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This paper deals with a multi-class priority queueing system with customer transfers that occur only from lower priority queues to higher priority queues. Conditions for the queueing system to be stable/unstable are obtained. An auxiliary queueing system is introduced, for which an explicit product-form solution is found for the stationary distribution of queue lengths. Sample path relationships between the queue lengths in the original queueing system and the auxiliary queueing system are obtained, which lead to bounds on the stationary distribution of the queue lengths in the original queueing system. Using matrix-analytic methods, it is shown that the tail asymptotics of the stationary distribution is exact geometric, if the queue with the highest priority is overloaded. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for computing minimal ordered Coxian representations of phase-type distributions whose Laplace-Stieltjes transform has only real poles. We first identify a set of necessary and sufficient conditions for an ordered Coxian representation to be minimal with respect to the number of phases involved. The conditions establish a relationship between the Coxian representations of a Coxian distribution and the derivatives of its distribution function at zero. Based on the conditions, the algorithm is developed. Three numerical examples show the effectiveness of the algorithm and some geometric properties associated with ordered Coxian representations. [ABSTRACT FROM AUTHOR]

The benefits of pooling risks, manifested in inventory management by consolidating multiple random demands in one location, are well known. What is less well understood are the determinants of the magnitude of the savings. Recently there has been speculation about the impact of demand variabilities on the benefits of risk pooling. We provide an example where increased variability of the individual demands actually reduces the benefits of risk pooling. We prove, however, that if we restrict increased variability to a common linear transformation, the greater the demand variabilities the larger the benefits of consolidating them, in agreement with intuition. We also provide bounds on the benefits of the consolidation of demands. Our results do not require independence of the demands, apply to any number of pooled demands, and are obtained in a pure cost-driven model. [ABSTRACT FROM AUTHOR]

We compute and analyze the probability that a particular random variable will assume the smallest value among a set of random variables. This work was motivated by wanting to predict the "winner" in R&D and patent "races". Some general results and comparative statics arc provided. For symmetric distributions we derive hounds on the probabilities of interest, We compute the probabilities of who will be the smallest (fastest) for normal, lognormal. Weibull. Pareto. binomial and PH-distributions. We also analyze several models of multivariate exponential distributions. [ABSTRACT FROM AUTHOR]

This paper develops two algorithms for computing the average total cost per product and other performance measures for a makcto-order inventory-production system. The two algorithms are developed by using matrix analytic methods. The first algorithm is based on the matrix-geometric solution of the Quasi-Birth-and-Death (QBD) Markov process. The second algorithm is based on the fundamental period of the QBD Markov process. The advantages and disadvantages of the two algorithms are discussed. [ABSTRACT FROM AUTHOR]

This paper studies the matrix R, which is the minimal nonnegative solution to a nonlinear matrix equation, raised in matrix analytic methods. Based on some partial orders defined on the transition matrix of Markov chains of GI/M/1 type, the monotonicity of the corresponding matrix R and its Perron­Frobenius eigenvalue is investigated. The results are useful in estimating tail probabilities of stationary distributions of Markov chains of GI/M/1 type and constructing upper bounds for the matrix R. Applications to the GI/MAP/1 queue are discussed as well. [ABSTRACT FROM AUTHOR]

For a queueing system with a low traffic intensity, the expected number of customers in the queue is small. However, with a bursty input process, long queues may build up in a short time. In this paper, we study light traffic queueing systems with bursty input processes. We study the distributions of queue lengths, waiting times, busy and active periods, and their corresponding expansions when the traffic intensity is small. Special attention goes to some conditional distributions of queue lengths, waiting times, and system-active periods. The expansions given in this paper provide a potential asymptotic approach to the computation of various descriptors of queueing sys- tems. The coefficients of those expansions reflect some important features of episodic queues. We also report numerical results which give a graphic view of our approximations and of the effect of the burstiness of the input and service processes on the queues. [ABSTRACT FROM AUTHOR]

A preface for the 2008 issue of "Annals of Operations Research" is presented.