A 2-by-2 buffered switch is the basic element of certain parallel data-processing networks. For a switch fed by two independent Bernoulli input streams, we find the joint distribution of the number of messages waiting in the two buffers at equilibrium, in the form of a bivariate generating function. The derivation uses complex-variable techniques developed by Kingman and by Flatto and McKean for the “shortest queue problem.” A number of asymptotic results are given, the principal one being the variance of the total number of waiting messages in the heavy-traffic limit.

This paper is divided into two distinct parts: the first considers a loss network, the second a queueing network. In each case, we consider a fully connected network consisting of a large number of links (queues) and operating under a dynamic routing policy known as least busy alternative routing. Using weak convergence results, we can examine the behavior of the networks as the number of links (queues) increases to infinity. We find that, despite the models having similarities and being amenable to the same analytical tools, they exhibit important differences in character.

This paper presents Monte Carlo techniques for evaluating equilibrium availability and mean up and down periods of a renewable network for a wide class of network operational criteria. The suggested method is based on a graph evolution model that overcomes the main difficulty–hitting low-probability “border” states of the criterion. Theoretical efficiency of the method is briefly discussed and numerical results are presented.

In this paper, we exactly analyze the performance of the slotted ALOHA access scheme with capture in a multichannel packet radio communication environment for the IFT (immediate-first-transmission) protocol and the DFT (delayed-first-transmission) protocol. We derive four moment generating functions for the following performance measures: (1) the number of packet deparures in each group of capture level in any slot, (2) the interval time between wo consecutive slot ends with the same number of departures, (3) the interval time between two consecutive slot ends with at least one departure and the number of departures in each group in that slot, and (4) the packet delay for each group. We calculate the averages and higher moments of these performance measures by differentiating the moment generating functions and numerically compare the systems with and without ower capture. The system consists of a finite population of Nstations, both fixed and mobile, that are divided into L different capture groups and access a set of parallel M channels to transmit their packets. Capture effect means that a packet transmitted by a station with a highest capture level can be received accurately, even when other packets in lower capture levels are simultaneously transmitted on the same channel and in the same slot. Numerical comparison to a multichannel system without capture is made. Capture effects on channel utilization, mean packet delay, and coefficients of variation of packet delay and interdeparture time are examined.

This paper considers routing to parallel queues in which each queue has its own single server and service times are exponential with nonidentical parameters. We give conditions on the cost function such that the optimal policy assigns customers to a faster queue when that server has a shorter queue. The queues may have finite buffers, and the arrival process can be controlled and can depend on the state and routing policy. Hence our results on the structure of the optimal policy are also true when the assigning control is in the “last” node of a network of service centers. Using dynamic programming we show that our optimality results are true in distribution.

Consider m machines in series with unlimited intermediate buffers and n jobs available at time zero. The processing times of job j on all m machines are equal to a random variable Xj with distribution Fj. Various cost functions are analyzed using stochastic order relationships. First, we focus on minimizing where cj is the weight (holding cost) and Tj the completion time of job j. We establish that if are in a class of distributions we define as SIFR, and and are increasing sequences of likelihood ratio-ordered and stochastic-ordered random variables, respectively, the job sequence [1, 2, … n ] is optimal among all static permutation schedules. Second, for arbitrary processing time distributions, if is an increasing sequence of likelihood ratio-ordered (hazard rate-ordered) random variables and the costs are nonincreasing, then a general cost function is minimized by the job sequence [1,2,…, n] in the stochastic ordering (increasing convex ordering) sense.

Four practically important extensions of the classical age-replacement problem are analyzed using Markov decision theory: (1) opportunity maintenance, (2) imperfect repair, (3) non-zero repair times, and (4) Markov degradation of the working unit. For this general model, we show that the optimal maintenance policy is of the control limit type and that the average costs are a unimodal function of the control limit. An efficient optimization procedure is provided to find the optimal policy and its average costs. The analysis extends and unifies existing results.

Markov modulated fluid models are studied in this paper. When the input of the fluid model is represented by one Markov chain, two approaches are given that result in asymptotic expressions for the overflow probability. Both approaches are based on large deviations theories. The equivalence of the expressions is proved. When the input is represented by N similar Markov chains, a reduction property is derived.

This paper deals with the two-dimensional stochastic process (X(t), V(t)) where dX(t) = V(t)dt, V(t) = W(t) + ν for some constant ν and W(t) is a one-dimensional Wiener process with zero mean and variance parameter σ2= 1. We are interested in the first-passage time of (X(t), V(t)) to the plane X = 0 for a process starting from (X(0) = −x, V(0) = ν) with x > 0. The partial differential equation for the Laplace transform of the first-passage time density is transformed into a Schrödinger-type equation and, using methods of global analysis, such as the method of dominant balance, an approximation to the first-passage density is obtained. In a series of simulations, the quality of this approximation is checked. Over a wide range of x and ν it is found to perform well, globally in t. Some applications are mentioned.