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).

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.

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].

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.

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.

The stability properties of the bandwidth allocation algorithm First Fit are analyzed for some distributions on the sizes of the requests. Fluid limits are used to get the ergodicity results. When there are two possible sizes, the description of the transient behavior involves a finite Markov chain on the exit states of a transient Markov chain on a countable state space. The explicit expression of this exit matrix is given.

This paper investigates blocking probabilities obtained from multidimensional truncated Poisson distributions. For blocking probabilities typically arising in layered cellular mobile communications networks, the large deviations results of Gazdzicki et al. [9] are extended to state spaces determined by multiple constraints. The results yield asymptotically exact expressions that provide an accurate approximation of probabilities up to 1%, which considerably extends the applicability of large deviations results and enables efficient approximation of blocking probabilities for realistic mobile communications networks.

To protect the Dutch polders against flooding, more than 2500 km of dikes have been constructed. Due to settlement, subsoil consolidation, and relative sea-level rise, these dikes slowly sink “away into the sea” and should therefore be heightened regularly (at present, every 50 years). In this respect, one is interested in safe and cost-optimal dike heightenings for which the sum of the initial cost of investment and the future (discounted) cost of maintenance is minimal.

For optimization purposes, a maintenance model has been developed for dikes subject to uncertain crest-level decline. On the basis of engineering knowledge, crest-level decline has been modeled as a monotone stochastic process with expected decline being either linear or nonlinear (i.e., linear after transformation) in time. For both models and for a particular unit time, the increments are distributed according to mixtures of exponentials.

In a case study, the maintenance decision model has been applied to the problem of heightening the Dutch “Oostmolendijk.”