Optimal capacity expansion

We consider the problem of temporal expansion of the capacity of, say, a plant or road given estimates of its desired usage (demand). The basic problem is: given a sequence of predicted demands for N time periods, determine the optimal investment decision in each period to minimize a linear investment cost and a strictly convex cost of capacity. The relationship between capacity and the investment decisions is assumed to be linear, but time varying. Constraints on both the individual decisions and on the sum of the decisions are considered. An algorithm for solving this problem is derived.     

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.     

Some results of the queueing system E/M/c

This paper analyses the E/M/c queueing system and shows how to calculate the expected number in the system, both at a random epoch and immediately preceding an arrival. These expectations are expressed in terms of certain initial probabilities which are determined by linear equations. The advantages and disadvantages of this method are also discussed.     

Congestion tolls: Equilibrium and optimality

An example of a network with flow costs depending on congestion is presented for which no system of tolls and subsidies exists which can ensure that all equilibria in the game of route selection are Pareto optimal.     

An approach to the allocation of common costs of multi-mission systems

Many Naval systems, as well as other military and civilian systems, generate multiple missions. An outstanding problem in cost analysis is how to allocate the costs of such missions so that their true costs can be determined and resource allocation optimized. This paper presents a simple approach to handling this problem for single systems. The approach is based on the theory of peak-load pricing as developed by Marcel Boiteux. The basic principle is that the long-run marginal cost of a mission must be equal to its “price.” The implication of this is that if missions can cover their own marginal costs, they should also be allocated some of the marginal common costs. The proportion of costs to be allocated is shown to a function of not only the mission-specific marginal costs and the common marginal costs, but also of the “mission price.” Thus, it is shown that measures of effectiveness must be developed for rational cost allocation. The measurement of effectiveness has long been an intractable problem, however. Therefore, several possible means of getting around this problem are presented in the development of the concept of relative mission prices.     

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.