We establish functional central limit theorems (FCLTs) for a cumulative input process to a fluid queue from the superposition of independent on–off sources, where the on periods and off periods may have heavy-tailed probability distributions. Variants of these FCLTs hold for cumulative busy-time and idle-time processes associated with standard queueing models. The heavy-tailed on-period and off-period distributions can cause the limit process to have discontinuous sample paths (e.g., to be a non-Brownian stable process or more general Lévy process) even though the converging processes have continuous sample paths. Consequently, we exploit the Skorohod M1 topology on the function space D of right-continuous functions with left limits. The limits here combined with the previously established continuity of the reflection map in the M1 topology imply both heavy-traffic and non-heavy-traffic FCLTs for buffer-content processes in stochastic fluid networks.

Let F and G be life-length distributions such that F [D over less-than or equals] G. We solve the following problem: How should (X,Y) be generated in order to maximize [hollow letter P](X = Y), under the conditions X [D over equals] F, Y [D over equals] G, and X ≤ Y? We also find a necessary and sufficient condition for the existence of such a maximal coupling with the property that X and Y are independent, conditioned that X < Y. It is pointed out that using familiar Poisson process thinning methods does not produce (X,Y) which maximizes [hollow letter P](X = Y).

We show that several truncation properties of queueing systems are consequences of a simple property of censored stochastic processes. We first consider a discrete-time stochastic process and show that its censored process has a truncated stationary distribution. When the stochastic process has continuous time, we present a similar result under the additional condition that the process is locally balanced. We apply these results to single-server batch arrival batch service queues with finite buffers and queueing networks with finite buffers and batch movements, and extend the well-known results on truncation properties of the MX/G/1/k queues and queueing networks with jump-over blocking.

We model a single-hop mobile network under centralized control with N service classes as a system of N weighted cost parallel queues with M (1 ≤ M < N) servers, arrivals, varying binary connectivity, and Bernoulli service success at each queue. We consider scheduling problems in this system and, under various assumptions on arrivals and connectivity, derive conditions sufficient, but not necessary, to guarantee the optimality of an index policy.

Results and conditions which quantify the decrease in dependence with lag for a stationary Markov process and enable one to compare the dependence for two stationary Markov processes are obtained. The notions of dependence used in this article are the supermodular ordering and the concordance ordering. Both discrete-time and continuous-time Markov processes are considered. Some applications of the main results are given. In queueing theory, the monotonicity results of the waiting time of the nth customer as well as the stationary waiting time in an MR/GI/1 queue and the stationary workload in a Markov-modulated queue are established, thus strengthening previous results while simplifying their derivation. This article is a continuation of those by Fang et al. [7] and Hu and Joe [10].

Customers arrive sequentially to a service system where the arrival times form a Poisson process of rate λ. The system offers a choice between a private channel and a public set of channels. The transmission rate at each of the public channels is faster than that of the private one; however, if all of the public channels are occupied, then a customer who commits itself to using one of them attempts to connect after exponential periods of time with mean μ−1. Once connection to a public channel has been made, service is completed after an exponential period of time, with mean ν−1. Each customer chooses one of the two service options, basing its decision on the number of busy channels and reapplying customers, with the aim of minimizing its own expected sojourn time. The best action for an individual customer depends on the actions taken by subsequent arriving customers. We establish the existence of a unique symmetric Nash equilibrium policy and show that its structure is characterized by a set of threshold-type strategies; we discuss the relevance of this concept in the context of a dynamic learning scenario.

We consider a K-node queueing system sharing a setup server. Each node has a node server, a finite buffer, and a service position. Each job in the buffer at a node requires a setup by the setup server to receive service from the node server at the service position. The arrival process of jobs at each node is Poisson, the distribution of node service times at each node is general, and the setup times have a common exponential distribution. The setup server behaves like M setup servers (i.e., the server can simultaneously process up to M jobs). We consider two setup mechanisms by the setup server. One is that for a setup of job at each node, both the waiting position (occupied by the job) and service position are used. The other is that only the service position is used for a setup. The model operating under the former or latter is referred to as Model I or II, respectively. For each node in Model I or II, we construct a corresponding setup server queue (CSQ). We show that the stationary distribution of Model I or II is given by a product form of the stationary distributions of CSQs.

We study an example of R. Bellman's gold-mining problem related to a programming job on the computer. The problem is formulated by dynamic programming and the optimal strategy is explicitly derived. The Bayesian version when the parameter involved is unknown is also solved by the same method. It is shown that the optimal strategy in each of two versions has the “no-island” (or, in other words, “control-limit”) property.

We show that if the payoff of a European option is a convex function of the prices of the security at a fixed set of times, then the geometric Brownian motion risk neutral option price is increasing in the volatility of the security. We also give efficient simulation procedures for determining the no-arbitrage prices of European barrier, Asian, and lookback options.

The linear k-within-(r, s)-out-of-(m, n):F lattice system consists of mn components arranged in m rows and n columns and fails whenever there is at least one rectangle of dimension r × s which contains k or more failed components. We propose recursive formulas for the calculation of the linear k-within-(r, s)-out-of-(m, n):F lattice system. The computing complexity of the system reliability using the recursive formulas is O((n − s)ms+1 + m2s) for r = m and O((r + 1)rs(m−r+1)[(n − s)m + 2r(s−1)ms]) for r < m.

We examine several approaches to derive lower and upper bounds on tail probabilities of discrete distributions. Numerical comparisons exemplify the quality of the bounds.

Let τk|n denote the lifetime of a k-out-of-n system constructed by using n components with independent (not necessarily identically distributed) lifetimes. It is shown that τk|n is smaller than τk−1|n−1 in the hazard rate order for any k and that τk|n−1 is smaller than τk|n in the reversed hazard rate order for any k. We thus strengthen and complement some results in Boland et al. [2] and Block et al. [1].

In [7], several conjectures are listed about uniformly most reliable graphs, and, to date, no counterexamples have been found. These include the conjectures that an optimal reliable graph has degrees that are almost regular, has maximum girth, and has minimum diameter. In this article, we consider simple graphs and present one counterexample and another possible counterexample of these conjectures: maximum girth (i.e., maximize the length of the shortest circuit of the graph G) and minimum diameter (i.e., minimize the maximum possible distance between any pair of vertices).

We consider sufficient conditions for stochastic equivalence of convex ordered random variables. Our main results apply to all convex ordered distributions on the real line and improve on a recent result of Huang and Lin [8] for equality in distribution of convex ordered survival times. Illustrative applications include testing for equality in distribution with convex ordered alternatives and demonstrating several earlier results on stochastic equivalence as special cases.

Achieving high throughput in input-queued switches has been found to be difficult, especially when traffic is nonuniform in the sense that different inputs have very different cell generation rates. We show that for general arrival processes, 100% throughput can be achieved with a simple algorithm that is very easy to implement.

We consider a switch in which in each time slot, at most one cell may be transmitted from each input, and at most one cell may be received at each output. Cells that are destined for output j arrive at input i according to a stationary and ergodic process, and arrivals are queued at the input. The problem is to decide which inputs are to transmit to which outputs in each time slot in order to maximize throughput. Necessary conditions for stability are that the total arrival rate to each input must be less than 1, and the total arrival rate destined to each output must be less than 1. We propose a simple scheduling algorithm and show that with this algorithm the necessary conditions for stability are also sufficient.

In this paper, we introduce and analyze simple, new inspection policies for maintaining deteriorating equipment with non-self-announcing failures. These policies utilize information from the inspection/repair history as well as the system lifetime distribution to schedule future inspections. Numerical results indicate that the policies can significantly outperform standard (periodic) maintenance strategies by providing higher availability for a given inspection rate.

The classical regenerative method of simulation output analysis exploits the regenerative structure of a stochastic process to break up a path into independent and identically distributed cycles based on a single sequence of regeneration times. If a process is regenerative with respect to more than one sequence of regeneration times, the classical regenerative method does not exploit the additional structure, and the variance of the resulting estimator for certain performance measures (e.g., the time-average variance constant) can vary greatly, depending on the particular regeneration sequence chosen. In a previous article, we introduced an efficiency-improvement technique for regenerative simulation of processes having two sequences of regeneration times based on permuting regenerative cycles associated with the second sequence of regeneration points. In this article, we show how to exploit more than two regeneration sequences. In particular, for birth–death Markov chains, the regenerations associated with hitting times to each state can all be exploited. We present empirical results that show significant variance reductions in some cases, and the results seem to indicate that the permuted estimator for the time-average variance constant can have a variance that is independent of the primary regeneration sequence used to run the simulation.

In this paper, we study the dependence properties of spacings. It is proved that if X1,..., Xn are exchangeable random variables which are TP2 in pairs and their joint density is log-convex in each argument, then the spacings are MTP2 dependent. Next, we consider the case of independent but nonhomogeneous exponential random variables. It is shown that in this case, in general, the spacings are not MTP2 dependent. However, in the case of a single outlier when all except one parameters are equal, the spacings are shown to be MTP2 dependent and, hence, they are associated. A consequence of this result is that in this case, the variances of the order statistics are increasing. It is also proved that in the case of the multiple-outliers model, all consecutive pairs of spacings are TP2 dependent.

Random k-set pool designs are known to be efficient but suffer the presence of clones having identical test sets (hence indistinguishable). We propose a random pool design with distinct k-sets. We give an algorithm to generate the design and compute the expected numbers of unresolved negatives and unresolved positives. We show a relation between the two numbers which holds also for other random designs; hence, it can be used to obtain their expected numbers of unresolved positives which are not known. Among these other random designs, the random size-k design is a new design.

Single-server queueing systems with mixed traffic are a flexible modeling tool that have been used to analyze polling systems and database striping strategies. They also have applications in manufacturing and telecommunication systems. Ordinary (open) customers arrive according to a Poisson process, receive service, and leave the system. Permanent (closed) customers remain in the system, reentering the queue after receiving service. This work examines the transient behavior of the permanent customers. The cycle times and output/departure process for the permanent customers are described.