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57
Performance Bounds for Queueing Networks and Scheduling Policies
, 1994
"... Except for the class of queueing networks and scheduling policies admitting a product form solution for the steadystate distribution, little is known about the performance of such systems. For example, if the priority of a part depends on its class (e.g., the buffer that the part is located in), t ..."
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Cited by 82 (16 self)
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Except for the class of queueing networks and scheduling policies admitting a product form solution for the steadystate distribution, little is known about the performance of such systems. For example, if the priority of a part depends on its class (e.g., the buffer that the part is located in), then there are no existing results on performance, or even stability. However, in most applications such as manufacturing systems, one has to choose a control or scheduling policy, i.e., a priority discipline, that optimizes a performance objective. In this paper we introduce a new technique for obtaining upper and lower bounds on the performance of Markovian queueing networks and scheduling policies. Assuming stability, and examining the consequence of a steadystate for general quadratic forms, we obtain a set of linear equality constraints on the mean values of certain random variables that determine the performance of the system. Further, the conservation of time and material gives an au...
Sequencing and routing in multiclass queueing networks part I: Feedback regulation
 SIAM J. Control Optim
"... Abstract. Part II continues the development of policy synthesis techniques for multiclass queueing networks based upon a linear fluid model. The following are shown: (i) A relaxation of the fluid model based on workload leads to an optimization problem of lower dimension. An analogous workloadrelax ..."
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Cited by 56 (12 self)
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Abstract. Part II continues the development of policy synthesis techniques for multiclass queueing networks based upon a linear fluid model. The following are shown: (i) A relaxation of the fluid model based on workload leads to an optimization problem of lower dimension. An analogous workloadrelaxation is introduced for the stochastic model. These relaxed control problems admit pointwise optimal solutions in many instances. (ii) A translation to the original fluid model is almost optimal, with vanishing relative error as the networkload ρ approaches one. It is pointwise optimal after a short transient period, provided a pointwise optimal solution exists for the relaxed control problem. (iii) A translation of the optimal policy for the fluid model provides a policy for the stochastic networkmodel that is almost optimal in heavy traffic, over all solutions to the relaxed stochastic model, again with vanishing relative error. The regret is of order  log(1 − ρ).
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.
Structural Results for the Control of Queueing Systems Using EventBased Dynamic Programming
, 1999
"... In this paper we study monotonicity results for optimal policies of various queueing and resource sharing models. The standard approach is to propagate, for each specific model, certain properties of the dynamic programming value function. By concentrating on the events and the properties instead ..."
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Cited by 44 (3 self)
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In this paper we study monotonicity results for optimal policies of various queueing and resource sharing models. The standard approach is to propagate, for each specific model, certain properties of the dynamic programming value function. By concentrating on the events and the properties instead of on the value function we propose a unified treatment of monotonicity results for Markovian models. This is illustrated with one and twodimensional models. 1 Introduction Monotonicity results for optimal policies for queuing models are usually derived in the following way. After having formulated the value function of a particular model, it is shown inductively that this value function satisfies certain properties, from which the results are derived. The first to apply this approach, to an admission control problem for a single queue, was Lippman [11]. He proved that the dynamic programming (dp) value function of his specific model is convex, from which it follows that the optimal pol...
A survey of Markov decision models for control of networks of queues
 QUEUEING SYSTEMS
, 1993
"... We review models for the optimal control of networks of queues, Our main emphasis on models based on Markov decision theory and the characterization f the structure of optimal control policies. ..."
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Cited by 28 (0 self)
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We review models for the optimal control of networks of queues, Our main emphasis on models based on Markov decision theory and the characterization f the structure of optimal control policies.
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.
Optimal statefree, sizeaware dispatching for heterogeneous M/G/type systems
 Performance Evaluation Journal
, 2005
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Managing response time in a callrouting problem with service failure
 Oper. Res
, 2005
"... Traditional research on routing in queueing systems usually ignores service quality related factors. In this paper, we analyze the routing problem in a system where customers call back when their problems are not completely resolved by the service customer representatives (CSRs). We introduce the ..."
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Cited by 17 (0 self)
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Traditional research on routing in queueing systems usually ignores service quality related factors. In this paper, we analyze the routing problem in a system where customers call back when their problems are not completely resolved by the service customer representatives (CSRs). We introduce the concept of call resolution probability, and we argue that it constitutes a good proxy for call quality. For each call, both the call resolution probability (p) and the average service time (1/µ) are CSR dependent. We use an MDP formulation to obtain analytical results and insights about the optimal routing policy that minimizes the average total time of call resolution including callbacks. In particular, we provide sufficient conditions under which it is optimal to route to the CSR with the highest call resolution rate (pµ) among those available. We also develop efficient heuristics that can be easily implemented in practice.
Bounding of Performance Measures for a Thresholdbased Queueing System with Hysteresis
 In Proceedings of 1997 ACM SIGMETRICS Conf
, 1997
"... In this paper, we consider a Kserver thresholdbased queueing system with hysteresis in which the number of servers, employed for servicing customers, is governed by a forward threshold vector F= (F1 ; F2 ; : : : ; FK \Gamma1 ) (where F1 ! F2 ! \Delta \Delta \Delta ! FK \Gamma1 ) and a reverse thre ..."
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Cited by 13 (3 self)
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In this paper, we consider a Kserver thresholdbased queueing system with hysteresis in which the number of servers, employed for servicing customers, is governed by a forward threshold vector F= (F1 ; F2 ; : : : ; FK \Gamma1 ) (where F1 ! F2 ! \Delta \Delta \Delta ! FK \Gamma1 ) and a reverse threshold vector R= (R1 ; R2 ; : : : ; RK \Gamma1 ) (where R1 !R2 ! \Delta \Delta \Delta ! RK \Gamma1 ). There are many applications where a thresholdbased queueing system can be of great use. The main motivation for using a thresholdbased approach in such applications is that they incur significant server setup, usage, and removal costs. And, as in most practical situations, an important concern is not only the system performance but rather its cost/performance ratio. The motivation for use of hysteresis is to control the cost during momentary fluctuations in workload. An important and distinguishing characteristic of our work is that in our model we consider the time to add a server to be non...
Optimal Control of Assignment of Jobs to Processors under Heavy Traffic
 Stochastics and Stochastic Reports
, 1999
"... The paper is concerned with the optimal control of the assignment of jobs from several arriving random streams to one of a bank of processors. Owing to the difficulty of the general problem, a heavy traffic approach is used. The required work depends on the processor to which it is assigned. The inf ..."
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Cited by 13 (3 self)
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The paper is concerned with the optimal control of the assignment of jobs from several arriving random streams to one of a bank of processors. Owing to the difficulty of the general problem, a heavy traffic approach is used. The required work depends on the processor to which it is assigned. The information that the assignment can be based on is quite flexible, and several information structures (data on which the control is based) are considered. The assignment can be made on arrival or when the job is to be processed. There can be bursty arrivals (the bursts depending on randomly varying environmental factors), rather general nonlinear cost functions and other complications. It is shown, under reasonably general conditions, that the optimal costs for the physical systems converge to the optimal cost for the heavy traffic limit problem, as the heavy traffic parameter goes to its limit. Numerical data is presented to illustrate some of the potential uses of the limit process for obtain...