Multiclass Queueing Networks With Time Varying Arrivals

Author : Ruth Sagron
Publisher :
ISBN 13 :
Total Pages : 128 pages
Book Rating : 4.:/5 (129 download)

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Download or read book Tandem Queuing Model for Production Line with Downtimes written by Ruth Sagron and published by . This book was released on 2017 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Queuing networks are frequently used to predict the performance of complex manufacturing systems. Yet, existing queuing network approximations cannot properly cope with downtime events (e.g. set-up, maintenance) in manufacturing lines. These events involve significant interference among classes and generate non-renewable flows with very high variability, while causing starvation as well as blocking of bottleneck queues. Frequently, simulation models are used in such practical situations. Yet, they are expensive and time-consuming to model, update, and run. We consider systems with downtimes as multi-class systems in open and tandem queuing networks, with class-dependent service and routing, in which Class-1 represents the class of interest, and Class-2 represents the downtime events. We focus our analysis on a tandem queue in which the last queue is a bottleneck which may experience starvation, thus blocking in not in our scope. Two-moment decomposition, which is a common method for performance prediction in queueing networks, is the natural choice. Thus, the primary objective of this work is improving the existing multiclass decomposition methods with deterministic routing. Decomposition methods decompose the queuing network into a set of separate queues having independent arrival processes. Since in a tandem topology the departure from one queue is the arrival to the next, the focus in this work is turned to departure processes. First, we investigate these processes in a single queue. Then we analyze and improve the second moment approximations of the departure processes within the tandem queues. Here, in addition to the Class-1 arrival and service processes, interference created by Class-2 is taken into consideration; therefore, analyzing the departure process for each class is needed. In the first phase of the work, we investigate the inter-departure time distribution in a G/G/1 queue. Initially, we exploit the probabilistic interpretation of the phase-type distributions for deriving an explicit expression of the Laplace-Stieltjes transform (LST) of the inter-departure times in various cases of PH/G/1 queues. Then we use these results in expressing the LST of the inter-departure times in more general queues. By the specific result of a Cm/G/1 queue, we show that the LST of inter-departure times of any Km/G/1 queue can be expressed explicitly. In addition, we show that the LST of inter-departure times of any G/G/1 queue with continuous inter-arrival distribution can be approximated appropriately by a PH/G/1 queue. These results play an important role in improving the accuracy of approximations used for studying and predicting the performance of open queuing networks. In our work, these results improve the efficiency of our approximation method, as is detailed in the third phase. In the second phase of the work, we introduce the bottleneck phenomenon caused by interference (e.g. by downtimes) within the network, while improving the basic structure of class-departure variability. Our analysis illustrates that this variability can be expressed as the sum of two components. The first component reflects the withinclass effect - the variability caused by the class' own inter-arrival and service time distributions, and the second reflects the between-class effect - the variability caused by interactions with other classes. We integrate the existing decomposition methods with two variability functions, one for each effect. Our analysis shows that the withinclass effect can be approximated by the existing variability function proposed by Kim (2005), while the between-class effect requires a new function. In this phase, we propose an initial function for the latter effect requiring high computation efforts due to many sub-simulations. In the third phase of the work, we introduce an advanced function for the betweenclass effect: Regression-Based Variability Function. This function depends on downstream waiting time and exploits the analysis of departure from a single queue, while employing the developments in the first phase on this work. The RegressionBased Variability Function model significantly reduces computation efforts, except for one sub-simulation for each traffic intensity level. With this model, we also show that predicting the performance of n-tandem queues is possible by reducing the focus to 2tandem queues for each traffic intensity level. Our proposed method has been examined via simulation for scenarios of n-tandem queues with bottleneck under downtimes with FCFS and priority policies. In such scenarios, the results demonstrate a relative error three times smaller than the best relevant existing procedures in the literature. -- abstract.