters, from the very small ...
On Customer Contact Centers with a CallBack Option: Customer Decisions, Routing Rules, and System Design
, 2004
"... Organizations worldwide use contact centers as an important channel of communication and transaction with their customers. This paper describes a contact center with two channels, one for realtime telephone service, and another for a postponed callback service offered with a guarantee on the maxim ..."
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Cited by 78 (13 self)
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Organizations worldwide use contact centers as an important channel of communication and transaction with their customers. This paper describes a contact center with two channels, one for realtime telephone service, and another for a postponed callback service offered with a guarantee on the maximum delay until a reply is received. Customers are sensitive to both realtime and callback delay and their behavior is captured through a probabilistic choice model. The dynamics of the system are modeled as an M/M/N multiclass system. We rigorously justify that as the number of agents increases, the system’s load approaches its maximum processing capacity. Based on this observation, we perform an asymptotic analysis in the manyserver, heavy traffic regime to find an asymptotically optimal routing rule, characterize the unique equilibrium regime of the system, approximate the system performance, and finally, propose a staffing rule that picks the minimum number of agents that satisfies a set of operational constraints on the performance of the system.
Efficiencydriven heavytraffic approximations for manyserver queues with abandonments
 Management Science
, 2004
"... Motivated by the desire to understand the performance of serviceoriented call centers, which often provide lowtomoderate quality of service, this paper investigates the efficiencydriven (ED) limiting regime for manyserver queues with abandonments. The starting point is the realization that, in ..."
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Cited by 74 (35 self)
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Motivated by the desire to understand the performance of serviceoriented call centers, which often provide lowtomoderate quality of service, this paper investigates the efficiencydriven (ED) limiting regime for manyserver queues with abandonments. The starting point is the realization that, in the presence of substantial customer abandonment, callcenter servicelevel agreements (SLA’s) can be met in the ED regime, where the arrival rate exceeds the maximum possible service rate. Mathematically, the ED regime is defined by letting the arrival rate and the number of servers increase together so that the probability of abandonment approaches a positive limit. To obtain the ED regime, it suffices to let the arrival rate and the number of servers increase with the traffic intensity ρ held fixed with ρ> 1 (so that the arrival rate exceeds the maximum possible service rate). Even though the probability of delay necessarily approaches 1 in the ED regime, the ED regime can be realistic because, due to the abandonments, the delays need not be excessively large. This paper establishes ED manyserver heavytraffic limits and develops associated approximations for performance measures in the M/M/s/r + M model, having a Poisson arrival process, exponential service times, s servers, r extra waiting spaces and exponential abandon times (the final +M). In the ED regime, essentially the same limiting behavior occurs when the abandonment rate α approaches 0 as when the number of servers s approaches ∞; indeed, it suffices to assume that s/α → ∞. The ED approximations are shown to be useful by comparing them to exact numerical results for the M/M/s/r + M model obtained using an algorithm developed in Whitt (2003), which exploits numerical transform inversion.
Martingale proofs of manyserver heavytraffic limits for Markovian queues
 PROBABILITY SURVEYS
, 2007
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A staffing algorithm for call centers with skillbased routing
 Manufacturing and Service Operations Management
, 2005
"... informs ® doi 10.1287/msom.1050.0086 © 2005 INFORMS Call centers usually handle several types of calls, butitis usually notpossible or costeffective to have every agent be able to handle every type of call. Thus, the agents tend to have different skills, in different combinations. In such an environ ..."
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Cited by 57 (7 self)
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informs ® doi 10.1287/msom.1050.0086 © 2005 INFORMS Call centers usually handle several types of calls, butitis usually notpossible or costeffective to have every agent be able to handle every type of call. Thus, the agents tend to have different skills, in different combinations. In such an environment, it is challenging to route calls effectively and determine the staff requirements. This paper addresses both of these routing and staffing problems by exploiting limited crosstraining. Consistent with the literature on flexible manufacturing, we find that minimal flexibility can provide great benefits: Simulation experiments show that when (1) the servicetime distribution does not depend on the call type or the agent and (2) each agent has only two skills, in appropriate combinations, the performance is almost as good as when each agent has all skills. We apply this flexibility property to develop an algorithm for both routing and staffing, aiming to minimize the total staff subject to perclass performance constraints. With appropriate flexibility, it suffices to use a suboptimal routing algorithm. Simulation experiments show that the overall procedure can be remarkably effective: The required staff with limited crosstraining can be nearly the same as if all agents had all skills. Hence, the overall algorithm is nearly optimal for that scenario.
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 51 (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 #.
HeavyTraffic Limits for the G/H ∗ 2 /n/m Queue
, 2005
"... We establish heavytraffic stochasticprocess limits for queuelength, waitingtime and overflow stochastic processes in a class of G/GI/n/m queueing models with n servers and m extra waiting spaces. We let the arrival process be general, only requiring that it satisfy a functional central limit the ..."
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Cited by 49 (12 self)
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We establish heavytraffic stochasticprocess limits for queuelength, waitingtime and overflow stochastic processes in a class of G/GI/n/m queueing models with n servers and m extra waiting spaces. We let the arrival process be general, only requiring that it satisfy a functional central limit theorem. To capture the impact of the servicetime distribution beyond its mean within a Markovian framework, we consider a special class of servicetime distributions, denoted by H ∗ 2, which are mixtures of an exponential distribution with probability p and a unit point mass at 0 with probability 1 − p. These servicetime distributions exhibit relatively high variability, having squared coefficients of variation greater than or equal to one. As in Halfin and Whitt (1981, Heavytraffic limits for queues with many exponential servers, Oper. Res. 29 567–588), Puhalskii and Reiman (2000, The multiclass GI/PH/N queue in the HalfinWhitt regime. Adv. Appl. Probab. 32 564–595), and Garnett, Mandelbaum, and Reiman (2002. Designing a call center with impatient customers. Manufacturing Service Oper. Management, 4 208–227), we consider a sequence of queueing models indexed by the number of servers, n, and let n tend to infinity along with the traffic intensities �n so that √ n�1 − �n � → � for − � <�<�. To treat finite waiting rooms, we let mn / √ n → � for 0 <�≤�. With the special H ∗ 2 servicetime distribution, the limit processes are
Engineering solution of a basic callcenter model
 Management Science
, 2005
"... An algorithm is developed to rapidly compute approximations for all the standard steadystate performance measures in the basic callcenter queueing modelM/GI/s/r+GI, which has a Poisson arrival process, IID service times with a general distribution, s servers, r extra waiting spaces and IID custom ..."
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Cited by 41 (25 self)
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An algorithm is developed to rapidly compute approximations for all the standard steadystate performance measures in the basic callcenter queueing modelM/GI/s/r+GI, which has a Poisson arrival process, IID service times with a general distribution, s servers, r extra waiting spaces and IID customer abandonment times with a general distribution. Empirical studies indicate that the servicetime and abandontime distributions often are not nearly exponential, so that it is important to go beyond the MarkovianM/M/s/r+M special case, but the general servicetime and abandontime distributions make the realistic model very difficult to analyze directly. The proposed algorithm is based on an approximation by an appropriate Markovian M/M/s/r+M(n) queueing model, where M(n) denotes statedependent abandonment rates. After making an additional approximation, steadystate waitingtime distributions are characterized via their Laplace transforms. Then the approximate distributions are computed by numerically inverting the transforms. Simulation experiments show that the approximation is quite accurate. The overall algorithm can be applied to determine desired staffing levels, e.g., the minimum number of servers needed to guarantee that, first, the abandonment rate is below any specified target value and, second, that the conditional probability that an arriving customer will be served within a specified deadline, given that the customer eventually will be served, is at least a specified target value.