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28
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
Optimal Server Allocation in Reconfigurable Clusters with Multiple Job Types
 Computational Science and its Applications (ICCSA 2004
, 2003
"... We examine a system where the servers in a cluster may be switched dynamically and preemptively from one kind of work to another. The demand consists of M jobs... ..."
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Cited by 22 (4 self)
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We examine a system where the servers in a cluster may be switched dynamically and preemptively from one kind of work to another. The demand consists of M jobs...
A SURVEY ON THE BANDIT PROBLEM WITH SWITCHING COSTS
, 2004
"... The paper surveys the literature on the bandit problem, focusing on its recent development in the presence of switching costs. Switching costs between arms makes not only the Gittins index policy suboptimal, but also renders the search for the optimal policy computationally infeasible. This survey w ..."
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Cited by 22 (0 self)
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The paper surveys the literature on the bandit problem, focusing on its recent development in the presence of switching costs. Switching costs between arms makes not only the Gittins index policy suboptimal, but also renders the search for the optimal policy computationally infeasible. This survey will first discuss the decomposability properties of the arms that make the Gittins index policy optimal, and show how these properties break down upon the introduction of costs on switching arms. Having established the failure of the simple index policy, the survey focus on the recent efforts to overcome the difficulty of finding the optimal policy in the bandit problem with switching costs: characterization of the optimal policy, exact derivation of the optimal policy in the restricted environments, and lastly approximation of optimal policy. The advantages and disadvantages of the above approaches are discussed.
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.
Dynamic Server Assignment in a TwoQueue Model
 European Journal of Operational Research
, 1997
"... We consider a polling model of two M=G=1 queues, served by a single server. The service policy for this polling model is of threshold type. Service at queue 1 is exhaustive. Service at queue 2 is exhaustive unless the size of queue 1 reaches some level T during a service at queue 2; in the latte ..."
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Cited by 12 (2 self)
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We consider a polling model of two M=G=1 queues, served by a single server. The service policy for this polling model is of threshold type. Service at queue 1 is exhaustive. Service at queue 2 is exhaustive unless the size of queue 1 reaches some level T during a service at queue 2; in the latter case the server switches to queue 1 at the end of that service. Both zero and nonzero switchover times are considered. We derive exact expressions for the joint queue length distribution at customer departure epochs, and for the steadystate queuelength and sojourn time distributions. In addition, we supply a simple and very accurate approximation for the mean queue lengths, which is suitable for optimization purposes. AMS Subject Classification (1991): Primary: 60K25, Secondary: 90B22 Keywords & Phrases: Queueing, polling, ATM, threshold service, queue length distribution. 1 Introduction In this paper we consider a model of two M=G=1 queues, which are served by a single serve...
Dynamic Server Allocation in Heterogeneous Clusters
 Procs. of HETNETs ’03 : First International Working Conference on Performance Modelling and Evaluation of Heterogeneous Networks
, 2003
"... We examine the optimization of a system where the servers in a cluster may be switched dynamically and preemptively from one kind of work to another. The demand consists of two job types joining separate queues, with different arrival and service characteristics, and also different relative importan ..."
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Cited by 9 (1 self)
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We examine the optimization of a system where the servers in a cluster may be switched dynamically and preemptively from one kind of work to another. The demand consists of two job types joining separate queues, with different arrival and service characteristics, and also different relative importance represented by appropriate holding costs. The switching of a server from queue 1 to queue 2, or vice versa, incurs a cost which may be monetary or may involve a period of unavailability. The optimal switching policy...
Queueingtheoretic solution methods for models of parallel and distributed systems
 Performance Evaluation of Parallel and Distributed Systems Solution Methods. CWI Tract 105 & 106
, 1994
"... This paper aims to give an overview of solution methods for the performance analysis of parallel and distributed systems. After a brief review of some important general solution methods, we discuss key models of parallel and distributed systems, and optimization issues, from the viewpoint of solutio ..."
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Cited by 8 (3 self)
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This paper aims to give an overview of solution methods for the performance analysis of parallel and distributed systems. After a brief review of some important general solution methods, we discuss key models of parallel and distributed systems, and optimization issues, from the viewpoint of solution methodology.
On the Value Function of a Priority Queue with an Application to a Controlled Polling Model
, 2000
"... We give a closedform expression for the discounted weighted queue length and switching costs of a twoclass singleserver queueing model under a preemptive priority rule. ..."
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Cited by 7 (1 self)
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We give a closedform expression for the discounted weighted queue length and switching costs of a twoclass singleserver queueing model under a preemptive priority rule.
Dynamic Allocation of Servers in a Grid Hosting Environment
 Procs. 5th IEEE/ACM Int. Conf. on Grid Computing
, 2004
"... A grid hosting environment is described, where servers may be reconfigured dynamically from one type of work to another in response to changes in demand. The problem of carrying out these reconfigurations in the most efficient manner is addressed by means of stochastic modelling and optimization. A ..."
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Cited by 5 (1 self)
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A grid hosting environment is described, where servers may be reconfigured dynamically from one type of work to another in response to changes in demand. The problem of carrying out these reconfigurations in the most efficient manner is addressed by means of stochastic modelling and optimization. A heuristic policy which is close to optimal over a wide range of parameters is introduced. A prototype system based on existing resource management software has been developed to demonstrate the concepts described.