A stochastic process {Xt(s)} is viewed as a collection of random variables parameterized by time (t) and the initial state (s). {Xt(s)} is termed spatiotemporally increasing and convex if, in a sample-path sense, it is increasing in s and t and satisfies a directional convexity property, which implies that it is increasing and convex in s and in t (individually) and is supermodular in (s, t). Simple sufficient conditions are established for a uniforniizable Markov process to be spatiotemporally increasing and convex. The results are applied to study the convex orderings in GI/M(n)/l and M(n)/G/1 queues and to solve the optimal allocation of a joint setup among several production facilities. For a counting process that possesses a stochastic intensity, we show that its spatiotemporal behavior can be characterized by its conditional intensity via a birth process.

Motivated by packetwise transmission of data in telecommunications, we introduce a fluid model with a continuous burst arrival process ψ = {(tn, Sn):n ≥ 0}. Each epoch, tn, begins a burst of length Sn that is, a continuous flow of fluid (work, information, etc.) at rate 1 to a system. The system processes fluid at rate 1. The model more generally can be used to approximate a storage system where fluid arrives over time due to many different (unrelated) sources. We analyze the model using sample path techniques (ψ is assumed deterministic, having arisen as a sample path from some underlying probability space) and by doing so obtain a variety of expressions for such quantities as average work inc system and average work in service as well as the empirical distribution for work in service. The expressions are given in terms of familiar quantities (such as customer delay) from the corresponding classic single- and infinite-channel queues that we construct from the same arrival sample path. In particular, we obtain an interesting decomposition of work in terms of the work in these two wellknown queueing models. In our final remarks, we also point out the optimality features of this model when compared to other models having different rules regulating the flow of burst work. In addition, we also give some stochastic ordering results when comparing two burst systems of the M/GI/1 or GI/M/1 type.

We consider the optimal scheduling of a finite capacity shuttle in a two-node network with imperfect information. When shuttle trips do not depend on the number of passengers carried, we prove optimality and monotonicity of threshold policies. We derive conditions for dispatching that reduce the computational effort required to compute an optimal threshold policy. We prove a counter-example to the optimality of threshold policies for finite horizon problems where trip lengths increase stochastically in the number of passengers carried.

We consider two nodes in tandem. At each node or service center, there are two exponential servers present with the same service rate μ and each with its own queue. Customers arrive at the first node according to a Poisson process with arrival rate λ. At their arrival, they have to be assigned to one of the servers, so they are routed to one of the queues at node 1. Customers leaving center 1 enter node 2 and are routed to one of the queues at node 2. In this paper, we consider the case with full information and the case with partial information.

We continue the study of our general cost structure for a maintained system. Here we focus on the optimization questions for an age or block policy. The notion of a marginal cost function is rigorously formulated and its utility investigated. Various applications are considered, including a new model in which minimal repairs are performed as long as the total accumulated repair costs do not exceed a fixed amount.

Sensitivity analysis represents an important aspect of network flow design problems. For example, what is the incremental increase in system flow of increasing the diameters of specified pipes in a water distribution network? Although methods exist for solving this problem in the deterministic case, no comparable methodology has been available when the network's arc capacities are subject to random variation. This paper provides this methodology by describing a Monte Carlo sampling plan that allows one to conduct a sensitivity analysis for a variable upper bound on the flow capacity of a specified arc. The proposed plan has two notable features. It permits estimation of the probabilities of a feasible flow for many values of the upper bound on the arc capacity from a single data set generated by the Monte Carlo method at a single value of this upper bound. Also, the resulting estimators have considerably smaller variancesthan crude Monte Carlo sampling would produce in the same setting. The success of the technique follows from the use of lower and upper bounds on each probability of interest where the bounds are generated from an established method of decomposing the capacity state space.

Two approaches for simulating the reliability function are considered–one using the total hazard estimator and the other using importance sampling. It is shown both for the Wheatstone Bridge System and for a triangular system that the total hazard estimator has significantly smaller variance when compared both to the standard importance sampling estimator and to an improved version of it.

An external uniformization technique was developed by Ross [4] to obtain approximations of transition probabilities of finite Markov chains in continuous time. Yoon and Shanthikumar [7] then reported through extensive numerical experiments that this technique performs quite well compared to other existing methods. In this paper, we show that external uniformization results from the strong law of large numbers whose underlying distributions are exponential. Based on this observation, some remarks regarding properties of the approximation are given.

This paper proposes a logistic approximation to the upper tail of the t distribution and its inverse that is more convenient and more accurate than those of Shah and Allen [3], and Koehler [1] and Lin [2], when measured in terms of the number of keystrokes and absolute relative errors, respectively.

We present a fast algorithm for random numbers distributed uniformly on (0,1). In contrast to most other generators, it uses no floating point operations. Instead, the internal bit representation of the numbers is generated directly from a random bit source. It can easily be implemented in high-level languages like Modula-2 and shows good empirical behavior.