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18
Martingale proofs of many-server heavy-traffic limits for Markovian queues
- PROBABILITY SURVEYS
, 2007
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The modern call-center: A multi-disciplinary 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 customer-facing channel for firms in many different industries. Call centers have been a fertile area for operations management researchers in several are ..."
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Cited by 62 (6 self)
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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 customer-facing channel for firms in many different industries. Call centers have been a fertile area for operations management researchers in several areas, 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 as a result. 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.
Fair dynamic routing in large-scale heterogeneous-server systems
, 2008
"... In a call center, there is a natural trade-off 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 trade-off 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 steady-state 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 many-server heavy-traffic 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 near-optimal 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 steady-state expected customer waiting time for identical desired workload divisions.
Queues with Many Servers: The Virtual Waiting-Time Process in the QED Regime
, 2007
"... We consider a multi-server queue (G/GI/N) in the Quality- and Efficiency-Driven (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) (Efficiency-Driven) while waiting time is O(1/ N) (Quality-Driven). ..."
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Cited by 24 (1 self)
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We consider a multi-server queue (G/GI/N) in the Quality- and Efficiency-Driven (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) (Efficiency-Driven) while waiting time is O(1/ N) (Quality-Driven). 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,
Value-based routing and preference-based routing in customer contact centers
- Production and Operations Management
, 2004
"... Telephone call centers and their generalizations- customer contact centers- usually handle sev-eral types of customer service requests (calls). Since customer service representatives (agents) have different call-handling abilities and are typically cross-trained in multiple skills, contact centers e ..."
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Cited by 14 (0 self)
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Telephone call centers and their generalizations- customer contact centers- usually handle sev-eral types of customer service requests (calls). Since customer service representatives (agents) have different call-handling abilities and are typically cross-trained in multiple skills, contact centers exploit skill-based routing (SBR) to assign calls to appropriate agents, aiming to re-spond properly as well as promptly. Established agent-staffing and SBR algorithms ensure that agents have the required call-handling skills and that call routing is performed so that constraints are met for standard congestion measures, such as the percentage of calls of each type that abandon before starting service and the percentage of answered calls of each type that are delayed more than a specified number of seconds. We propose going beyond tra-ditional congestion measures to focus on the expected value derived from having particular agents handle various calls. Expected value might represent expected revenue or the likelihood of first-call resolution. Value might also reflect agent call-handling preferences. We show how value-based routing (VBR) and preference-based routing (PBR) can be introduced in the con-text of an existing SBR framework, based on static-priority routing using a highly-structured
Steady-state analysis of a multi-server queue in the Halfin-Whitt regime
, 2008
"... We examine a multi-server queue in the Halfin-Whitt (Quality- and Efficiency-Driven) 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 lattice-valued distribution with a finite suppor ..."
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Cited by 14 (0 self)
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We examine a multi-server queue in the Halfin-Whitt (Quality- and Efficiency-Driven) 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 lattice-valued distribution with a finite support. We consider the steady-state 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 steady-state 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) steady-state 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 single-server queue in the conventional heavy-traffic regime. The results are derived by analyzing Lyapunov functions.
Cross-Selling in a Call Center with a Heterogeneous Customer Population
, 2006
"... This is the technical appendix accompanying the paper, “Cross-Selling in a Call Center with a Heterogeneous Customer Population, ” [3]. The organization of this appendix is as follows: we begin in §B with the completion of the proof of Proposition 1, whose sketch was given in §A of [3]. We continue ..."
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Cited by 11 (3 self)
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This is the technical appendix accompanying the paper, “Cross-Selling in a Call Center with a Heterogeneous Customer Population, ” [3]. The organization of this appendix is as follows: we begin in §B with the completion of the proof of Proposition 1, whose sketch was given in §A of [3]. We continue in §C with some preliminaries required for the performance analysis of (S)-(C).
Routing and staffing in large-scale service systems: The case of homogeneous impatient customers and heterogeneous servers
, 2011
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When promotions meet operations: Cross-selling and its effect on call-center performance
, 2006
"... We study cross-selling operations in call centers. The following question is addressed: How many customer service representatives are required (staffing) and when should cross-selling opportunities be exercised (control) in a way that will maximize the expected profit of the firm while maintaining a ..."
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Cited by 6 (3 self)
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We study cross-selling operations in call centers. The following question is addressed: How many customer service representatives are required (staffing) and when should cross-selling opportunities be exercised (control) in a way that will maximize the expected profit of the firm while maintaining a pre-specified service level target. We tackle these questions by characterizing scheduling and staffing schemes that are asymptotically optimal in the limit, as the system load grows to infinity. Our main finding is that a threshold priority (TP) control, in which cross-selling is exercised only if the number of callers in the system is below a certain threshold, is asymptotically optimal in great generality. The asymptotic optimality of TP reduces the staffing problem to the solution of a simple deterministic problem, in some cases, and to a simple search procedure in others. Our asymptotic approach establishes that our staffing and control scheme is near-optimal for large systems. In addition, we numerically demonstrate that TP performs extremely well even for relatively small systems.
State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems
, 2006
"... We consider a class of queueing systems that consist of server pools in parallel and multiple customer classes. Customer service times are assumed to be exponentially distributed. We study the asymptotic behavior of these queueing systems in a heavy traffic regime that is known as the Halfin and Wh ..."
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Cited by 6 (3 self)
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We consider a class of queueing systems that consist of server pools in parallel and multiple customer classes. Customer service times are assumed to be exponentially distributed. We study the asymptotic behavior of these queueing systems in a heavy traffic regime that is known as the Halfin and Whitt many-server asymptotic regime. Our main contribution is a general framework for establishing state space collapse results in this regime for parallel server systems. In our work, state space collapse refers to a decrease in the dimension of the processes tracking the number of customers in each class waiting for service and the number of customers in each class being served by various server pools. We define and introduce a “state space collapse ” function, which governs the exact details of the state space collapse. We show that a state space collapse result holds in many-server heavy traffic if a corresponding deterministic hydrodynamic model satisfies a similar state space collapse condition. Our methodology is similar in spirit to that in Bramson [10], which focuses on the conventional heavy traffic regime. We illustrate the applications of our results by establishing state space collapse results in many-server diffusion limits of static-buffer-priority V-parallel server systems, N-model parallel server systems, and minimum-expected-delay–faster-server-first distributed server pools systems. We show for these systems that the condition on the hydrodynamic model can easily be checked using the standard tools for fluid models.
