Benjamin Avi-Itzhak

Approximate Queuing Models for Multiprogramming Computer Systems

In a multiprogramming computer system several jobs may be handled simultaneously by utilizing the central processing unit in processing one job while other jobs are being served by the peripheral devices. Our analysis of such a computer system proceeds in the following way. First we view the system as a closed queuing network with a fixed number of jobs, and obtain exact results for customer cycle times and server utilization. Then we use these results to develop an approximate model for the open system where the computer is fed by randomly arriving jobs. For the approximate model we obtain simple closed-form expressions for the delay distribution. The approximate model is then tested by comparing its result for the expected sojourn time to the exact results that we obtain for some special cases.

A Time-Sharing Queue with a Finite Number of Customers

A time-sharing queue serving a finite number of customers is described. It is assumed that both the service time and the time elapsing between termination of service and the next arrival of the same customer at the queue (service station) are exponential. The model was studied by Krishnamoorthi and Wood, but their results are not in complete agreement with the results of this paper. In addition, some new results are presented in terms of steady-state expectations.

Queuing Systems with Enforced Idle Time

Enforced idle time occurs in any queuing system in which it is possible for the server to be idle and the queue length to be nonzero simultaneously. This paper examines queuing systems in which the server is constrained to start service only at fixed intervals of time, with arrivals of customers and service completions occurring continuously. The GI/M/N, GI/D/N, M/D/N, and GI/G/1 queuing systems with enforced idle time are studied and some closed form steady-state results are presented. An application to railroad car pool systems is suggested.

Variable Load Pricing in the Face of Loss of Load Probability

In contrast to traditional methods which impose capacity costs on peak customers only, it is shown that, depending upon the design criterion employed in planning for the capacity expansion of the power system, off-peak marginal cost prices should also be imputed with some marginal capacity costs. Taking the loss of load probability (LOLP) design criterion as an example, we establish this conclusion formally, and suggest an algorithm to apportion accurately marginal capacity costs to various periods. The algorithm is then extended for power systems planned to meet a given loss of energy probability (LEOP) design target. Provisions to incorporate random deviations of customers demand and maintenance requirements in the calculation process are also suggested.

A Time-Sharing Model with Many Queues

This paper presents a mathematical study of a time-sharing system with a single server and many queues. In each queue a customer receives one quantum of service and is then sent to the end of the next queue, provided his service demand has not been completely satisfied. When a quantum of service is completed, the server attends to the first customer in the lowest-index nonempty queue. The discipline of the highest indexed queue is round-robin, while all other queues obey the FIFO rule. Newly arrived customers join the end of the first queue. The paper derives mathematical expressions for the main performance measures and illustrates them by graphical means.