Optimal control of service rates in networks of queues

Weber, Richard; Stidham, Shaler

doi:10.2307/1427380

Cited by 205 publications

(110 citation statements)

References 25 publications

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“…Under relatively general conditions, Stidham and Weber [8] prove that there exists a stationary policy that is optimal within the larger class of potentially non-stationary policies, making heavy use of their own results in an earlier paper [9]. In proving the existence of a stationary optimal policy for the problem of service rate control, Stidham and Weber [8] impose two assumptions that do not necessarily hold in our model:…”

Section: Literature Reviewmentioning

confidence: 99%

Dynamic Control of a Queue with Adjustable Service Rate

George¹,

Harrison

2001

Operations Research

198

183

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We consider a single-server queue with Poisson arrivals, where holding costs are continuously incurred as a non-decreasing function of the queue length. The queue length evolves as a birth-and-death process with constant arrival rate λ = 1 and with state-dependent service rates µ n that can be chosen from a fixed subset A of [0, ∞).Finally, there is a non-decreasing cost-of-effort function c(·) on A, and service costs are incurred at rate c(µ n ) when the queue length is n. The objective is to minimize average cost per time unit over an infinite planning horizon. The standard optimality equation of average-cost dynamic programming allows one to write out the optimal service rates in terms of the minimum achievable average cost z * . Here we present a method for computing z * which is so fast and so transparent that it may reasonably be described as an explicit solution for the problem of service rate control. The optimal service rates are non-decreasing as a function of queue length, and are bounded if the holding cost function is bounded. From a managerial standpoint it is natural to compare z * , the minimum average cost achievable with state-dependent service rates, against the minimum average cost achievable with a single fixed service rate. The difference between those two minima represents the economic value of a responsive service mechanism, and numerical examples are presented which show that it can be substantial.

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Section: Literature Reviewmentioning

confidence: 99%

Dynamic Control of a Queue with Adjustable Service Rate

George¹,

Harrison

2001

Operations Research

198

183

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show abstract

“…Such structural properties of optimality can be proven by showing the convexity of the value function in the Bellman optimality equation, see for example [14] and [6]. Similar convexity properties also hold for networks of queues [15]. Adopting the optimal control, several strategic questions can be answered as well, such as the desirable distance of the buffer location from the distribution center in order to regulate trucks optimally.…”

Section: Introductionmentioning

confidence: 96%

Near-Optimal Switching Strategies for a Tandem Queue

Leeuwen

Núñez-Queija

2017

International Series in Operations Research &Amp; Management Science

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Motivated by various applications in logistics, road traffic and production management, we investigate two versions of a tandem queueing model in which the service rate of the first queue can be controlled. The objective is to keep the mean number of jobs in the second queue as low as possible, without compromising the total system delay (i.e. avoiding starvation of the second queue). The balance between these objectives is governed by a linear cost function of the queue lengths. In the first model, the server in the first queue can be either switched on or off, depending on the queue lengths of both queues. This model has been studied extensively in the literature. Obtaining the optimal control is known to be computationally intensive and time consuming. We are particularly interested in the scenario that the first queue can operate at larger service speed than the second queue. This scenario has received less attention in literature. We propose an approximation using an efficient mathematical analysis of a near-optimal threshold policy based on a matrix-geometric solution of the stationary probabilities that enables us to compute the relevant stationary measures more efficiently and determine an optimal choice for the threshold value. In some of our target applications, it is more realistic to see the first queue as a (controllable) batch-server system. We follow a similar approach as for the first model and obtain the structure of the optimal policy as well as an efficiently computable near-optimal threshold policy. We illustrate the appropriateness of our approximations using simulations of both models.

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“…See Rosberg et al [18], Weber and Stidham [28], [24], and Altman and Koole [1]. Our model is also a Markov decision model but it is di¤erent in that all uncontrollable transition rates in the network are state dependent, rather than …xed and independent of the system state.…”

Section: Motivation and Literature Reviewmentioning

confidence: 99%

Optimal Production Policies With Multistage Stochastic Demand Lead Times

Kim

Ahn

Righter

2009

Prob. Eng. Inf. Sci.

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We study the value of multi-stage advance demand information (MADI) in a production system in which customers place an order in advance of their actual need, and each order goes through multiple stages before it becomes due. Any order which is not immediately …lled at its due date will be backordered. The producer must decide whether to produce or not based on real-time information regarding current and future orders. We formulate the problem as a Markov decision process and analyze the impact of the demand information on the production policy and the cost. We show that the optimal production policy is a state-dependent base-stock policy, and we show that it has certain monotonicity properties. We also introduce a simple heuristic policy that is signi…cantly easier to compute and that inherits the structural properties of the optimal policy. In addition, we show that its base-stock levels bound those of the socially optimal policy. Numerical study identi…es the conditions under which MADI is most bene…cial and shows that the heuristic performs almost as well as the optimal policy when MADI is most bene…cial.

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Optimal control of service rates in networks of queues

Cited by 205 publications

References 25 publications

Dynamic Control of a Queue with Adjustable Service Rate

Dynamic Control of a Queue with Adjustable Service Rate

Near-Optimal Switching Strategies for a Tandem Queue

Optimal Production Policies With Multistage Stochastic Demand Lead Times

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