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.

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.

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.

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 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.

An operational profile describes, in a probabilistic way, how a software is utilized by its users. It makes the testing procedure more realistic and efficient. We consider a model where the software is tested sequentially in all of the operations that it is designed to perform. The stochastic and deterministic model parameters involving costs and failures all depend on the operations. In particular, the failure process generated by each fault is quite general and debugging is not necessarily perfect. Our aim is to find the optimal testing durations in all of the operations in order to minimize the total expected cost. This problem leads to an interesting nonlinear programming formulation that can be solved using well-known procedures in convex optimization.

The Waxman graphs are frequently chosen in simulations as topologies resembling communications networks. For the Waxman graphs, we present analytic, exact expressions for the link density (average number of links) and the average number of paths between two nodes. These results show the similarity of Waxman graphs to the simpler class G>p(N). The first result enables one to compare simulations performed on the Waxman graph with those on other graphs with same link density. The average number of paths in Waxman graphs can be useful to dimension (or estimate) routing paths in networks. Although higher-order moments of the number of paths in Gp(N) are difficult to compute analytically, the probability distribution of the hopcount of a path between two arbitrary nodes seems well approximated by a Poisson law.

This article concerns Markov decision chains with finite state and action spaces, and a control policy is graded via the expected total-reward criterion associated to a nonnegative reward function. Within this framework, a classical theorem guarantees the existence of an optimal stationary policy whenever the optimal value function is finite, a result that is obtained via a limit process using the discounted criterion. The objective of this article is to present an alternative approach, based entirely on the properties of the expected total-reward index, to establish such an existence result.