Performance Bounds for Scheduling Queueing Networks

The goal of this paper is to assess the improvement in performance that might' be achieved by optimally scheduling a multiclass open queueing network. A stochastic process is defined whose steady-state mean value is less than or equal to the mean number of customers in a queueing network under any arbitrary scheduling policy. Thus, this process offers a lower bound on performance when the objective of the queueing network scheduling problem is to minimize the mean number of customers in the network. Since this bound is easily obtained from a computer simulation model of a queueing network, its main use is to aid job-shop schedulers in determining how much further improvement (relative to their proposed policies) might be achievable from scheduling. Through computational examples, we identify some factors that affect the tightness of the bound

Routing in multi-class queueing networks

PhD ThesisWe consider the problem of routing (incorporating local scheduling) in a distributed network. Dedicated jobs arrive directly at their specified station for processing. The choice of station for generic jobs is open. Each job class has an associated holding cost rate. We aim to develop routing policies to minimise the long-run average holding cost rate. We first consider the class of static policies. Dacre, Glazebrook and Nifio-Mora (1999) developed an approach to the formulation of static routing policies, in which the work at each station is scheduled optimally, using the achievable region approach. The achievable region approach attempts to solve stochastic optimisation problems by characterising the space of all possible performances and optimising the performance objective over this space. Optimal local scheduling takes the form of a priority policy. Such static routing policies distribute the generic traffic to the stations via a simple Bernoulli routing mechanism. We provide an overview of the achievements made in following this approach to static routing. In the course of this discussion we expand upon the study of Becker et al. (2000) in which they considered routing to a collection of stations specialised in processing certain job classes and we consider how the composition of the available stations affects the system performance for this particular problem. We conclude our examination of static routing policies with an investigation into a network design problem in which the number of stations available for processing remains to be determined. The second class of policies of interest is the class of dynamic policies. General DP theory asserts the existence of a deterministic, stationary and Markov optimal dynamic policy. However, a full DP solution may be unobtainable and theoretical difficulties posed by simple routing problems suggest that a closed form optimal policy may not be available. This motivates a requirement for good heuristic policies. We consider two approaches to the development of dynamic routing heuristics. We develop an idea proposed, in the context of simple single class systems, by Krishnan (1987) by applying a single policy improvement step to some given static policy. The resulting dynamic policy is shown to be of simple structure and easily computable. We include an investigation into the comparative performance of the dynamic policy with a number of competitor policies and of the performance of the heuristic as the number of stations in the network changes. In our second approach the generic traffic may only access processing when the station has been cleared of all (higher priority) jobs and can be considered as background work. We deploy a prescription of Whittle (1988) developed for RBPs to develop a suitable approach to station indexation. Taking an approximative approach to Whittle's proposal results in a very simple form of index policy for routing the generic traffic. We investigate the closeness to optimality of the index policy and compare the performance of both of the dynamic routing policies developed here

Markov-modulated and feedback fluid queues

In the last twenty years the field of Markov-modulated fluid queues has received considerable attention. In these models a fluid reservoir receives and/or releases fluid at rates which depend on the actual state of a background Markov chain. In the first chapter of this thesis we give a short introduction on how the stationary distribution for such a model is usually found, as well as a literature overview on Markov-modulated and related uid queues. The rest of the thesis is concerned with �nding stationary distributions for some types of fluid models that have received little or no attention until now. The two main contributions are the following.\ud 1. We focus on models in which the state space of the regulating Markov process is infinitely large, either denumerable or not. Regarding the first type, we mainly look into regulating processes that are of birth-death type. We present procedures to find the stationary distribution, using the theory of orthogonal polynomials. In the nondenumerable case, we look into simple systems of fluid queues, in which one fluid queue regulates the behaviour of another (one example being a fluid tandem queue).\ud 2. We look into models in which the state of the fluid reservoir in quences the behaviour of the regulating process, so that the latter does not constitute a Markov process. We call suchlike systems feedback fluid queues, to emphasize the two-way dependence between fluid reservoir and regulating process

Discrete Event Systems: Models and Applications; Proceedings of an IIASA Conference, Sopron, Hungary, August 3-7, 1987

Work in discrete event systems has just begun. There is a great deal of activity now, and much enthusiasm. There is considerable diversity reflecting differences in the intellectual formation of workers in the field and in the applications that guide their effort. This diversity is manifested in a proliferation of DEM formalisms. Some of the formalisms are essentially different. Some of the "new" formalisms are reinventions of existing formalisms presented in new terms. These "duplications" reveal both the new domains of intended application as well as the difficulty in keeping up with work that is published in journals on computer science, communications, signal processing, automatic control, and mathematical systems theory - to name the main disciplines with active research programs in discrete event systems. The first eight papers deal with models at the logical level, the next four are at the temporal level and the last six are at the stochastic level. Of these eighteen papers, three focus on manufacturing, four on communication networks, one on digital signal processing, the remaining ten papers address methodological issues ranging from simulation to computational complexity of some synthesis problems. The authors have made good efforts to make their contributions self-contained and to provide a representative bibliography. The volume should therefore be both accessible and useful to those who are just getting interested in discrete event systems

Dynamic scheduling of manufacturing systems with setups and random disruptions

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 249-256).Manufacturing systems are often composed of machines that can produce a variety of items but that most undergo time-consuming (and possibly costly) setups when switching between product types. Scheduling these setups efficiently can have important economic effects on the performance of the plant and involves a tradeoff between throughput, inventory, and operating costs. In addition, the schedule must be robust to random disruptions such as failures or raw material shortages, which are common in production environments. In this thesis, we study policies that address the setup scheduling problem dynamically, in response to current conditions in the system. A new heuristic, called the Hedging Zone Policy (HZP), is introduced and developed. It is a dynamic-sequence policy that always produces the current part type at its maximum production rate until a fixed base stock level is reached. Then, before switching setups, the policy might produce the current part type at its demand rate for some additional time. When selecting changeovers, the HZP implements two types of decision rules. If the difference between base stock and surplus level is small for all part types, the item with the largest weighted difference is selected. Otherwise, the policy uses a fixed priority ranking to select between items that are far from their base stock value. In order to demonstrate the benefits of our policy, we also adapt and implement several other heuristics that have been proposed in the literature for related models. The policies are first analyzed in a purely deterministic setting. The stability of the HZP is addressed and it is shown that a poor selection of its parameters leads to a condition in which some low-priority parts are ignored, resulting in an unstable system. Using Lyapunov's direct method, we obtain an easy-to-evaluate and not-too-conservative condition that ensures production of all part types with bounded surplus. We then compare, through a series of extensive numerical experiments with three-part-type systems, the deterministic performance of the policies in both make-to-order and make-to-stock settings. We show that the HZP outperforms other policies within its class in both cases, a fact that is mainly attributed to its priority-based decisions. When compared to the approximate optimal cost of the problem, our policy performs very well in the make-to-order case, while the simplicity of its base stock structure makes it less competitive in the deterministic make-to-stock problem. The results are then leveraged for the study of a stochastic model, where we consider the effect of random disruptions in the form of machine failures. We prove that our model converges to a fluid limit under an appropriate scaling. This fact allows us to employ our deterministic stability conditions to verify the stochastic (rate) stability of the failure-prone system. We also extend our previous numerical experiments by characterizing the performance of the policies in the stochastic setting. The results show that the HZP still outperforms other policies in the same class. Furthermore, we find that except for cases where failures occur much less or much more frequently than changeovers, the HZP outperforms a fixed-sequence policy that is designed to track a pre-determined, near-optimal deterministic schedule.by Fernando Tubilla.Ph.D