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CYCLIC RESERVATION SCHEMES FOR EFFICIENT OPERATION OF MULTIPLEQUEUE SINGLESERVER SYSTEMS
 ANNALS OF OPERATIONS RESEARCH 35(1992)I87208 187
, 1992
"... We study two new cyclic reservation schemes for the efficient operation of systems consisting of a single server and multiple queues. The schemes are the Globally Gated regime and the CyclicReservation MultipleAccess (CRMA). Both procedures possess mechanisms for prioritizing the queues and lend t ..."
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Cited by 40 (11 self)
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We study two new cyclic reservation schemes for the efficient operation of systems consisting of a single server and multiple queues. The schemes are the Globally Gated regime and the CyclicReservation MultipleAccess (CRMA). Both procedures possess mechanisms for prioritizing the queues and lend themselves to a closedform analysis. The combination of these two properties allows for effective and efficient operation of the systems, for which we provide a thorough delay analysis and derive simple rules for optimal operation.
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
Optimality of index policies for stochastic scheduling with switching penalties
 J. Appl. Probab
, 1992
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 21 (9 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Heuristic Scheduling of Parallel Heterogeneous Queues with SetUps
 MANAGEMENT SCIENCE
, 1996
"... We consider the problem of allocating a single server to a system of queues with Poisson arrivals. Each queue represents a class of jobs and possesses a holding cost rate, general service distribution, and general setup time distribution. The objective is to minimize the expected holding cost due t ..."
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Cited by 20 (7 self)
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We consider the problem of allocating a single server to a system of queues with Poisson arrivals. Each queue represents a class of jobs and possesses a holding cost rate, general service distribution, and general setup time distribution. The objective is to minimize the expected holding cost due to the waiting of jobs. A setup time is required to switch from one queue to another. We provide a limited characterization of the optimal policy and a simple heuristic scheduling policy for this problem. Simulation results demonstrate the effectiveness of our heuristic over a wide range of problem instances.
Multiproduct systems with both setup times and costs: Fluid bounds and schedules
 Operations Research
, 2004
"... This paper considers a multiproduct, singleserver production system where both setup times and costs are incurred whenever the server changes product. The system is maketoorder with a per unit backlogging cost. The objective is to minimize the longrun average cost per unit time. Using a fluid m ..."
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Cited by 18 (0 self)
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This paper considers a multiproduct, singleserver production system where both setup times and costs are incurred whenever the server changes product. The system is maketoorder with a per unit backlogging cost. The objective is to minimize the longrun average cost per unit time. Using a fluid model, we provide a closedform lower bound on system performance. This bound is also shown to provide a lower bound for stochastic systems when scheduling is static, but is only an approximation when scheduling is dynamic. Heavytraffic analysis yields a refined bound that includes secondmoment terms. The fluid bound suggests both dynamic and static scheduling In this paper we consider a production environment where a number of different products are produced on a single machine and setup activities are necessary when switches of product type are made. These setup activities require both time and cost that depend on the specific product type. Throughout the paper we assume that the setups do not depend on the previous product produced
Stochastic Scheduling of Parallel Queues with SetUp Costs
 QUEUEING SYSTEMS THEORY AND APPLICATIONS
, 1995
"... We consider the problem of allocating a single server to a system of queues with Poisson arrivals. Each queue represents a class of jobs and possesses a holding cost rate, general service distribution, and a setup cost. The objective is to minimize the expected cost due to the waiting of jobs and t ..."
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Cited by 15 (3 self)
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We consider the problem of allocating a single server to a system of queues with Poisson arrivals. Each queue represents a class of jobs and possesses a holding cost rate, general service distribution, and a setup cost. The objective is to minimize the expected cost due to the waiting of jobs and the switching of the server. A setup cost is required to effect an instantaneous switch from one queue to another. We partially characterize an optimal policy and provide a simple heuristic scheduling policy. The heuristic's performance is evaluated in the cases of two and three queues by comparison with a numerically obtained optimal policy. Simulation results are provided to demonstrate the effectiveness of our heuristic over a wide range of problem instances with four queues.
The achievable region method in the optimal control of queueing systems; formulations, bounds and policies
 QUEUEING SYST
, 1995
"... We survey a new approach that the author and his coworkers have developed to formulate stochastic control problems (predominantly queueing systems) as mathematicalprogramming problems. The central idea is to characterize the region of achievable performance in a stochastic control problem, i.e., fi ..."
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Cited by 15 (4 self)
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We survey a new approach that the author and his coworkers have developed to formulate stochastic control problems (predominantly queueing systems) as mathematicalprogramming problems. The central idea is to characterize the region of achievable performance in a stochastic control problem, i.e., find linear or nonlinear constraints on the performance vectors that all policies satisfy. We present linear and nonlinear relaxations of the performance space for the following problems: Indexable systems (multiclass single station queues and multiarmed bandit problems), restless bandit problems, polling systems, multiclass queueing and loss networks. These relaxations lead to bounds on the performance of an optimal policy. Using information from the relaxations we construct heuristic nearly optimal policies, The theme in the paper is the thesis that better formulations lead to deeper understanding and better solution methods. Overall the proposed approach for stochastic control problems parallels efforts of the mathematical programming community in the last twenty years to develop sharper formulations (polyhedral combinatorics and more recently nonlinear relaxations) and leads to new insights ranging from a complete characterization and new algorithms for indexable systems to tight lower bounds and nearly optimal algorithms for restless bandit problems, polling systems, multiclass queueing and loss networks.
Server Assignment Policies for Maximizing the SteadyState Throughput of Finite Queueing Systems
 Management Science
, 2001
"... This paper is organized as follows. In Section 2, we show that if the service rates where i = 1,...,3// and j = 1,...,N, only depend on either the server i or the station j (and not on both the server and the station), then all nonidling policies will yield optimal throughput. In Section 3, we assu ..."
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Cited by 15 (7 self)
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This paper is organized as follows. In Section 2, we show that if the service rates where i = 1,...,3// and j = 1,...,N, only depend on either the server i or the station j (and not on both the server and the station), then all nonidling policies will yield optimal throughput. In Section 3, we assume that all service times are exponentially distributed and translate the original (continuous time) throughput optimization problem into an equivalent (discrete time) Markov decision problem. In Section 4, we determine the form of the optimal server assignment policy for MarkovJan systems of two queueing stations in tandem with two servers. In Section 5, we present a simple server assignment heuristic for tandem systems with an equal number of servers and stations and use numerical results obtained for MarkovJan networks with three or five stations in tandem to show that this heuristic generally appears to yield nearoptimal throughput. Finally, Section 6 contains some concluding remarks
Optimal Stochastic Scheduling of Forest Network with Switching Penalties,’ mimeo
, 1993
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 14 (8 self)
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The stochastic economic lot scheduling problem: heavy traffic analysis of dynamic cyclic policies
, 2000
"... We consider two queueing control problems that are stochastic versions of the economic lot scheduling problem: A single server processes N customer classes, and completed units enter a finished goods inventory that services exogenous customer demand. Unsatisfied demand is backordered, and each class ..."
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Cited by 13 (2 self)
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We consider two queueing control problems that are stochastic versions of the economic lot scheduling problem: A single server processes N customer classes, and completed units enter a finished goods inventory that services exogenous customer demand. Unsatisfied demand is backordered, and each class has its own general service time distribution, renewal demand process, and holding and backordering cost rates. In the first problem, a setup cost is incurred when the server switches class, and the setup cost is replaced by a setup time in the second problem. In both problems we employ a longrun average cost criterion and restrict ourselves to a class of dynamic cyclic policies, where idle periods and lot sizes are statedependent, but the N classes must be served in a fixed sequence. Motivated by existing heavy traffic limit theorems, we make a time scale decomposition assumption that allows us to approximate these scheduling problems by diffusion control problems. Our analysis of the approximating setup cost problem yields a closedform dynamic lotsizing policy and a computational procedure for an idling threshold. We derive structural results and an algorithmic procedure for the setup time problem. A computational study compares the proposed policy and several alternative policies to the numerically computed optimal policy.