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.     

A linear programming approach to geometric programs

A cutting plane method, based on a geometric inequality, is described as a means of solving geometric programs. While the method is applied to the primal geometric program, it is shown to retain the geometric programming duality relationships. Several methods of generating the cutting planes are discussed and illustrated on some example problems.     

Minimax trees,paths, and cut sets

The notions of minimax paths, trees, and cut sets are defined for undirected graphs; and relationships between these entities are established. Simple solution procedures based on these relationships are presented.     

A complete importance ranking for components of binary coherent systems,with extensions to multi-state systems

Means of measuring and ranking a system's components relative to their importance to the system reliability have been developed by a number of authors. This paper investigates a new ranking that is based upon minimal cuts and compares it with existing definitions. The new ranking is shown to be easily calculated from readily obtainable information and to be most useful for systems composed of highly reliable components. The paper also discusses extensions of importance measures and rankings to systems in which both the system and its components may be in any of a finite number of states. Many of the results about importance measures and rankings for binary systems are shown to extend to the more sophisticated multi-state systems. Also, the multi-state importance measures and rankings are shown to be decomposable into a number of sub-measures and rankings.     

Coordinated replenishments of items under time-varying demand: Dynamic programming formulation

We consider a group (or family) of items having deterministic, but time-varying, demand patterns. The group is defined by a setup-cost structure that makes coordination attractive (a major setup cost for each group replenishment regardless of how many of the items are involved). The problem is to determine the timing and sizes of the replenishments of all of the items so as to satisfy the demand out to a given horizon in a cost-minimizing fashion. A dynamic programming formulation is illustrated for the case of a two-item family. It is demonstrated that the dynamic programming approach is computationally reasonable, in an operational sense, only for small family sizes. For large families heuristic solution methods appear necessary.     

Congestion analysis of a computer core storage system

This paper studies the congestion problems of the computer core storage units. The principle of storage request interleaving is briefly discussed as means of increasing thruput. An analytic model is proposed to analyze the core storage system with a two-way interleaving feature. The model, an approximation to the physical system, is an extension of a queueing model with bulk service considered by Bailey in Ref. [1].     

A tactical warfare simulation program

The Tactical Warfare Simulation Program is a procedure by which the major interactions among opposing military units and terrain features can be treated in a tactical limited warfare situation. It is a critical-area, sequence-of-event model and is programmed in SIM-SCRIPT. In this program a military unit is described by such properties as strength, size, location, velocity, and attrition rates. Some of the events which can occur to a military unit are entering/leaving terrain features, becoming engaged/disengaged with opposing units, retreating, reaching an objective, and breaking. Following a discussion of the general features of the program, a study of a hypothetical war is presented.     

Optimal policy for a dynamic multi-echelon inventory model

A general multiperiod multi-echelon supply system consisting of n facilities each stocking a single product is studied. At the beginning of a period each facility may order stock from an exogenous source with no delivery lag and proportional ordering costs. During the period the (random) demands at the facilities are satisfied according to a given supply policy that determines to what extent stock may be redistributed from facilities with excess stock to those experiencing shortages. There are storage, shortage, and transportation costs. An ordering policy that minimizes expected costs is sought. If the initial stock is sufficiently small and certain other conditions are fulfilled, it is optimal to order up to a certain base stock level at each facility. The special supply policy in which each facility except facility 1 passes its shortages on to a given lower numbered facility called its direct supplier is examined in some detail. Bounds on the base stock levels are obtained. It is also shown that if the demand distribution at facility j is stochastically smaller (“spread” less) than that at another facility k having the same direct supplier and if certain other conditions are fulfilled, then the optimal base stock level (“virtual” stock out probability) at j is less than (greater than) or equal to that at facility k.