Optimal control for multi-servers queueing systems under periodic review

This paper deals with the problem of finding the optimal dynamic operating policy for an M/M/S queue. The system is observed periodically, and at the beginning of each period the system controller selects the number of service units to be kept open during that period. The optimality criterion used is the total discounted cost over a finite horizon.     

Some comparative & design aspects of fixed cycle production systems

A serial production line is defined wherein a unit is produced if, and only if, all machines are functioning. A single buffer stock with finite capacity is to be placed immediately after one of the first N-1 machines in the N machine line. When all machines have equal probability of failure it is shown that the optimal buffer position is exactly in the middle of the line. This result is synthesized with the earlier work of Koenigsberg and Buzacott including an analysis of the covariance between transition states. An alternative model formulation is presented and integrated with previous results. Finally, a sufficient condition and solution procedure is derived for the installation of a buffer where there is a possible trade-off between increasing the reliability of the line versus adding a buffer stock.     

On the discrete-time queue length distribution under markov-dependent phases

The technique of probability generating functions has been applied to solve the steady state behavior of a discrete-time, single-channel, queueing problem wherein the arrivals to the queue at consecutive time-marks are statistically independent, but the service is accomplished in phases which are Markov-dependent. Special cases of importance have been discussed. In the end, mean number of phases, its special cases, the mean queue lengths, and the variances have been ascertained.     

Optimal policies for a multi-echelon inventory system with demand forecasts

Consider an inventory system consisting of two installations, the stocking point and the field. Each period two decisions must be made: how much to order from outside the system and how much to ship to the field. The first decision is made based on the total amounts of stock then at the two installations. Next a forecast of the demand in the current period is sent from the field to the stocking point. Based upon a knowledge of the joint distribution of the forecast and the true demand, and the amounts of stock at the two installations, a decision to ship a certain amount of stock to the field is taken. The goal is to make these two decisions so as to minimize the total n-period cost for the system. Following the factorization idea of Clark and Scarf (1960), the optimal n period ordering and shipping policy, taking into account the accuracy of the demand forecasts, can be derived so as to make the calculation comparable to those required by two single installations.     

Landmarks in defense literature

Military Leadership: In Pursuit of Excellence: edited by Robert L. Taylor and William E. Rosenbach. Westview Press, Boulder, Colorado, 253 pp. 1984.     

An M/M/1 queue with a general bulk service rule

A model of an M/M/1, bulk queue with service rates dependent on the batch size is developed. The operational policy is to commence service when at least L customers are available with a maximum batch size of K. Arriving customers are not allowed to join in-process service. The solution procedure utilizes the matrix geometric methodology and reduces to obtaining the inverse of a square matrix of dimension K + 1 - L. For the case where the service rates are not batch size dependent, the limiting probabilities can be written in closed form. A numerical example illustrates the variability of the system cost as a function of the minimum batch service size L.     

A new method to solve steady state queueing equations

There are a great number of queueing systems, including the M^X/M^Y/c, the Gl^X/M/c and the discrete Gl/G/1 queue in which the state probabilities are determined by repeated queue equations. This paper gives a simple, efficient and numerically stable algorithm to caiculate the state probabilities and measure of performance for such systems. The method avoids both complex arithmetric and matrix manipulations.     

A note on splitting the bump in an elimination factorization

This exposition presents a method for incorporating a technique known as “splitting the bump” within an elimination form reinversion algorithm. This procedure is designed to reduce fill-in during reinversion and should improve the efficiency of linear programming systems which already use the superior elimination form of the inverse.     

Optimal control of price through restricted production

Consider a regulated monopolist whose current profits would be maximized if they could charge a price p?, where p? exceeds the current market price. By reducing production below current consumer demand the monopolist can create an illusion of a shortage and induce the regulator to allow a price increase. Conditions are given for which the production rate that maximizes the monopolist's expected discounted profits over an infinite horizon will have the property that the amount of unsatisfied consumer demand will be a non-increasing function of current market price.     

Computing the discounted return in markov and semi-markov chains

This paper addresses the problem of computing the expected discounted return in finite Markov and semi-Markov chains. The objective is to reveal insights into two questions. First, which iterative methods hold the most promise? Second, when are interative methods preferred to Gaussian elimination? A set of twenty-seven randomly generated problems is used to compare the performance of the methods considered. The observations that apply to the problems generated here are as follows: Gauss-Seidel is not preferred to Pre-Jacobi in general. However, if the matrix is reordered in a certain way and the author's row sum extrapolation is used, then Gauss-Seidel is preferred. Transforming a semi-Markov problem into a Markov one using a transformation that comes from Schweitzer does not yield improved performance. A method analogous to symmetric successive overrelaxation (SSOR) in numerical analysis yields improved performance, especially when the row-sum extrapolation is used only sparingly. This method is then compared to Gaussian elimination and is found to be superior for most of the problems generated.