Traveling times in a FIFO-stochastic event graph are compared in increasing convex ordering for different arrival processes. As a special case, a stochastic lower bound is obtained for the sojourn time in a tandem network of FIFO queues with a Markov arrival process. A counterexample shows that the extended Ross conjecture is not true for discrete-time arrival processes.

We consider a single-server queuing system with two job classes under service policies of threshold type. The server switches from type 1 to type 2 when either the former queue is empty or the latter reaches size T; it switches from type 2 to type 1 when the former queue size drops below T and the latter is not empty. The joint queue-length distribution is determined for preemptive and nonpreemptive implementations using both analytic techniques and the power series algorithm.

Multiclass single-server systems with significant setup times (polling models) are common in industry. This article considers asymptotics for polling models with increasing setup times. Two types of polling model are considered, namely (a) polling models with polling tables, exhaustive service, and deterministic setups, and (b) cyclic exhaustive service polling models with general setups under heavy traffic. It is shown that as the mean setup time increases to infinity, the scaled intervisit time for each queue (time between service of that queue) converges in probability to a constant. This, in turn, is shown to imply that scaled steady-state waiting time converges in distribution to either a uniform distribution or a simple discrete random variable multiplied by a uniform random variable as setups tend to infinity. These results lead to considerable insight into the behavior of systems with setups, and conclusions are drawn with respect to previous studies.

A pool design is random if it varies according to a probability distribution. There are four types of random design proposed in the literature: random incidence design, random k-set design, random distinct k-set design, and random k-size design. Recently Hwang gave an approximation to estimate the number of unresolved positives for random distinct k-set design. In this article, we give exact formulas for all four types of random designs for estimating the number of unresolved positives. We also do some numerical comparisons of the four designs.

A one-dimensional diffusion process is controlled in the interval [−d, d]. The aim is to maximize the survival time in [−d, d]. Two cost criteria, which do not depend on the control variable, are considered. Particular problems are solved explicitly.

Bounds for aging properties in mixtures and their derivatives are provided. Such bounds allow control of the behavior of those characteristics through the aging properties of the distributions in the mixture. We also obtain some results for discrete mixtures involving exponential distributions. In addition, well-known mixture-preserving properties for several distribution classes are derived with little algebraic complexity.

In view of the growing importance of reversed hazard rate (RHR) in reliability analysis and stochastic modeling, we have considered different implicative relationships with respect to the monotonic behavior of RHR. In that context, a few characterizing properties have also been presented based on expected inactivity time.

A stochastic dynamic program incurs two types of cost: a service cost and a quality of service (delay) cost. The objective is to minimize the expected average service cost, subject to a constraint on the average quality of service cost. When the state space S is finite, we show how to compute an optimal policy for the general constrained problem under weak conditions. The development uses a Lagrange multiplier approach and value iteration. When S is denumerably infinite, we give a method for computation of an optimal policy, using a sequence of approximating finite state problems. The method is illustrated with two computational examples.