We study the scheduling of jobs in a system of two interconnected service stations, called Q1 and Q2, on m(m ≥ 2) identical machines available in parallel, so that every machine can process any jobs in Q1 or Q2. Preemption is allowed. Under certain conditions on the arrival, service, and interconnection processes, we determine a scheduling policy that minimizes the expected makespan.

A carousel is a computer-controlled warehousing system, which is widely used to store small- and medium-sized goods. One of the most important performance characteristics of such systems is the pick time of an order, which mostly depends on the travel time of the carousel. In this article, we consider some reasonable heuristics for order picking. In particular, we establish properties of the Nearest Item (NI) heuristic. This one is frequently used in practice. We derive tight upper bounds for the travel time under the NI heuristic and closed-form expressions for its mean and variance. We also present a simple two-moment approximation for the distribution of the travel time. In addition, we find the mean, variance, and distribution for the number of turns.

We present a performance analysis of a multiaddress call extraction server. The extraction server splits a multiaddress call into individual calls. The operation mechanisms of the server are complicated, and it is difficult to apply the standard Markov chain technique directly. Assuming the case when the server is offered by saturated input, we propose a simple probabilistic method to give the probability distribution that is related to the number of extracted calls. Applying the method, we also obtain the throughput of the extraction server. Assuming an unsaturated input, we evaluate the mean waiting time of an individual call using a diffusion approximation. Numerical simulations are performed and compared with our results. These results indicate the accuracy of our modeling approach.

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 two single-server queues in tandem. The customers receive service at the first station and then they proceed to the second. There are no intermediate waiting positions and, so, the blocking phenomenon is observed. The arriving customers who find the first station unavailable (busy or blocked) behave like retrial customers. We consider the case of “constant retrial policy.” For such a system, we obtain the system state probabilities in steady state in terms of generating functions. We present also some interesting measures of the system performance and directly deduce results for the corresponding ordinary (without retrials) model. We consider, finally, the special case of exponential service times as an example.

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.

We present the production version of two EOQ-type models in heavy traffic. The output is interpreted by random demand and the input by a deterministic production plus random returns. In the ON part of the cycle, the inventory content is a reflected Brownian motion, and in the OFF part, it is a Brownian motion with a negative drift. The ON/OFF periods generate an alternative renewal process and the content-level process is a regenerative process. Two control policies are considered. In one policy that is natural under conditions of continuous review, production is stopped when the content level in the ON period reaches a predetermined level q. In the other policy, which resembles periodic review, production is stopped when the ON time reaches a predetermined time t0.

In this article, we study a method to compare queueing systems and their fluid limits. For a certain class of queueing systems, it is shown that the expected workload (and certain functions of the workload) is higher in the queueing system than in the fluid approximation. This class is characterized by convexity of the value function in the state component(s) where external arrivals occur. The main example that we consider is a tandem of multiserver queues with general service times and Markov-modulated arrivals. The analysis is based on dynamic programming and the use of phase-type distributions. Numerical examples to illustrate the results are also given.

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.

We consider a batch scheduling problem in which the processing time of a batch of jobs equals the maximum of the processing times of all jobs in the batch. This is the case, for example, for burn-in operations in semiconductor manufacturing and other testing operations. Processing times are assumed to be random, and we consider minimizing the makespan and the flow time. The problem is much more difficult than the corresponding deterministic problem, and the optimal policy may have many counterintuitive properties. We prove various structural properties of the optimal policy and use these to develop a polynomial-time algorithm to compute the optimal policy.

Consider the GI/GI/1 queue with the Last-Come First-Served Preemptive-Resume service discipline. We give intuitive explanations for (1) the geometric nature of the stationary queue length distribution and (2) the mutual independence of the residual service requirements of the customers in the queue, both considered at arbitrary time points. These distributions have previously been established in the literature by either first considering the system at arrival instants or using balance equations. Our direct arguments provide further understanding of properties 1 and 2.

Tandem queues with finite buffers have been widely discussed as basic models of communication and manufacturing systems. The cycle time is the important measure in such systems. In this article, we consider finite tandem queues with communication blocking and general service-time distributions. We introduce an order on pairs of random variable sets to give effective upper bounds for the expected cycle times.

Using a weak derivation approach to gradient estimation, we consider the problem of pricing an American call option on stock paying dividends at discrete times. Similar simulation-based sensitivity estimators were introduced earlier by Fu and Hu (1995) who used smoothed perturbation analysis. We improve upon their results by presenting an estimator with a uniformly lower variance. In addition, we reduced the multidimensional optimization problem of pricing an option with multiple ex-dividend dates to a one-dimensional one. Numerical examples indicate that this approach saves a considerable amount of computation time. Our estimator holds uniformly for a class of payoff functions, and applications to other types of options will be addressed in the article.

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.

Variance reduction techniques are often underused in simulation studies. In this article, we indicate how certain ones can be efficiently employed when analyzing queuing models. The first technique considered is that of dynamic stratified sampling; the second is the utilization of multiple control variates; the third concerns the replacement of random variables by their conditional expectations when trying to estimate the expected value of a sum of random variables.

We consider a fluid system in which during off-times the buffer content increases as a piecewise linear process according to some general semi-Markov process, and during on-times, it decreases with a state-dependent rate (or remains at zero). The lengths of off-times are exponentially distributed. We show that such a system has a stationary distribution which satisfies a decomposition property where one component in the decomposition is associated with some dam process and the other with a clearing process. For the cases of constant and linear decrease rates, the steady-state Laplace–Stieltjes transform and moments of the buffer content are computed explicitly.

We study vehicle waiting times at a traffic lane that is shared by traffic from two directions. In contrast to crossovers, we focus on instances where the vehicle passing time of the shared infrastructure can be large. The motivation for this model arises from our research on underground transportation systems. We examine vehicle waiting times under periodic control rules (i.e., the driving direction on the infrastructure is switched between two directions according to a fixed time schedule). We analyze both symmetric and asymmetric systems (i.e., vehicle arrival rates as well as effective green and red periods may be different for both directions). In fact, we are dealing with a single server, two-queue polling system with random setup times and periodic (nonexhaustive) service discipline. We develop approximations for the mean waiting time and we show by comparison to simulation results that the accuracy is usually in the range of 1–2% for Poisson arrivals. Also, we indicate how our approximations can be generalized to compound Poisson arrivals.

The purpose of this article is to describe various conditions on the parameters of pairs of nonhomogeneous Poisson or pure birth processes under which the corresponding epoch times or interepoch intervals are stochastically ordered in various senses. We derive results involving the usual stochastic order, the multivariate hazard rate order, the multivariate likelihood ratio order, as well as the dispersive and the mean residual life orders. A sample of applications involving generalized Yule processes, load-sharing models, and minimal repairs in reliability theory illustrate the usefulness of the new results.

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.

For a normal sample with unknown mean, the almost universally used estimator of the variance, σ2, is “the sample variance.” This estimator is the minumum variance unbiased estimator of σ2, but it is inadmissible under square error loss. It is dominated by the maximum likelihood estimator, which is also inadmissible. We consider a class of estimators and compare these estimators under a class of loss functions which we call “log symmetric.”