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15
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...
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
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...
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.
Server Allocation in Grid Systems with On/Off Sources
 in: Proceedings of ISPA 2006 Workshops, Lecture Notes in Computing Science
, 2006
"... Abstract. A system consisting of a number of servers, where demands of different types arrive in bursts (modelled by interrupted Poisson processes), is examined in the steady state. The problem is to decide how many servers to allocate to each job type, so as to minimize a cost function expressed in ..."
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Cited by 3 (2 self)
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Abstract. A system consisting of a number of servers, where demands of different types arrive in bursts (modelled by interrupted Poisson processes), is examined in the steady state. The problem is to decide how many servers to allocate to each job type, so as to minimize a cost function expressed in terms of average queue sizes. First, an exact analysis is provided for an isolated IP/M/n queue. The results are used to compute the optimal static server allocation policy. The latter is then compared to two heuristic policies which employ dynamic switching of servers from one queue to another (such switches take time and hence incur costs). 1
Dynamic Operating Policies for Commercial Hosting Environments
 5th UK eScience All Hands Meeting
, 2006
"... This paper reports on two strands of work that are being undertaken as part of the EPSRC funded DOPCHE project. The paper focuses on open software architectures for dynamic operating policies and a performance model used to nd optimal operating policies. 1 ..."
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Cited by 2 (0 self)
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This paper reports on two strands of work that are being undertaken as part of the EPSRC funded DOPCHE project. The paper focuses on open software architectures for dynamic operating policies and a performance model used to nd optimal operating policies. 1
Monotonicity Of Optimal Performance Measures For Polling Systems
 Probability in the Engineering and Informational Sciences
, 1997
"... We consider scheduling a single server in a multiclass queue subject to setup times and setup costs. We examine the issue of whether or not reductions in the mean and variance of the setup time distributions can lead to degraded system performance. Provided that setups are reduced according ..."
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Cited by 2 (1 self)
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We consider scheduling a single server in a multiclass queue subject to setup times and setup costs. We examine the issue of whether or not reductions in the mean and variance of the setup time distributions can lead to degraded system performance. Provided that setups are reduced according to a stochastically smaller ordering, we show that if an optimal policy is used both for the original system as well as for the system with reduced setup times, then an improvement in performance is guaranteed. Even in cases for which a truly optimal policy is unknown, idling can be employed to avoid degradation of performance as setup times are cut. We extend this approach to show that system performance is monotonic with respect to service time distributions, switching costs, holding costs, and uniform reductions in the arrival rates. Extensions to sequencedependent setups and job feedback are noted. 1. Introduction We consider the problem of scheduling a single server in a mul...
Beyond the cµ Rule: Dynamic Scheduling Of A TwoClass Loss Queue
, 1997
"... We consider scheduling a single server in a twoclass M/M/1 queueing system with finite buffers subject to holding costs and rejection costs for rejected jobs. We use dynamic programming to investigate the structural properties of optimal policies. Provided that the delay of serving a job is alwa ..."
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Cited by 1 (0 self)
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We consider scheduling a single server in a twoclass M/M/1 queueing system with finite buffers subject to holding costs and rejection costs for rejected jobs. We use dynamic programming to investigate the structural properties of optimal policies. Provided that the delay of serving a job is always less costly than rejecting an arrival, we show that the optimal policy has a monotonic threshold type of switching curve; otherwise, numerical analysis indicates that the threshold structure may not be optimal.