Toward a study of bidding processes part IV - games with unknown costs

This paper represents a continuation of three previous papers [1-.3] in the study of competitive bidding processes. It treats the case where a bidder's knowledge of his competitor's cost i s given by a probability distribution over a certain interval. The results obtained extend the work of Vickrey [4] to the case where the cost intervals a r e not necessarily symmetric.     

Bounds on parallel-processing of queues with multiple-phase jobs

Currently, both the hardware and software designs of many large computing systems aim at improved system performance through exploitation of parallelism in multiprocessor systems. In studying these systems, mathematical modelling and analysis constitute an important step towards providing design tools that can be used in building such systems. With this view the present paper describes a queueing model of a multiprocessor system operating in a job-shop environment in which arriving jobs consist of a random number of segments (sub-jobs). Two service disciplines are considered: one assumes that the sub-jobs of a given job are capable of parallel operation on different processors while the other assumes that the same sub-jobs must be operated in a strictly serial sequ'snce. The results (in particular, the mean number in the system and waiting time in queue) obtained for these two disciplines are shown to be bounds for more general job structures.     

Statistical decision analysis of stochastic linear programming problems

This paper presents a statistical decision analysis of a one-stage linear programming problem with deterministic constraints and stochastic criterion function. Procedures for obtaining numerical results are given which are applicable to any problem having this general form. We begin by stating the statistical decision problems to be considered, and then discuss the expected value of perfect information and the expected value of sample information. In obtaining these quantities, use is made of the distribution of the optimal value of the linear programming problem with stochastic criterion function, and so we discuss Monte Carlo and numerical integration procedures for estimating the mean of this distribution. The case in which the random criterion vector has a multivariate Normal distribution is discussed separately, and more detailed methods are offered. We discuss dual problems, including some relationships of this work with other work in probabilistic linear programming. An example is given in Appendix A showing application of the methods to a sample problem. In Appendix B we consider the accuracy of a procedure for approximating the expected value of information.     

Book reviews

Export or Die: Britain's Defence Trade with Iran and Iraq. by Davina Miller, London: Cassell, 1996, ISBN 0-304-33852-4 (hbk), £40.00, 04-33853-2 (pbk), £11.99.

The Storm Passed By: Ireland and the Battle of the Atlantic, 1940-1941. by Trevor Allen, Dublin: Irish Academic Press, 1996, ISBN 0-7165-2616-6, (hbk) £17.50.

Arms Control Toward the 21st Century. by Jeffrey A. Larsen and Greqory J. Rattray (eds). Boulder: Lynne Rienner, 1996.

Asia-Pacific Security, Less Uncertainty, New Opportunities. Edited by Gary Klintworth. Melbourne: Addison Wesley Longman, 1996, ISBN 0-582-80321-7, £24.99.

Masters of War, Military Dissent and Politics in the Vietnam Era. by Robert Buzzanco, Cambridge: Cambridge University Press, 1996, ISBN 0-521-48046-9 (hbk), £29.95

Controlling the Arms Trade: the West Versus the Rest. By Paul Cornish, London: Bowerdean Publishing Co., 1996, ISBN 0-906097-44-4 (pbk), £9.99.

Secret Agencies: US Intelligence in a Hostile World. by Loch K. Johnson, London: Yale University Press, 1997, ISBN 0-300-06611-2 (hbk), £22.50.     

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 note on a computational model for a data/voice communication queueing system

Certain types of communication nodes can be viewed as multichannel queueing systems with two types of arrival streams. Data arrivals are characterized by high arrival and service rates and have the ability to queue if all service channels are busy. Voice arrivals have small arrival and service rates and do not have the ability to wait when the channels are full. Computational procedures are presented for obtaining the invariant probabilities associated with the queueing model.     

Theoretical analysis of the general linear model for lanchester - type combat between two homogeneous forces

This paper studies Lanchester-type combat between two homogeneous forces modeled by the so-called general linear model with continuous replacements/withdrawals. It demonstrates that this model can be transformed into a simpler canonical form, which is also shown to arise from fixed-force-level-breakpoint battles modeled by Lanchester-type equations for modern warfare. Analytical expressions for the force levels for the general variable coefficient linear model with continuous replacements/withdrawals are constructed out of so-called general Lanchester functions for the model without replacements/withdrawals, for which all solutions are shown to be nonoscillatory in the strict sense. These force-level results are unfortunately so complicated and opaque that the constant-coefficient version of the model must be studied before any insights into the dynamics of combat may be analytically obtained. Thus, fairly complete results are given for the general linear model with constant attrition-rate coefficients and constant rates of replacement/withdrawal. However, the expressions for the force levels are still so complicated that we have not been able to develop battle-outcome prediction conditions directly from them alone but have had to establish general results on the qualitative behavior of solutions. A significant result (and one that greatly complicates the prediction of battle outcome) is that all solutions to the model with replacements/withdrawals are no longer necessarily nonoscillatory in the strict sense, i.e., both sides force levels can take on negative values if the force-on-force attrition equations are not “turned off” at the right time. Thus, this paper shows that the addition of continuous replacements/withdrawals to a Lanchester-type model may significantly change the qualitative behavior of the force-level trajectories. Battle-outcome prediction conditions are nevertheless given, and important insights into the dynamics of combat are briefly indicated.     

Geometry of the total time on test transform

Total time on test (TTT) plots provide a useful graphical method for tentative identification of failure distribution models. Identification is based on properties of the TTT transform. New properties of the TTT transform distribution are obtained. These results are useful to the user of TTT plots. Although IFR (DFR) distributions are particularly easy to identify from TTT plots, the user must exercise caution relative to identification of IFR A (DFRA) distributions.     

The U.S. versus the Soviet incentive models

This paper is concerned with models of the use of performance incentives in the Soviet Union and United States. The principal analytical result is an extension of an analysis of the methods whereby Soviet planners make the decision about production targets a variable under control of the producer, who is the only one possessing a knowledge of the uncertain condition of production. It is shown that this device can be viewed as a classical inventory problem. There is also an examination of the “U.S. incentive program” referring to multi-incentive contracts in which the profits received by the private producers are related to performance, outcome and cost. The analysis describes how this device can be extended to solve the target output selection problem of the Soviet planning system.     

Theoretical analysis of lanchester-type combat between two homogeneous forces with supporting fires

This paper studies combat between two homogeneous forces modelled with variable-coefficient Lanchester-type equations of modern warfare with supporting fires not subject to attrition. It shows that this linear differential-equation model for combat with supporting fires may be transformed into one without the supporting fires so that all the previous results for variable-coefficient Lanchester-type equations of modern warfare (without supporting fires) may be invoked. Consequently, new important results for representing the solution (i.e. force levels as functions of time) in terms of canonical Lanchester functions and also for predicting force annihilation are developed for this model with supporting fires. Important insights into the dynamics of combat between two homogeneous forces with such supporting fires are discussed.