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114
Performance Evaluation and Policy Selection in Multiclass Networks
, 2002
"... This paper concerns modelling and policy synthesis for regulation of multiclass queueing networks. A 2parameter network model is introduced to allow independent modelling of variability and mean processingrates, while maintaining simplicity of the model. Policy synthesis is based on consideration ..."
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Cited by 46 (26 self)
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This paper concerns modelling and policy synthesis for regulation of multiclass queueing networks. A 2parameter network model is introduced to allow independent modelling of variability and mean processingrates, while maintaining simplicity of the model. Policy synthesis is based on consideration of more tractable workload models, and then translating a policy from this abstraction to the discrete network of interest. Translation is made possible through the use of safetystocks that maintain feasibility of workload trajectories. This is a wellknown approach in the queueing theory literature, and may be viewed as a generic approach to avoid deadlock in a discreteevent dynamical system. Simulation is used to evaluate a given policy, and to tune safetystock levels. These simulations are accelerated through a variance reduction technique that incorporates stochastic approximation to tune the variance reduction. The search for appropriate safetystock levels is coordinated through a cutting plane algorithm. Both the policy synthesis and the simulation acceleration rely heavily on the development of approximations to the value function through fluid model considerations.
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.
Asymptotic optimality of maximum pressure policies in stochastic processing networks
 Annals of Applied Probability
, 2008
"... We consider a class of stochastic processing networks. Assume that the networks satisfy a complete resource pooling condition. We prove that each maximum pressure policy asymptotically minimizes the workload process in a stochastic processing network in heavy traffic. We also show that, under each q ..."
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Cited by 43 (4 self)
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We consider a class of stochastic processing networks. Assume that the networks satisfy a complete resource pooling condition. We prove that each maximum pressure policy asymptotically minimizes the workload process in a stochastic processing network in heavy traffic. We also show that, under each quadratic holding cost structure, there is a maximum pressure policy that asymptotically minimizes the holding cost. A key to the optimality proofs is to prove a state space collapse result and a heavy traffic limit theorem for the network processes under a maximum pressure policy. We extend a framework of Bramson [Queueing Systems Theory Appl. 30 (1998) 89–148] and Williams [Queueing Systems Theory Appl. 30 (1998b) 5–25] from the multiclass queueing network setting to the stochastic processing network setting to prove the state space collapse result and the heavy traffic limit theorem. The extension can be adapted to other studies of stochastic processing networks.
Scheduling a multiclass queue with many exponential servers: Asymptotic optimality in heavytraffic
 THE ANNALS OF APPLIED PROBABILITY
, 2004
"... We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal. Our cost is an expected cumulative discounted function, line ..."
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Cited by 42 (14 self)
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We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal. Our cost is an expected cumulative discounted function, linear or nonlinear, of appropriately normalized performance measures. As a special case, the cost per unit time can be a function of the number of customers waiting to be served in each class, the number actually being served, the abandonment rate, the delay experienced by customers, the number of idling servers, as well as certain combinations thereof. We study the system in an asymptotic heavytraffic regime where the number of servers n and the offered load r are simultaneously scaled up and carefully balanced: n ≈ r + β √ r for some scalar β. This yields an operation that enjoys the benefits of both heavy traffic (high server utilization) and light traffic (high service levels.)
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.
Heavy traffic analysis of open processing networks with complete resource pooling: asymptotic optimality of discrete review policies
 ANN. APPL. PROBAB
, 2005
"... We consider a class of open stochastic processing networks, with feedback routing and overlapping server capabilities, in heavy traffic. The networks ..."
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Cited by 23 (0 self)
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We consider a class of open stochastic processing networks, with feedback routing and overlapping server capabilities, in heavy traffic. The networks
Analysis of multiserver systems via dimensionality reduction of Markov chains
 School of Computer Science, Carnegie Mellon University
, 2005
"... The performance analysis of multiserver systems is notoriously hard, especially when the system involves resource sharing or prioritization. We provide two new analytical tools for the performance analysis of multiserver systems: moment matching algorithms and dimensionality reduction of Markov chai ..."
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Cited by 22 (4 self)
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The performance analysis of multiserver systems is notoriously hard, especially when the system involves resource sharing or prioritization. We provide two new analytical tools for the performance analysis of multiserver systems: moment matching algorithms and dimensionality reduction of Markov chains (DR). Moment matching algorithms allow us to approximate a general distribution with a phase type (PH) distribution. Our moment matching algorithms improve upon existing ones with respect to the computational efficiency (we provide closed form solutions) as well as the quality and generality of the solution (the first three moments of almost any nonnegative distribution are matched). Approximating job size and interarrival time distributions by PH distributions enables modeling a multiserver system by a Markov chain, so that the performance of the system is given by analyzing the Markov chain. However, when the multiserver system involves resource sharing or prioritization, the Markov chain often has a multidimensionally infinite state space, which makes the analysis computationally hard. DR allows us to closely approximate a multidimensionally infinite Markov chain with a Markov
Telephone call centers: A tutorial and literature review
 Computer Access and Internet Use, (Working Paper at http:// www2000.ogsm.vanderbilt.edu/papers/race/science.html). Bridging the Racial Divide on the Internet, Science
, 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 19 (5 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 characterize 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.