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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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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
Scheduling Policies for an Antiterrorist Surveillance System
, 2008
"... This paper concerns scheduling policies in a surveillance system aimed at detecting a terrorist attack in time. Terrorist suspects arriving at a public area are subject to continuous monitoring, while a surveillance team takes their biometric signatures and compares them with records stored in a ter ..."
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This paper concerns scheduling policies in a surveillance system aimed at detecting a terrorist attack in time. Terrorist suspects arriving at a public area are subject to continuous monitoring, while a surveillance team takes their biometric signatures and compares them with records stored in a terrorist database. Because the surveillance team can screen only one terrorist suspect at a time, the team faces a dynamic scheduling problem among the suspects. We build a model consisting of an M/G/1 queue with two types of customers—red and white—to study this problem. Both types of customers are impatient, but the reneging time distributions are different. The server only receives a reward by serving a red customer, and can use the time a customer has spent in the queue to deduce its likely type. In a few special cases, a simple service rule—such as firstcomefirstserve—is optimal. We explain why the problem is in general difficult, and develop a heuristic policy motivated by the fact that terrorist attacks tend to be rare events.
Polling Systems with Periodic Server Routing in HeavyTraffic: Renewal Arrivals
"... This paper considers heavytraffic limit theorems for polling models with periodic server routing with general renewal arrivals and with mixtures of gated and exhaustive service policies, in a general parameter setting. We provide a strong conjecture for the limiting waitingtime distribution in a g ..."
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This paper considers heavytraffic limit theorems for polling models with periodic server routing with general renewal arrivals and with mixtures of gated and exhaustive service policies, in a general parameter setting. We provide a strong conjecture for the limiting waitingtime distribution in a general parameter setting when the load tends to 1, under proper heavytraffic scalings. The results in this paper, which generalize those in [14] for the special case of Poisson arrivals, are obtained by following the nonPoisson transient systems approach developed in [6]. Numerical results with simulations support the correctness our results, and moreover, show that the expressions for the waitingtime distributions in the limiting case lead to sharp approximations for the waitingtime distributions for stable polling systems with medium and heavy load. Keywords: polling system, polling table, periodic routing, delay, waiting time, heavytraffic, This paper considers heavytraffic limit theorems for polling models with periodic server routing under renewal arrivals. As such, we generalize results in Olsen and Van der Mei [14], which were proven for these systems under Poisson arrivals in steadystate. In such systems the order in which
Applications of polling systems M.A.A. Boon∗
, 2011
"... Since the first paper on polling systems, written by Mack in 1957, a huge number of papers on this topic has been written. A typical polling system consists of a number of queues, attended by a single server. In several surveys, the most notable ones written by Takagi, detailed and comprehensive des ..."
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Since the first paper on polling systems, written by Mack in 1957, a huge number of papers on this topic has been written. A typical polling system consists of a number of queues, attended by a single server. In several surveys, the most notable ones written by Takagi, detailed and comprehensive descriptions of the mathematical analysis of polling systems are provided. The goal of the present survey paper is to complement these papers by putting the emphasis on applications of polling models. We discuss not only the capabilities, but also the limitations of polling models in representing various applications. The present survey is directed at both academicians and practitioners.
Finite Buffer Polling Models with Routing
, 2002
"... This paper analyzes a finite buffer polling system with routing. Finite buffers are used to model the limited capacity of the system, and routing is used to represent the need for additional service. The most significant result of the analysis is the derivation of the generating function for queue l ..."
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This paper analyzes a finite buffer polling system with routing. Finite buffers are used to model the limited capacity of the system, and routing is used to represent the need for additional service. The most significant result of the analysis is the derivation of the generating function for queue length when buffer sizes are limited and a representation of the system workload. The queue lengths at polling instants are determined by solving a system of recursive equations, and an embedded Markov chain analysis and numerical inversion are used to derive the queue length distributions. This system may be used to represent production models with setups and lost sales or expediting.
Finitecapacity Multiclass Production Scheduling with Setup Times
, 1998
"... We treat the scheduling of a single server in a finitebuffer capacity, multiclass, maketoorder production system subject to inventory holding costs, setup times, and customer rejection costs. We employ theoretical and numerical analysis of a Markov decision process model to investigate the stru ..."
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We treat the scheduling of a single server in a finitebuffer capacity, multiclass, maketoorder production system subject to inventory holding costs, setup times, and customer rejection costs. We employ theoretical and numerical analysis of a Markov decision process model to investigate the structure of optimal policies and the performance of heuristic policies. We establish the monotonicity of optimal performance with respect to the system parameters. Based on our insights, we provide a heuristic policy called the Capacitated Modified Index Rule (CMIR) for capacitated scheduling with customer loss penalties. The CMIR heuristic can easily be precomputed and stored for realtime control. Numerical benchmarking with respect to the optimal performance as well as an existing heuristic suggests that CMIR is very effective. Keywords: Polling system; Finite buffer; Capacitated production scheduling; Markov decision process model; Nearoptimal heuristic scheduling 1. Introduction We foc...
Analysis of MultiClass Queueing Systems with Finite Buffers and Setup Times Using Decomposition Methods
"... In this paper, we consider two variants of a multiclass queueing system with a single server, finite buffers, and setup times. In the first variant, a setup occurs every time the server turns to a different class of customers, even if the queue of the scanned customer class is empty. In the second ..."
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In this paper, we consider two variants of a multiclass queueing system with a single server, finite buffers, and setup times. In the first variant, a setup occurs every time the server turns to a different class of customers, even if the queue of the scanned customer class is empty. In the second variant, the server skips empty queues and a setup is performed only at queues that contain at least one customer. We propose decomposition methods for the analysis of the steadystate behavior of both system variants. We also show that multiproduct kanban systems with setup times and lost sales are possible applications of the discussed models and we give numerical results that indicate the accuracy of the proposed approximation methods. Keywords: