We investigate the dependence induced among multiple Markov chains when they are simulated in parallel using a shared Poisson stream of potential event occurrences. One expects this dependence to facilitate comparisons among systems; our results support this intuition. We give conditions on the transition structure of the individual chains implying that the coupled process is an associated Markov chain. Association implies that variance is reduced in comparing increasing functions of the chains, relative to independent simulations, through a routine argument. We also give an apparently new application of association to the problem of selecting the better of two systems from limited data. Under conditions, the probability of incorrect selection is asymptotically smaller when the systems compared are associated than when they are independent. This suggests a further advantage to linking multiple systems through parallel simulation.

We consider a closed queueing network with a fixed number of customers, where a single server moves cyclically between N stations, rending service in each station according to some given discipline (Gated, Exhaustive, or the Globally Gated regime). When service of a customer (message) ends in station j, it is routed to station k with probability Pjk. We derive explicit expressions for the probability generating function and the moments of the number of customers at the various queues at polling instants and calculate the mean cycle duration and throughput for each service discipline. We then obtain the first moments of the queues' length at an arbitrary point in time. A few examples are given to illustrate the analysis. Finally, we address the problem of optimal dynamic control of the order of stations to be served.

Construction of a certain class of component tests for verification of series system reliability requires the use of some properties of the Poisson distribution that are not commonly known or used. This paper states and proves these results.

Most of the previous work on (s, S) inventory systems assumes that lead times for orders are such that orders never cross in time; i.e., the arrival of orders follows the same sequence as the placement of the orders. In this paper we consider more general mechanisms for random lead times. Because the introduction of a general random lead time mechanism makes the system essentially intractable for most performance measures of interest, simulation is a. natural candidate for estimating performance and/or optimizing the system. Two important issues in simulation are the stability and ergodicity of the system. Therefore, we first study some theoretical implications of the mechanism by providing conditions for which the system is stable and Harris ergodic, with the accompanying wide-sense regenerative properties. We then consider the problem of gradient estimation during simulation. Using the technique of perturbation analysis, we derive sample path-based gradient estimates for the finite-horizon average cost per period with respect to the parameters s and S and give a sample path proof of unbiasedness. We then show how stability and ergodicity can be used to simplify the estimators in the limiting infinite-horizon case and to establish strong consistency of the resulting estimators.

Necessary and sufficient conditions for the regularity and recurrence of right-skip-free Markov chains are established. These generalize classical results for the case of birth-and-death processes. Expressions for the general right eigenvectors of such chains are also given.

Results and conditions that quantify the decrease in dependence with lag for stationary Markov chains are obtained. Notions of dependence that are used are the concordance or positive quadrant dependence ordering, measures of dependence based on ψ-divergences such as the relative entropy measure of dependence, and the Goodman-Kruskal measure of association. The general results are mainly for first-order Markov chains, but there are also some results for higher order Markov chains.

In this paper we consider a fluid model of a single buffer in a random external environment modeled by an Ornstein-Uhlenbeck process. Such a model appears as the limiting case of the multiplexing model of Anick, Mitra, and Sondhi [2] in a heavy traffic environment. We use the change of measure technique to derive an exponential upper bound on the tail probabilities of the steady-state buffer content. We also establish an asymptotic upper and lower exponential bounds on the tail probabilities.

In this paper we analyze a queueing network consisting of parallel queues and arriving customers that have to be assigned to one of the queues. The assignment rule may not depend on the numbers of customers in the queues. Our goal is to find a policy that is optimal with respect to the long-run average cost. We will consider two cases: holding costs and waiting times. A recently developed algorithm for Markov decision chains with partial state information is applied. It turns out that the periodic policies found by this algorithm are close, if not equal, to the optimal ones.

This paper provides simple conditions for when the reliability of a system of independent components is better (worse) than the average reliability of the components. This result is useful in cases where little is known of the component reliabilities or the structure.

In this note using the notion of node criticality in Boland, Proschan, and Tong [2] and modular decompositions of coherent systems, we obtain algorithms and guidelines for allocating components in a k-out-of-R parallel modules system to maximize the system reliability. An illustrative example is given to compare a special case of our results with the previous result for series-parallel systems due to El-Neweihi, Proschan, and Sethuraman [5].

In contrast to the usual approach of using a normalizing transformation, a direct approximation for the percentiles of the t distribution is developed by using techniques of exploratory data analysis. The approximation is convenient to use and has sufficient accuracy for many applications of the t distribution.