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13
Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling
 QUEUEING SYSTEMS
, 1993
"... We present an introductory review of recent work on the control of open queueing networks. We assume that customers ofdifferent types arrive at a network and pass through the system via one of several possible routes; the set of routes available to a customer depends on its type. A route through th ..."
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Cited by 63 (5 self)
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We present an introductory review of recent work on the control of open queueing networks. We assume that customers ofdifferent types arrive at a network and pass through the system via one of several possible routes; the set of routes available to a customer depends on its type. A route through the network is an ordered set of service stations: a customer queues for service at each station on its route and then leaves the system. The two methods of control we consider are the routing of customers through the network, and the sequencing of service at the stations, and our aim is to minimize the number of customers in the system. We concentrate especially on the insights which can be obtained from heavy traffic analysis, and in particular from Harrison's Brownian etwork models. Our main conclusion is that in many respects dynamic routing simplifies the behaviour of networks, and that under good control policies itmay well be possible to model the aggregate b haviour of a network quite straightforwardly.
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.
Dynamic Scheduling of a TwoClass Queue with Setups
, 1994
"... We analyze two scheduling problems for a queueing system with a single server and two customer classes. Each class has its own renewal arrival process, general service time distribution, and holding cost rate. In the first problem, a setup cost is incurred when the server switches from one class to ..."
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Cited by 36 (3 self)
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We analyze two scheduling problems for a queueing system with a single server and two customer classes. Each class has its own renewal arrival process, general service time distribution, and holding cost rate. In the first problem, a setup cost is incurred when the server switches from one class to the other, and the objective is to minimize the longrun expected average cost of holding customers and incurring setups. The setup cost is replaced by a setup time in the second problem, where the objective is to minimize the average holding cost. By assuming that a recently derived heavy traffic principle holds not only for the exhaustive policy but for nonexhaustive policies, we approximate (under standard heavy traffic conditions) the dynamic scheduling problems by diffusion control problems. The diffusion control problem for the setup cost problem is solved exactly, and asymptotics are used to analyze the corresponding setup time problem. Computational results show that the proposed scheduling policies are within several percent of optimal over a broad range of problem parameters. We consider two dynamic scheduling problems for a singleserver queueing system with two classes of customers. In both problems, each class possesses its own renewal arrival process, general service time distribution, and holding cost rate, and the server incurs a setup when switching from one class to the other. In the setup cost
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.
Critical Thresholds for Dynamic Routing in Queueing Networks
, 2002
"... This paper studies dynamic routing in a parallel server queueing network with a single Poisson arrival process and two servers with exponential processing times of different rates. Each customer must be routed at the time of arrival to one of the two queues in the network. We establish that this sys ..."
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Cited by 15 (1 self)
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This paper studies dynamic routing in a parallel server queueing network with a single Poisson arrival process and two servers with exponential processing times of different rates. Each customer must be routed at the time of arrival to one of the two queues in the network. We establish that this system operating under a threshold policy can be well approximated by a onedimensional reflected Brownian motion when the arrival rate to the network is close to the processing capacity of the two servers. As the heavy traffic limit is approached, thresholds which grow at a logarithmic rate are critical in determining the behavior of the limiting system. We provide necessary and sufficient conditions on the growth rate of the threshold for (i) approximation of the network by a reflected Brownian motion (ii) positive recurrence of the limiting Brownian diffusion and (iii) asymptotic optimality of the threshold policy.
Routing and staffing in largescale service systems: The case of homogeneous impatient customers and heterogeneous servers
, 2011
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Optimal dynamic remapping of parallel computations
 IEEE TRANSACTIONS ON COMPUTERS
, 1990
"... A large class of computations are characterized by a sequence of phases, with phase changes occurring unpredictably. We consider the decision problem regarding the remapping of workload to processors in a parallel computation when (i) Ihe uiility of remapping md the future behavior of the workload i ..."
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Cited by 6 (1 self)
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A large class of computations are characterized by a sequence of phases, with phase changes occurring unpredictably. We consider the decision problem regarding the remapping of workload to processors in a parallel computation when (i) Ihe uiility of remapping md the future behavior of the workload is uncertain, and (ii) phases exhibit stable execution requirements during a given phase, but requirements may change radically between phases. For these problems a workload assignment generated for one phase may hinder performance during the next phase. This problem is treated formally for a probabilistic model of computation with at most two phases. We address the fundamental problem of balancing the expected remapping performance gain against the delay cost. Stochastic dynamic programming is used to show that the remapping decision policy minimizing the expected running time of the computation has an extremely simple structure: the optimal decision at any decision step is followed by comparing the probability of remapping gain against a threshold. However, threshold calculation requires a priori estimation of the performance gain achieved by remap ping. Because this gain may not be predictable, we examine the performance of a heuristic policy that does not require estimation of the gain. In most cases we find nearly optimal performance if remapping
A Method For Computing Double Band Policies For Switching Between Two Diffusions
, 1996
"... : We develop a method for computing the optimal double band [b; B] policy for switching between two diffusions with continuous rewards and switching costs. The two switch levels [b; B] are obtained as perturbations of the single optimal switching point a of the control problem with no switching cos ..."
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: We develop a method for computing the optimal double band [b; B] policy for switching between two diffusions with continuous rewards and switching costs. The two switch levels [b; B] are obtained as perturbations of the single optimal switching point a of the control problem with no switching costs. More precisely, we find that in the case of average reward problems the optimal switch levels can be obtained by intersecting two curves: a) the function, fl(a), which represents the long run average reward if we were to switch between the two diffusions at a and switches were free and b) an horizontal line whose height depends on the size of the transaction costs. Our semianalytical approach reduces, for example, the solution of a problem recently posed by Perry and BarLev [20] to the solution of one nonlinear equation. A Method for Computing Double Band Policies for Switching Between Two Diffusions Florin Avram 1 Fikri Karaesmen 2 1 Department of Mathematics, Northeastern Uni...
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol 44, No.,. SEPTEMBER 1984 Convexity and Characterization of Optimal Policies in a Dynamic Routing Problem'
"... Abstract. An infinite horizon, expected average cost, dynamic routing problem is formulated for a simple failureprone queueing system, modelled as a continuous tithe, continuous state controlled stochastic process. We prove that the optimal average cost is independent of the initial state and that ..."
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Abstract. An infinite horizon, expected average cost, dynamic routing problem is formulated for a simple failureprone queueing system, modelled as a continuous tithe, continuous state controlled stochastic process. We prove that the optimal average cost is independent of the initial state and that the costtogo functions of dynamic programming are convex. These results, together with a set of optimality conditions, lead to the conclusion that optimal 'olicies are switching policies, characterized by a set of switching curves (or regions), each curve corresponding to a particular state of the nodes (servers). Key Words. Stochastic control, unreliable queueing systems, average cost, jump disturbances. 1.