Monotone control of queueing networks

Veatch, Michael H.; Wein, Lawrence M.

doi:10.1007/bf01158810

Cited by 55 publications

(38 citation statements)

References 11 publications

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“…The relations (15) show that the structural and monotone properties of the optimal control policy f can be derived by analysing the monotonicity properties of the value function v. Such properties for other types of controlled queues in a tandem were studied also in [12,15,31]. It was shown that the value function has some monotonicity properties like non-decreasing and superconvexity.…”

Section: Corollary 1 the Optimal Policymentioning

confidence: 99%

Optimal Control of a Two-Server Heterogeneous Queueing System with Breakdowns and Constant Retrials

Efrosinin¹,

Sztrik²

2016

Communications in Computer and Information Science

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Abstract. Heterogeneous servers which can differ in service speed and reliability are becoming more popular in the modelling of modern communication systems. For a two-server queueing system with one nonreliable server and constant retrial discipline we formulate an optimal allocation problem for minimizing a long-run average cost per unit of time. Using a Markov decision process formulation we prove a number of monotone properties for the increments of the dynamic-programming value function. Such properties imply the optimality of a two-level threshold control policy. This policy prescribes the usage of a less productive server if the number of customers in the queue becomes higher than a predefined level which depends on the state of a non-reliable more powerful server. We provide also a heuristic solution for the optimal threshold levels in explicit form as a function of system parameters.

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Section: Corollary 1 the Optimal Policymentioning

confidence: 99%

Optimal Control of a Two-Server Heterogeneous Queueing System with Breakdowns and Constant Retrials

Efrosinin¹,

Sztrik²

2016

Communications in Computer and Information Science

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“…The policy is monotone if it satisfies 1. Monotone switching: See Veatch and Wein (1992) for a discussion of monotonicity. Ha (1992) proves that the optimal policy is monotone for the case of two products with µ 1 = µ 2 and backordering.…”

Section: Dynamic Scheduling Problemmentioning

confidence: 99%

Scheduling a Make-To-Stock Queue: Index Policies and Hedging Points

Veatch

Wein

1996

Operations Research

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120

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A single machine produces several different classes of items in a make-to-stock mode. We consider the problem of scheduling the machine to regulate finished goods inventory, minimizing holding and backorder or holding and lost sales costs. Demands are Poisson, service times are exponentially distributed, and there are no delays or costs associated with switching products. A scheduling policy dictates whether the machine is idle or busy, and specifies the job class to serve in the latter case. Since the optimal solution can only be numerically computed for problems with several products, our goal is to develop effective policies that are computationally tractable for a large number of products. We develop index policies to decide which class to produce, including Whittle's "restless bandit" index, which possesses a certain asymptotic optimality. Several idleness policies are derived, and the best policy is obtained from a heavy traffic diffusion approximation. Nine sample problems are considered in a numerical study, and the average suboptimality of the best policy is less than 3%.

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“…We extend this result to cover the case when the server can serve at either station and also to include machine breakdowns. Our approach establishes properties of the value function directly, rather than showing that properties are preserved by value iteration as in Hajek [4] and Veatch and Wein [6].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Allocation of Reconfigurable Resources in a Two-Stage Tandem Queueing System With Reliability Considerations

Lewis

Veatch

2006

IEEE Trans. Automat. Contr.

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Consider a two stage tandem queueing system, with dedicated machines in each stage. Additional reconfigurable resources can be assigned to one of these two stations without setup cost and time.In a clearing system (without external arrivals) both with and without machine failures, we show the existence of an optimal monotone policy. Moreover, when all of the machines are reliable, the switching curve defined by this policy has slope greater than or equal to -1. This continues to hold true when the holding cost rate is higher at the first stage and machine failures are considered.

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Monotone control of queueing networks

Cited by 55 publications

References 11 publications

Optimal Control of a Two-Server Heterogeneous Queueing System with Breakdowns and Constant Retrials

Optimal Control of a Two-Server Heterogeneous Queueing System with Breakdowns and Constant Retrials

Scheduling a Make-To-Stock Queue: Index Policies and Hedging Points

Dynamic Allocation of Reconfigurable Resources in a Two-Stage Tandem Queueing System With Reliability Considerations

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