Tijms, H. C.A first course in stochastic models / Henk C. Tijms. p. cm. Includes bibliographical references and index. ISBN 0-471-49880-7 (acid-free paper)-ISBN 0-471-49881-5 (pbk. : acid-free paper) 1. Stochastic processes. I. Title. QA274.T46 2003 519.2 3-dc21 2002193371 British Library Cataloguing in Publication DataA catalogue record for this book is available from the British Library ISBN 0-471-49880-7 (Cloth) ISBN 0-471-49881-5 (Paper)

In many practical applications or multi-item inventory systems significant economies of scale can be exploited when coordinating replenishment orders for groups of items. This paper considers a continuous review multi-item inventory system with compound Poisson demand processes; excess demands are backlogged and each replenishment requires a lead time. There is a major setup cost associated with any replenishment of the family of items, and a minor (item dependent) setup cost when including a particular item in this replenishment. Moreover there are holding and penalty costs. We present an algorithm which searches for a simple coordinated control rule minimizing the long-run average cost per unit time subject to a service level constraint per item on the fraction of demand satisfied directly from on-hand inventory. This algorithm is based on a heuristic decomposition procedure and a specialized policy-iteration method to solve the single-item subproblems generated by the decomposition procedure. The model applies to multi-location inventory systems with similar cost structures for coordinated deliveries.multi-item inventory systems, coordinated replenishments, compound Poisson demand processes, service level constraint, policy-iteration algorithm

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Many real-world situations involve queueing systems in which customers wait for service for a limited time only and leave the system if service has not begun within that time. This paper considers a multiserver queueing system with impatient customers, where the customers arrive according to a Poisson process and the service requirements have a general distribution. A simple and insightful solution is presented for the loss probability. The solution is exact for exponential services and is an excellent heuristic for general service times.M/G/c queue, impatience, loss probability, heuristic

A queueing situation often encountered in practice is that in which customers wait for service for a limited time only and leave the system if not served during that time. This paper considers a single-server queueing system with Poisson input and general service times, where a customer becomes a lost customer when his service has not begun within a fixed time after his arrival. For performance measures like the fraction of customers who are lost and the average delay in queue of a customer we obtain exact and approximate results that are useful for practical applications.