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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
Fluid Polling Systems
"... We study Nqueues singleserver fluid polling systems, where a fluid is continuously flowing into the queues at queuedependent rates. When visiting and serving a queue, the server reduces the amount of fluid in that queue at a queuedependent rate. Switching from queue i to queue j requires two ra ..."
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We study Nqueues singleserver fluid polling systems, where a fluid is continuously flowing into the queues at queuedependent rates. When visiting and serving a queue, the server reduces the amount of fluid in that queue at a queuedependent rate. Switching from queue i to queue j requires two randomduration steps: (i) departing queue i, and (ii) reaching queue j. The length of time the server resides in a queue depends on the service regime. We consider three main regimes: Exhaustive, Gated and GloballyGated. Two polling procedures are analyzed: (i) cyclic and (ii) probabilistic. Under steadystate, we derive the Laplace–Stieltjes transform (LST), mean and second moment of the amount of flow at each queue at polling instants, as well as at an arbitrary moment. We further calculate the LST and mean of the ’waiting time ’ of a drop at each queue and derive expressions for the mean total load in the system for the various service regimes. Finally, we explore optimal switching procedures.
Fairness and Efficiency for Polling Models with the κGated Service Discipline
, 2010
"... We study a polling model where we want to achieve a balance between the fairness of the waiting times and the efficiency of the system. For this purpose, we introduce the κgated service discipline. It is a hybrid of the classical gated and exhausted disciplines, and consists of using κi gated servi ..."
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We study a polling model where we want to achieve a balance between the fairness of the waiting times and the efficiency of the system. For this purpose, we introduce the κgated service discipline. It is a hybrid of the classical gated and exhausted disciplines, and consists of using κi gated service phases at queue i before the server switches to the next queue. We derive the distributions and means of the waiting times, a pseudo conservation law for the weighted sum of the mean waiting times, and the fluid limits of the waiting times. Our goal is to optimize the κi’s so as to minimize the differences in the mean waiting times, i.e. to achieve maximal fairness, without giving up too much on the efficiency of the system. From the fluid limits we derive a heuristic rule for setting the κi’s. In a numerical study the heuristic is shown to perform well.
ResponseTime Approximations For MultiServer, MultiClass Production Systems With Significant Setups
, 1995
"... A multiserver polling model is a queueing model where many order classes share a set of identical servers and a setup time is incurred whenever a server changes class. This paper develops approximations for the waiting time distribution in a multiserver polling model with cyclic servetoexhaustio ..."
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A multiserver polling model is a queueing model where many order classes share a set of identical servers and a setup time is incurred whenever a server changes class. This paper develops approximations for the waiting time distribution in a multiserver polling model with cyclic servetoexhaustion service. These approximations are derived using previously established heavytraffic results and the assumption of significant setup times. They improve as the total setup over all classes increases. In a manufacturing environment, setups are only performed if there are orders waiting. We introduce the concept of positivequeue setups for the case where setups depend on the presence of orders, in contrast to the traditional polling model with emptyqueue setups. The approximation is derived both for systems with emptyqueue setups and systems with positivequeue setups. This study of polling models was motivated by a production scheduling problem at Raychem Corporation. The approximation f...
Performance Analysis of SessionLevel Load Balancing Algorithms
"... Load balancing (LB) is crucial for the efficient operation of big server clusters. In the past, many different LB strategies on the request level have been developed with great effectiveness in parallel applications. However, the LB problem is not yet solved completely; new applications and architec ..."
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Load balancing (LB) is crucial for the efficient operation of big server clusters. In the past, many different LB strategies on the request level have been developed with great effectiveness in parallel applications. However, the LB problem is not yet solved completely; new applications and architectures require new features. In particular, secure environments require that LB is done at session level instead of request level; that is, once a session has been assigned to a server, all subsequent service requests are directed to the assigned server. Despite the fact that many commercial products have been brought to the market to implement LB at the session level, little insight has been obtained into the efficiency of such sessionlevel LB algorithms, leaving ample room for performance improvement and optimization. Motivated by this, we study sessionlevel LB with a focus on algorithms that are simple and easy to implement in real systems. The performance of the load balancer is highly dependent on the request profiles of the different sessions and the information that is available for decision making. We make this tradeoff between the information that is available to the load balancer and the efficiency of the algorithm explicit by developing new algorithms, and compare their efficiency with existing algorithms. The algorithms are mainly based on the load of each server and the number of active sessions running on them. Extensive validation in an experimental setting shows that our algorithms outperform the existing ones, and as such, provide a simple, easytoimplement yet effective means to improve the efficiency of large server clusters.