The use of the total hazard variable in simulation is studied. When estimating the mean time until a certain event occurs, this variable can be a powerful variance-reducing control variate. When estimating a small probability, it can be utilized as a direct estimator. Applications to reliability, quality control, and queueing are given.

Suppose that you find yourself trapped in a maze about which you know nothing except that it has an exit point. We present an optimal strategy that will lead you to the exit point in minimum expected time. This strategy ensures that the expected total length of the arcs you traverse will not exceed the sum of the lengths of the arcs in the maze.

We introduce the concept of “strong interchangeability” of random vectors. Strongly interchangeable random vectors arise naturally in packetized voice channels, M/G/1 queues, symmetric queueing networks, and other standard symmetric distributions. We study some properties of strongly interchangeable random vectors. We show that if (X1, …, XN) is a strongly interchangeable random vector, then even though there is no Markov property, taboo probabilities can be used to compute the joint distribution of ŽN = min1≤n≤N σnk=IXk and ZN = max1≤n≤N σnk=1Xk. For a special instance of this problem that arises in packetized voice communication, it is shown that the resulting algorithm essentially has a complexity of order N4. When ( σnk=1Xk, n = 1,… N) is an associated random vector bound for the joint distribution of ŽN and ZN are obtained and applied to the packetized voice communication problem.

A simple random algorithm (SRA) is an algorithm whose behavior is governed by a first-order Markov chain. The expected time complexity of an SRA, given its initial state, is essentially the time to absorption of the underlying chain. The standard approach in computing the expected runtime is numerical. Under certain conditions on the probability transition matrix of an SRA, bounds on its expected runtime can be obtained using simple probabilistic arguments. In particular, one can obtain upper and lower (average time) logarithmic bounds for certain algorithms based on SRAs.

The capacity of the white Gaussian noise (WGN) channel is widely stated as S/N0 nats/unit time. This conclusion is commonly derived either formally, or from the capacity, W ln(l + S/N0W), of the corresponding band-limited channel with bandwidth W, by taking W→8. In this paper, the WGN channel capacity is instead found directly by treating WGN as an arbitrary noise sequence that whitens in a general sense. In addition, the coding theorems proved make explicit the class of allowable receivers, either finite- or infinite-dimensional correlation receivers, or unconstrained. The capacities for these three receiver classes are found to be, respectively: S/N0 for S> 0, and 0 for S = 0; and 8 for all S ≥ 0. In those cases where the capacity is infinite, actual transmitter–receiver pairs are specified that achieve capacity.

Observations may be taken from one of the two populations. A randomized selection rule is one that chooses the populations according to some determined odds. The odds for choosing a population the next time may be dependent on all the observations taken so far from both populations. In this paper, the odds are made for the randomized selection rule in such a way that the number of observations from the better population relative to the number of observations from the other population grows at prescribed rates, typically of exponential order or faster. The rules include randomized play-the-winner rules and randomized analogues of Robbins' rules. Some Monte Carlo investigations are conducted to study these randomized selection rules for moderate sample sizes.

In this paper, we are concerned with the simulation of Gaussian random fields by means of iterative stochastic algorithms, which are compared in terms of rate of convergence. A parametrized class of algorithms, which includes stochastic relaxation (Gibbs sampler), is proposed and its convergence properties are established. A suitable choice for the parameter improves the rate of convergence with respect to stochastic relaxation for special classes of covariance matrices. Some examples and numerical experiments are given.

A consecutive k−out−of-n: F system is a coherent system of n-ordered components that functions if and only if there is no consecutive run of k failures among the components. Examples of such systems exist in telecommunications, oil pipelines, and integrated circuitry. Most of the research in reliability of consecutive k−out-of-n: F systems assumes that the components function independently of one another. In this paper, we develop a model incorporating positive dependence between adjacent components and show that for k ≥ (n + l)/2, the reliability of the system is a decreasing function of this dependence.

The same applies when a success occurs in large fields; in this case, p1 = 0. If at least one success occurs in each oilfield after a certain number of wells are drilled, then we reach a position where the number of undiscovered fields is represented by simple Euler distributions, and the results of Section 4.1 showed that the optimal rule is a one-step look-ahead rule.