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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
Polling models with twostage gated service: Fairness versus efficiency
 Lecture Notes in Computer Science
"... Abstract. We consider an asymmetric cyclic polling system with general servicetime and switchover time distributions with socalled 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 pseud ..."
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Abstract. We consider an asymmetric cyclic polling system with general servicetime and switchover time distributions with socalled 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 pseudoconservation law, (2) describe how the mean delay at each of the queues can be obtained recursively via the socalled Descendant Set Approach, and (3) present a closedform expression for the expected delay at each of the queues when the load tends to unity (under proper heavytraffic scalings), which is the main result of this paper. The results are strikingly simple and provide new insights into the behavior of twostage polling systems, including several insensitivity properties of the asymptotic expected delay with respect to the system parameters. Moreover, the results provide insight in the delayperformance of twostage gated polling compared to the classical onestage gated service policies. The results show that the twostage gated service policy indeed leads to better fairness compared to onestage 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. 1
2Department of Technology Management
, 2006
"... The present paper considers the class of polling systems that allow a multitype branching process interpretation. This class contains the classical exhaustive and gated policies as special cases. We present an exact asymptotic analysis of the delay distribution in such systems, when the setup times ..."
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The present paper considers the class of polling systems that allow a multitype branching process interpretation. This class contains the classical exhaustive and gated policies as special cases. We present an exact asymptotic analysis of the delay distribution in such systems, when the setup times tend to infinity. The motivation to study these setup time asymptotics in polling systems is based on the specific application area of basestock policies in inventory control. Our analysis provides new and more general insights into the behavior of polling systems with large setup times.
2Department of Technology Management
, 2006
"... The present paper considers the class of polling systems that allow a multitype branching process interpretation. This class contains the classical exhaustive and gated policies as special cases. We present an exact asymptotic analysis of the delay distribution in such systems, when the setup times ..."
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The present paper considers the class of polling systems that allow a multitype branching process interpretation. This class contains the classical exhaustive and gated policies as special cases. We present an exact asymptotic analysis of the delay distribution in such systems, when the setup times tend to infinity. The motivation to study these setup time asymptotics in polling systems is based on the specific application area of basestock policies in inventory control. We believe that our analysis provides new and more general insights into the behavior of polling systems with large setup times.
Polling Models with TwoStage Gated Service: Fairness versus Efficiency ∗
, 2006
"... We consider an asymmetric cyclic polling system with general servicetime and switchover time distributions with socalled 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 pseudoconserva ..."
Abstract
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We consider an asymmetric cyclic polling system with general servicetime and switchover time distributions with socalled 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 pseudoconservation law, (2) describe how the mean delay at each of the queues can be obtained recursively via the socalled Descendant Set Approach, and (3) present a closedform expression for the expected delay at each of the queues when the load tends to unity (under proper heavytraffic scalings), which is the main result of this paper. The results are strikingly simple and provide new insights into the behavior of twostage polling systems, including several insensitivity properties of the asymptotic expected delay with respect to the system parameters. Moreover, the results provide insight in the delayperformance of twostage gated polling compared to the classical onestage gated service policies. The results show that the twostage gated service policy indeed leads to better fairness compared to onestage 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.
A twoqueue Markovian polling system with two priority levels in the first queue
"... In this paper, we deal with a twoqueue polling system attended by a single server. The server visits the queues according to a Markovian routing mechnism. There are twoclass customers in the first queue. Customers of each queue are served in the exhaustive discipline. For this model, we study the ..."
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In this paper, we deal with a twoqueue polling system attended by a single server. The server visits the queues according to a Markovian routing mechnism. There are twoclass customers in the first queue. Customers of each queue are served in the exhaustive discipline. For this model, we study the joint number of customers, the cycle time and the waiting times. we are also devoted to deriving the exact asymptotics for the scaled delay in the heavytraffic scenario. In addition, the scaled delays with large switchover times are discussed for the first time in the Markovian polling systems. Finally, we provide some simulations to surpport the asymptotic results. Keywords:
EURANDOM PREPRINT SERIES
"... A new method for deriving waitingtime approximations in polling systems with renewal arrivals ..."
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A new method for deriving waitingtime approximations in polling systems with renewal arrivals