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The Modern Call Center: A MultiDisciplinary Perspective on Operations Management Research
"... Call centers are an increasingly important part of today’s business world, employing millions of agents across the globe and serving as a primary customerfacing channel for firms in many different industries. Call centers have been a fertile area for operations management researchers in several dom ..."
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Call centers are an increasingly important part of today’s business world, employing millions of agents across the globe and serving as a primary customerfacing channel for firms in many different industries. Call centers have been a fertile area for operations management researchers in several domains, including forecasting, capacity planning, queueing, and personnel scheduling. In addition, as telecommunications and information technology have advanced over the past several years, the operational challenges faced by call center managers have become more complicated. Issues associated with human resources management, sales, and marketing have also become increasingly relevant to call center operations and associated academic research. In this paper, we provide a survey of the recent literature on call center operations management. Along with traditional research areas, we pay special attention to new management challenges that have been caused by emerging technologies, to behavioral issues associated with both call center agents and customers, and to the interface between call center operations and sales and marketing. We identify a handful of broad themes for future investigation while also pointing out several very specific research opportunities.
Steadystate analysis of a multiserver queue in the HalfinWhitt regime
, 2008
"... We examine a multiserver queue in the HalfinWhitt (Quality and EfficiencyDriven) regime: as the number of servers n increases, the utilization approaches 1 from below at the rate Θ(1 / √ n). The arrival process is renewal and service times have a latticevalued distribution with a finite suppor ..."
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We examine a multiserver queue in the HalfinWhitt (Quality and EfficiencyDriven) regime: as the number of servers n increases, the utilization approaches 1 from below at the rate Θ(1 / √ n). The arrival process is renewal and service times have a latticevalued distribution with a finite support. We consider the steadystate distribution of the queue length and waiting time in the limit as the number of servers n increases indefinitely. The queue length distribution, in the limit as n → ∞, is characterized in terms of the stationary distribution of an explicitly constructed Markov chain. As a consequence, the steadystate queue length and waiting time scale as Θ ( √ n) and Θ(1 / √ n) as n → ∞, respectively. Moreover, an explicit expression for the critical exponent is derived for the moment generating function of a limiting (scaled) steadystate queue length. This exponent depends on three parameters: the amount of spare capacity and the coefficients of variation of interarrival and service times. Interestingly, it matches an analogous exponent corresponding to a singleserver queue in the conventional heavytraffic regime. The results are derived by analyzing Lyapunov functions.
SPDE limits of manyserver queues
, 2010
"... Abstract. A manyserver queueing system is considered in which customers with independent and identically distributed service times enter service in the order of arrival. The state of the system is represented by a process that describes the total number of customers in the system, as well as a meas ..."
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Abstract. A manyserver queueing system is considered in which customers with independent and identically distributed service times enter service in the order of arrival. The state of the system is represented by a process that describes the total number of customers in the system, as well as a measurevalued process that keeps track of the ages of customers in service, leading to a Markovian description of the dynamics. Under suitable assumptions, a functional central limit theorem is established for the sequence of (centered and scaled) state processes as the number of servers goes to infinity. The limit process describing the total number in system is shown to be an Itô diffusion with a constant diffusion coefficient that is insensitive to the service distribution. The limit of the sequence of (centered and scaled) age processes is shown to be a Hilbert space valued diffusion that can also be characterized as the unique solution of a stochastic partial differential equation that is coupled with the Itô diffusion. Furthermore, the limit processes are
The G/GI/N queue in the HalfinWhitt regime I: infinite server queue system equations. Annals of Applied Probability
, 2007
"... In this paper, we study the G/GI/N queue in the HalfinWhitt regime. Our first result is to obtain a deterministic fluid limit for the properly centered and scaled number of customers in the system which may be used to provide a first order approximation to the queue length process. Our second resul ..."
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In this paper, we study the G/GI/N queue in the HalfinWhitt regime. Our first result is to obtain a deterministic fluid limit for the properly centered and scaled number of customers in the system which may be used to provide a first order approximation to the queue length process. Our second result is to obtain a second order stochastic approximation to the number customers in the system in the HalfinWhitt regime. This is accomplished by first centering the queue length process by its deterministic fluid limit and then normalizing by an appropriate factor. We then proceed to obtain an alternative but equivalent characterization of our limiting approximation which involves the renewal function associated with the service time distribution. This alternative characterization reduces to the diffusion process obtained by Halfin and Whitt [6] in the case of exponentially distributed service times. AMS 2000 Subject Classification60G15,60G44,60K25
Fluid models of manyserver queues with abandonment
, 2011
"... We study manyserver queues with abandonment in which customers have general service and patience time distributions. The dynamics of the system are modeled using measurevalued processes, to keep track of the residual service and patience times of each customer. Deterministic fluid models are establ ..."
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Cited by 8 (2 self)
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We study manyserver queues with abandonment in which customers have general service and patience time distributions. The dynamics of the system are modeled using measurevalued processes, to keep track of the residual service and patience times of each customer. Deterministic fluid models are established to provide firstorder approximation for this model. The fluid model solution, which is proved to uniquely exists, serves as the fluid limit of the manyserver queue, as the number of servers becomes large. Based on the fluid model solution, firstorder approximations for various performance quantities are proposed. Key words and phrases: manyserver queue, abandonment, measure valued process, quality driven, efficiency driven, quality and efficiency driven. 1
BRAVO for manyserver QED systems with finite buffers
, 2013
"... This paper demonstrates the occurrence of the feature called BRAVO (Balancing Reduces Asymptotic Variance of Output) for the departure process of a finitebuffer Markovian manyserver system in the QED (Quality and EfficiencyDriven) heavytraffic regime. The results are based on evaluating the limi ..."
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Cited by 3 (1 self)
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This paper demonstrates the occurrence of the feature called BRAVO (Balancing Reduces Asymptotic Variance of Output) for the departure process of a finitebuffer Markovian manyserver system in the QED (Quality and EfficiencyDriven) heavytraffic regime. The results are based on evaluating the limit of a formula for the asymptotic variance of death counts in finite birth–death processes. 1
Transient behavior of the HalfinWhitt diffusion
, 2008
"... Abstract: We consider the heavytraffic approximation to the GI/M/s queueing system in the HalfinWhitt regime, where both the number of servers s and the arrival rate λ grow large (taking the service rate as unity), with λ = s − β√s and β some constant. In this asymptotic regime, the queue length p ..."
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Abstract: We consider the heavytraffic approximation to the GI/M/s queueing system in the HalfinWhitt regime, where both the number of servers s and the arrival rate λ grow large (taking the service rate as unity), with λ = s − β√s and β some constant. In this asymptotic regime, the queue length process can be approximated by a diffusion process that behaves like a Brownian motion with drift above zero and like an OrnsteinUhlenbeck process below zero. We analyze the transient behavior of this hybrid diffusion process, including the transient density, approach to equilibrium, and spectral properties. The transient behavior is shown to depend on whether β is smaller or larger than the critical value β ∗ ≈ 1.85722, which confirms the recent result of Gamarnik and Goldberg [9].
Y (2012) A fair policy for the G/GI/N queue with multiple server pools. Working paper
"... We consider the G/GI/N queue with multiple server pools, each possessing a poolspecific service time distribution. The class of nonidling routing policies which we consider are referred to as ugreedy policies. These policies route incoming customers to the server pool with the longest weighted cu ..."
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We consider the G/GI/N queue with multiple server pools, each possessing a poolspecific service time distribution. The class of nonidling routing policies which we consider are referred to as ugreedy policies. These policies route incoming customers to the server pool with the longest weighted cumulative idle time in order to equitably spread incoming work amongst the server pools in the system. Our first set of results demonstrate that asymptotically in the HalfinWhitt regime and under any ugreedy policy, the diffusion scaled cumulative idle time processes of each of the server pools are held in fixed proportion to one another. We next provide a heavy traffic limit theorem for the process keeping track of the total number of customers in the system. Our limit may be characterized as the solution to a stochastic convolution equation which is driven by a Gaussian process. In order to prove our main results, we introduce a new methodology for studying the G/GI/N queue in the HalfinWhitt regime which has as its starting point a simple conservation of flow identity.
and
, 2008
"... We establish a heavytraffic limit theorem on convergence in distribution for the number of customers in a manyserver queue. 1 ..."
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We establish a heavytraffic limit theorem on convergence in distribution for the number of customers in a manyserver queue. 1