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Using a G/M/s/N queuing system model, we develop a processor utilization model for a simplified multiprocessor computer system. Jobs are assumed to arrive according to a general input process, and each job is assigned randomly to an available processor. A finite capacity input buffer is used if no processor is available. The mathematical model is based on the busy period analysis, and two utilization measures are derived: processor utilization (the fraction of processor occupation time during a busy cycle) and system utilization (the fraction of actual utilization time for all processors). A computational model for these utilization measures is developed through an imbedded Markov chain approach. Experimentation with the computational model reveals the sensitivity of the model to variability in the arrival process. Comparison of 2-processor and 4-processor systems from the operator perspective indicates a qualified preference for the behavior of the 2-processor system. This preference must be carefully interpreted since processor costs, the increase in overhead with an increase in processors, and behavioral variables reflecting the user perspective are excluded. [ABSTRACT FROM AUTHOR]

A reduced system is a smaller system derived in the process of analyzing a larger system. In solving for steady state probabilities of a Markov chain, generally the solution can be found by first solving a reduced system of equations which is obtained by appropriately partitioning the transition probability (or rate) matrix. Following Lal (1981), a Markov chain can be categorized as standard or nonstandard depending on the location of an invertible submatrix necessary for an efficient solution in a transition probability (or rate) matrix. In this paper, algorithms for the determination of steady state probabilities are developed by using (i) a backward recursion which is efficient for standard systems and (ii) a forward recursion which is efficient for nonstandard systems. It is also shown that the backward recursion can be used for finding the first passage time distribution and its mean and variance. [ABSTRACT FROM AUTHOR]

A transportation queueing process in which taxis arrive in a Poisson process and customers arrive as a renewal process independent of taxi-arrival process is controlled by calling extra taxis whenever the total number of customers lost to the system reaches a certain predetermined number. Transient and steady state behavior of this process is studied using renewal theoretic arguments. The optimum value of the control variable is also obtained so as to minimize the total cost to the system due to the waiting taxis and lost customers. [ABSTRACT FROM AUTHOR]

Queueing Theory has been attacked on two fronts. Some theoreticians say that Queueing Theory is closed. Some practitioners feel that there is very little in it for use. In view of this, it seems that after six decades of development it is time for stock taking. It is hoped that a discussion of the problems, achievements and the shortcomings of Queueing Theory will be helpful for both theorists and practitioners by putting things in proper perspective. This paper reviews some of the major strides taken by Queueing Theory with respect to its three constituent problems: (i) Behavioral, (ii) Statistical, and (iii) Operational. If one looks at the general picture of the developments in these area it is hard not to conclude that, in spite of the practitioners' accusations, the systems studied have become more and more realistic over the years. This review makes an attempt to bring this out. An extensive bibliography which is directive in nature rather than exhaustive should be helpful to an interested researcher or a practitioner in identifying the articles of his interest. A discussion of the future of Queueing Theory concludes the paper. [ABSTRACT FROM AUTHOR]

This paper presents a statistical technique for the control of the traffic intensity in single-server queuing systems with (i) Poisson arrivals and general service times and (ii) recurrent arrivals and exponential service times. The procedure is such that the system is readjusted only if the number of customers in the system either falls and stays beyond the upper control limit longer than a pre-assigned number of consecutive transitions or falls and stays below the lower control limit longer than a preassigned number of consecutive transitions. Methods are given to derive these two pairs of control limits using available transition probability tables, and tables of control limits have been provided for a selected number of parameter values in the queue with Poisson arrivals and general service times. [ABSTRACT FROM AUTHOR]

This paper defines two finite time measures that describe the transient behavior of queuing systems and investigates their convergence properties in some detail. These measures are: (i) a utilization factor that gives the fraction of time during which the system is expected to be busy, and (ii) an effectiveness factor that gives the ratio of the lengths of time during which the system is expected to be busy and idle, respectively. For the sake of convenience, these are expressed relative to their steady-state values. Tables are provided for these two measures in special cases. [ABSTRACT FROM AUTHOR]

Stochastic systems with multiple inputs are common in practice. This paper investigates such a system with random and scheduled inputs, and determines the equilibrium behavior of the basic process (a waiting-time process if the system is a queue, or a storage process if it is a storage system) by reducing the problem to the solution of an integral equation, which is solved by the method of factorization. [ABSTRACT FROM AUTHOR]

In this paper, treating time as a discrete variable, we study the transient behavior of a bulk-service queuing system in which the number of customers arriving within a fixed time interval follows a binomial probability distribution. The service times are assumed to be identically distributed and statistically independent. The busy period and queue length distributions have been obtained in terms of probability generating functions. [ABSTRACT FROM AUTHOR]

The article discusses the determination of transition probabilities for the single-server queuing system in which there is arbitrary service time distribution and in which customers arrive in Poisson pattern. The study is a continuation of N. U. Prabhu's work titled "Some Results for the Queue with Poisson Arrivals." It was concluded that the transforms of the transition probabilities can be obtained and are seen to be the same as those derived by Donald P. Gaver, Jr. by alternative methods in his study titled "Imbedded Markov Chain Analysis of a Waiting Line Process in Continuous Time."

This article presents a rejoinder to the article "The Value of Queueing Theory," by Jack Byrd. The major problem with the so-called operations research practitioners who decry the value of queueing theory is that they are not familiar with the areas where it is most useful. Many of the "valuable" queueing theory papers appear in application area journals such as "The Bell System Technical Journal," "Ericsson Technics," "Transportation Science," "Journal of the ACM," and "IBM Journal on Research and Development." The nature of the problems discussed in these articles is a far cry from the one represented by the illustrative examples of the article. Many times, standard models are not appropriate. It should be noted that in linear programming one learns a technique. But, if a queueing theory course is taught by analyzing some specific systems, one learns the properties of those specific systems. Therefore, there is a major need in operations research education to emphasize probabilistic modeling and analysis techniques using queueing systems as examples. Then students are not baffled by real life situations that do not fit with the ones they have studied in class or seen in books and journals.