A verification study of the stochastic salvo combat model

When the stochastic version of the salvo combat model was designed, several assumptions and approximations were made to keep its mathematical structure relatively simple. This paper examines the impact of those simplifications by comparing the outputs of the stochastic model to those from a Monte Carlo simulation across 486 scenarios. The model generally performed very well, even where the battle size was relatively small or the damage inflicted by each missile was not normally distributed. The model’s accuracy did decrease where missiles were positively correlated instead of independent.     

On a model of sequential point patterns

A finite point process motivated by the cooperative sequential adsorption model is proposed. Analytical properties of the point process are considered in details. It is shown that the introduced point process is useful for modeling both aggregated and regular point patterns. A possible scheme of maximum likelihood estimation of the process parameters is briefly discussed. V. Shcherbakov is on leave from Laboratory of Large Random Systems, Faculty of Mathematics and Mechanics, Moscow State University, Moscow.     

Two-target game model of an air combat with fire-and-forget all-aspect missiles

An air combat duel between similar aggressive fighter aircraft, both equipped with the same type of guided missiles, is formulated as a two-target differential game using the dynamic model of the game of two identical cars. Each of the identical target sets represents the effective firing envelope of an all-aspect fire-and-forget air-to-air missile. The firing range limits depend on the target aspect angle and are approximated by analytical functions. The maximum range, computed by taking into account the optimal missile avoidance maneuver of the target, determines the no-escape firing envelope. The solution consists of the decomposition of the game space into four regions: the respective winning zones of the two opponents, the draw zone, and the region where the game terminates by a mutual kill. The solution provides a new insight for future air combat analysis.This paper is based on the first author's D.Sc. Thesis. The research was supported by NASA Cooperative Agreement NCCW-4.     

A sequential exchange approach for minimizing earliness–tardiness penalties of single-machine scheduling with a common due date

This study focuses on a class of single-machine scheduling problems with a common due date where the objective is to minimize the total earliness–tardiness penalty for the jobs. A sequential exchange approach utilizing a job exchange procedure and three previously established properties in common due date scheduling was developed and tested with a set of benchmark problems. The developed approach generates results better than not only those of the existing dedicated heuristics but also in many cases those of meta-heuristic approaches. And the developed approach performs consistently well in various job settings with respect to the number of jobs, processing time and earliness–tardiness penalties for the jobs.     

On a sequential model of the algebra of finite-valued logic

We consider basic postulates for an interpretation of the algebra of finite-valued logic in which prepositional variables are interpreted as variables whose values are sequences. We obtain an analytic representation of the operations of two-valued logic for a class of recursive sequences—generalized arithmetic progressions. We exhibit certain generalizations, modifications, and applications of the proposed model.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 32, 1990, pp. 14–17.     

Analysis of a combat problem: The turret game

The turret game is defined and solved to illustrate the nature of games of combat. This game represents a highly simplified version of air combat, yet it is sufficiently complex so as to exhibit a rich variety of combat phenomena. A review of the formulation of -combat games is included in this paper.on sabbatical leave from Technion, Israel Institute of Technology, Haifa, Israel.     

A model of a sudden-death field-goal football game as a sequential duel

A highly simplified ‘football’ game is constructed where individuals can run or kick for a field goal. It represents an attempt to extend the domain of the modeling of duels to a broader category than those previously studied. There are some worthwhile similarities (and important differences) in military, sports and economic tactics which are reasonably well modeled as zero sum games.The theory of duels for military application has been reasonably well developed but there are at least two other activities beyond war in which the zero-sum game duel is worth considering. They are in sports and in the tactics of advertising campaigns or other economic activities where the budgets of A and B are set and the fight is a non-price duel over a market of fixed size. In this paper we concentrate on the extension of dueling to sports.Rather than claim immediate relevance to football as it is played, a highly simplified version of ⌉sudden-death’ scoring is introduced. The basic game is as follows. With equal probability the team toss to see who gets the ball. The team with the ball can either run or try to kick a field goal. The first team to score wins the game.     

Application of a location model to fire stations in Rotterdam

This report is an outgrowth of a research project carried out by the Operations Research Group of Twente University of Technology in cooperation with the Department Fire-Brigade Affairs (Home Office) and the Rotterdam Fire Department. The objectives of the project were to determine the minimal number of fire stations, their locations and the number of first attendance pumpers, so that each point in town can be reached within a prescribed attendance time with sufficient equipment.A road network approach was used for determining the set of possible location areas for fire stations followed by a set-covering approach for calculating the minimal number of stations. The hard points to tackle were the construction of robust networks, the determination of the possible location areas and the calculation of all the alternative locations of a minimal number of fire stations.A simulation was carried out to test whether the solutions given by the network approach were realistic.     

Stock exchange modeling with a price model involving variable variance and correlation coefficients

A price model with variance and correlation coefficients as random processes is analyzed. Parametric analysis is realized by means of “direct” and “inverse” trade algorithms. Results of numerical experiments are obtained on a computer using an INVERT program.     

Stochastic modelling of combat with reinforcement

The homogeneous combat when reinforcements are made at prespecified force levels has been modelled as a continuous-time discrete-state space Markov process. The effect of reinforcement on various combat characteristics, viz., the mean combat duration, the winning probabilities, the expected survivors, etc., is studied using the uniformization method. Two new concepts, i.e., Reinforcement Effectiveness Index and Reinforcement Parity Curve, have also been defined and are illustrated numerically.     

FIRESCAP: A computer simulation model of reaction to a fire alarm

We develop a theoretical model and its computer‐simulation translation of evacuation response to a fire alarm, based on past research on fire emergencies and on crowd behavior as well as on our past and continuing investigation of the Beverly Hills fire disaster. The simulation model presents graphically the status of individuals and socially tied pairs in a room as they initiate evacuation—typically in response to ambiguous information—and move toward alternative exits. Individual and pair status—including choice of exit—can change during evacuation in response to changing physical and social cues; statuses include pace of movement and cooperativeness‐competitiveness. We also present some experimental results on the sensitivity of the model's outcomes to variation in several parameters.     

Integrating Bayesian networks and decision trees in a sequential rule-based transportation model

Several activity-based transportation models are now becoming operational and are entering the stage of application for the modelling of travel demand. Some of these models use decision rules to support its decision-making instead of principles of utility maximization. Decision rules can be derived from different modelling approaches. In a previous study, it was shown that Bayesian networks outperform decision trees and that they are better suited to capture the complexity of the underlying decision-making. However, one of the disadvantages is that Bayesian networks are somewhat limited in terms of interpretation and efficiency when rules are derived from the network, while rules derived from decision trees in general have a simple and direct interpretation. Therefore, in this study, the idea of combining decision trees and Bayesian networks was explored in order to maintain the potential advantages of both techniques. The paper reports the findings of a methodological study that was conducted in the context of Albatross, which is a sequential rule based model of activity scheduling behaviour. To this end, the paper can be situated within the context of a series of previous publications by the authors to improve decision-making in Albatross. The results of this study suggest that integrated Bayesian networks and decision trees can be used for modelling the different choice facets of Albatross with better predictive power than CHAID decision trees. Another conclusion is that there are initial indications that the new way of integrating decision trees and Bayesian networks has produced a decision tree that is structurally more stable.     

Halting combustion waves with a fire break

A simple model for the propagation of an exothermic reaction is proposed in which the reactant ignites at a specified temperature. It is shown that the model supports waves of permanent form and the speed and stability of such waves is determined. Finally the behavior of this wave as it encounters a break in the fuel is considered. In particular results are obtained for the size of the break required to halt the wave.     

Numerical study of a two-dimensional mathematical model with variable heat exchange coefficient which arises in cryosurgery

We formulate and numerically solve a two-dimensional boundary value problem of Stefan type with nonlinear heat sources of a special kind and a variable heat exchange coefficient. The model under study arises in cryosurgery in the process of freezing some living biological tissue by a cryoinstrument of cylindrical shape placed on the surface of the tissue. The model takes into account the actually observed effect of spatial localization of heat. Some results of the computer simulation are presented.     

Local asymptotic normality of a sequential model for marked point processes and its applications

This paper deals with statistical inference problems for a special type of marked point processes based on the realization in random time intervals [0,_u]. Sufficient conditions to establish the local asymptotic normality (LAN) of the model are presented, and then, certain class of stopping times _u satisfying them is proposed. Using these stopping rules, one can treat the processes within the framework of LAN, which yields asymptotic optimalities of various inference procedures. Applications for compound Poisson processes and continuous time Markov branching processes (CMBP) are discussed. Especially, asymptotically uniformly most powerful tests for criticality of CMBP can be obtained. Such tests do not exist in the case of the non-sequential approach. Also, asymptotic normality of the sequential maximum likelihood estimators (MLE) of the Malthusian parameter of CMBP can be derived, although the non-sequential MLE is not asymptotically normal in the supercritical case.     

A multistage exchange trading model with asymmetric information and elements of bargaining

A modification of the discrete multistage exchange trading model with risky securities is considered. At each stage of trading, the players place their integer bids. One of the players knows the real price, while the other knows only its probability distribution. The transaction price is defined as a convex combination of the proposed bids with some given coefficient. The solution to an infinitely long game is obtained.