Polling Systems with Zero Switchover Times: A Heavy-Traffic Averaging Principle

Coffman, E. G.; Puhalskii, Anatolii A.; Reiman, Martin I.

doi:10.1214/aoap/1177004701

Cited by 83 publications

(117 citation statements)

References 10 publications

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“…In the special case of exhaustive service (that is, u{x) = x for all .r), Coffman, Puhalskii and Reiman (1994) show that the normalized total unfinished workload process weakly converges to^his diffusion process as p -> 1. If, in addition, c = (that is, p = 1), this diffusion process is a Bessel process.…”

Section: U[x)mentioning

confidence: 99%

“…In the setup cost problem, we also need to assume that the setup costs are very large, roughly two orders of magnitude larger than the holding cost rate. Following in the tradition of Foschini (1977) and Harrison (1988) The setup time problem is addressed in Section 2, and the averaging principle in Coffman, Puhalskii and Reiman (1994) leads to a limiting control problem that again is one-dimensional, although here we obtain an explicit diffusion control problem. The control, which represents the amount of low priority work to serve as a function of the total workload, appears in It turns out to be impossible to obtain a limit process for (M^i, W2) in the usual sense, because in the heavy traffic limit, the two-dimensional process moves back and forth along the cross diagonal at an infinite rate, the direction being determined by which of the two queues is being served; see Figure 1.…”

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confidence: 99%

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Dynamic Scheduling of a Two-Class Queue with Setups

Reiman¹,

Wein

1998

Operations Research

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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 long-run 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.

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Section: U[x)mentioning

confidence: 99%

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confidence: 99%

Dynamic Scheduling of a Two-Class Queue with Setups

Reiman¹,

Wein

1998

Operations Research

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“…Since the late 1960s polling models have received much attention in the literature [12,13]. There are several good reasons for considering heavy-traffic asymptotics, which have recently started to gain momentum in the literature, initiated by the pioneering work of Coffman et al [2,3] in the mid 90s. Exact analysis of the delay in polling models is only possible in some cases, and even in those cases numerical techniques are usually required to obtain the expected delay at each of the queues.…”

Section: Introductionmentioning

confidence: 99%

Polling Models with Two-Stage Gated Service: Fairness Versus Efficiency

Mei

Resing

2007

Lecture Notes in Computer Science

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Abstract.We consider an asymmetric cyclic polling system with general service-time and switch-over time distributions with so-called twostage gated service at each queue, an interleaving scheme that aims to enforce fairness among the different customer classes. For this model, we (1) obtain a pseudo-conservation law, (2) describe how the mean delay at each of the queues can be obtained recursively via the so-called Descendant Set Approach, and (3) present a closed-form expression for the expected delay at each of the queues when the load tends to unity (under proper heavy-traffic scalings), which is the main result of this paper. The results are strikingly simple and provide new insights into the behavior of two-stage polling systems, including several insensitivity properties of the asymptotic expected delay with respect to the system parameters. Moreover, the results provide insight in the delay-performance of two-stage gated polling compared to the classical one-stage gated service policies. The results show that the two-stage gated service policy indeed leads to better fairness compared to one-stage gated service, at the expense of a decrease in efficiency. Finally, the results also suggest simple and fast approximations for the expected delay in stable polling systems. Numerical experiments demonstrate that the approximations are highly accurate for moderately and heavily loaded systems.

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“…The objective is to minimize long-run average holding, backorder and transportation costs. The authors provide a heavy traffic analysis of the fixed TSP policy, adapting recent heavy traffic results of Coffman et al (1995aCoffman et al ( , 1995b for polling systems.…”

Section: Literature Reviewmentioning

confidence: 99%

Dynamic Vehicle Dispatching: Optimal Heavy Traffic Performance and Practical Insights

Gans

Ryzin

1999

Operations Research

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We analyze a general model of dynamic vehicle dispatching systems in which congestion is the primary measure of performance. In the model, a finite collection of tours are dynamically dispatched to deliver loads that arrive randomly over time. A load waits in queue until it is assigned to a tour. This representation, which is analogous to classical set-covering models, can be used to study a variety of dynamic routing and load consolidation problems. We characterize the optimal work in the system in heavy traffic using a lower bound from our earlier work (Gans and van Ryzin 1997) and an upper bound which is based on a simple batching policy. These results give considerable insight into how various parameters of the problem affect system congestion. In addition, our analysis suggests a practical heuristic which, in simulation experiments, significantly outperforms more conventional dispatching policies. The heuristic uses a few simple principles to control congestion, principles which can be easily incorporated within classical, static routing algorithms.

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Polling Systems with Zero Switchover Times: A Heavy-Traffic Averaging Principle

Cited by 83 publications

References 10 publications

Dynamic Scheduling of a Two-Class Queue with Setups

Dynamic Scheduling of a Two-Class Queue with Setups

Polling Models with Two-Stage Gated Service: Fairness Versus Efficiency

Dynamic Vehicle Dispatching: Optimal Heavy Traffic Performance and Practical Insights

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