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.

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.

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.

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.”

Steady-state availability has long been a popular descriptor of effectiveness for repairable systems because it captures both the operability and repairability aspects of the system. A related measure of effectiveness is the availability of continuous service, which is particularly relevant for safety critical applications. In this article, two different measures of this quantity are described for a repairable system whose state is described by an ergodic finite-state-space continuous-time Markov chain. Using these ideas, formulas for computing system long-run mean time between failures and the long-run system reliability function are derived.

It is well known that mixtures of decreasing failure rate (DFR) distributions are always DFR. It turns out that, very often, mixtures of increasing failure rate (IFR) distributions can decrease at least in some intervals of time. Usually, this property can be observed asymptotically as t → ∞. In this article, several types of underlying continuous IFR distribution are considered. Two models of mixing are studied: additive and multiplicative. The limiting behavior of a mixture failure rate function is analyzed. It is shown that the conditional characteristics (expectation and variance) of the mixing parameter are crucial for the limiting behavior. Several examples are presented and possible generalizations are discussed.

Let X1,..., Xn be independent exponential random variables with possibly different scale parameters. Kochar and Korwar [J. Multivar. Anal. 57 (1996)] conjectured that, in this case, the successive normalized spacings are increasing according to hazard rate ordering. In this article, we prove this conjecture in the case of a single-outlier exponential model when all except one of the parameters are identical. We also prove that the spacings are more dispersed and larger in the sense of hazard rate ordering when the vector of scale parameters is more dispersed in the sense of majorization.