This paper introduces a new methodology for obtaining the stationary waiting time distribution in single-server queues with Poisson arrivals. The basis of the method is the observation that the stationary density of the virtual waiting time can be interpreted as the long-run average rate of downcrossings of a level in a stochastic point process. Equating the total long-run average rates of downcrossings and upcrossings of a level then yields an integral equation for the waiting time density function, which is usually both a linear Volterra and a renewal-type integral equation. A technique for deriving and solving such equations is illustrated by means of detailed examples.

A model is proposed for predicting the result of a football match from the previous results of both teams. This model underlies the method of identifying nonlinear dependencies by fuzzy knowledge bases. Acceptable simulation results can be obtained by tuning fuzzy rules using tournament data. The tuning procedure implies choosing the parameters of fuzzy-term membership functions and rule weights by a combination of genetic and neural optimization techniques.

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The purpose of this paper is to describe the new System Point method for analyzing queues. It considers the stationary probability distribution of the waiting time in variations of the M/M/R queue with first come first served discipline for a large class of service mechanisms. It is shown that the stationary probability density function of the waiting time evaluated at w > 0 can be interpreted as the long run average of the number of times that the virtual wait becomes less than w, per unit time. Theorems are presented which establish this interpretation of the probability density function of the virtual waiting time in terms of point processes generated by level crossings in the state space. These theorems, in combination with the principle of stationary set balance, generate a system of model equations that can be written directly. In addition, the forms of these equations are often linear Volterra integral equations of the second kind with parameter, which yield direct analytical solutions. An analogous theorem is proved for a variant of M/G/1. Two illustrative examples are presented.

A broad class of production-inventory systems is studied in which a number of producing machines are susceptible to failure following which they must be repaired to make them operative again. The machines' production can also be stopped deliberately due to stocking capacity limitations or any other relevant considerations. The interplay between the processes involved, namely, production, demand, and failure/repair or reliability, in conjunction with the shutdown policy used, determine the inventory accumulation process and possible shortages. We first obtain the stationary distribution of the inventory process for different assumptions on the random behavior of the production, demand, and reliability processes. By employing level-crossing techniques, a mathematical analysis is carried out for a “core” model, which then serves the role of the nucleus for the study of a wide range of models. We compute performance measures that characterize the operation of the production-inventory system with respect to its service-level to customers, expected inventory stocked, machines' utilization, repairmen utilization, and so on. A numerical illustration is provided which shows the effect of machine breakdowns on service and inventory levels.

We consider an (S − 1, S) type perishable inventory system in which the maximum shelf life of each item is fixed. An order for an item is placed at each demand time as well as at each time that the maximum shelf life of an item is reached. The order lead times are constant, and the demand process for items is Poisson. Although the resulting process is ostensibly nonregenerative, we adapt level-crossing theory for the case of an S-dimensional Markov process to obtain its stationary law. Within this framework a number of model variants are solved.

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A system of two parallel queues where the arrivals from a single stream of customers join the shorter queue is considered. Arrivals form a homogeneous Poisson stream and the service times in each of the two queues are independent exponential variates. By treating one of the queues as bounded, the steady‐state probability vector for the system can be expressed in a modified matrix‐geometric form and can be computed efficiently. Computational procedures for the sojourn time distribution and characteristics of the departure stream are developed. Some numerical results are presented, and based on these results an efficient approximation scheme for the model is developed which can be readily extended to systems with more than two parallel queues.