On a nonsingular singular surface of a differential game

A differential game in which nonterminating play is assigned a fixed value is examined. The solution exhibits a new kind of singular surface which an optimal path takes an infinite time to cross. By playing nonoptimally in a sufficiently small neighborhood of this surface, the player who prefers the optimal (terminating) value to the value of nonterminating play can force the state across this surface and obtain a value arbitrarily close to the optimal.This work was carried out with the support of a CSIRO postgraduate studenship.     

Insights into the development of strategy from a complexity perspective

This paper provides an account of an ongoing project with an independent school in the UK. The project focuses on a strategy development intervention which, from the start, was systemic in orientation. The intention was to integrate simple systems concepts and approaches into the strategy development process to: address power relations in actively engaging a wide range of stakeholders with the school’s strategy-making process; generate a range of good ideas; and make the strategy-making process transparent in order to inspire stakeholder confidence in, and commitment to, it and its outcomes. This paper describes how seeking to meet these aims entailed a series of workshops during the course of which an awareness of the relevance, in our interpretation, of Complex Adaptive Systems concepts grew.     

Transforming a pseudo-polynomial algorithm for the single machine total tardiness maximization problem into a polynomial one

We consider the problem of maximizing total tardiness on a single machine, where the first job starts at time zero and idle times between the processing of jobs are not allowed. We present a modification of an exact pseudo-polynomial algorithm based on a graphical approach, which has a polynomial running time. This result settles the complexity status of the problem under consideration which was open.     

Combining a feedback linearization controller with a disturbance observer to control a chaotic system under external excitation

This paper proposes a robust controller which combines a feedback linearization controller with a disturbance observer. This controller can suppress the chaotic motion of an unknown nonlinear system even though it receives an unknown external force. Two numerical simulations are performed to demonstrate the feasibility of the proposed method.     

Exponential decay for a viscoelastic problem with a singular kernel

In this paper we consider a problem which arises in viscoelasticity. We prove exponential decay of solutions for the problem with a memory term involving a kernel which is singular at zero. This is established by introducing an appropriate Lyapunov type functional and using the energy method. This work extends earlier results.     

Overflow and losses in a network queue with a self-similar input

This paper considers a discrete time queuing system that models a communication network multiplexer which is fed by a self-similar packet traffic. The model has a finite buffer of size h, a number of servers with unit service time, and an input traffic which is an aggregation of independent source-active periods having Pareto-distributed lengths and arriving as Poisson batches. The new asymptotic upper and lower bounds to the buffer-overflow and packet-loss probabilities P are obtained. The bounds give an exact asymptotic of log P/log h when h → to ∞. These bounds decay algebraically slow with buffer-size growth and exponentially fast with excess of channel capacity over traffic rate. Such behavior of the probabilities shows that one can better combat traffic losses in communication networks by increasing channel capacity rather than buffer size. A comparison of the obtained bounds and the known upper and lower bounds is done. This revised version was published online in June 2006 with corrections to the Cover Date.     

Analysis of a single-server queue interacting with a fluid reservoir

We consider a single-server queueing system with Poisson arrivals in which the speed of the server depends on whether an associated fluid reservoir is empty or not. Conversely, the rate of change of the content of the reservoir is determined by the state of the queueing system, since the reservoir fills during idle periods and depletes during busy periods of the server. Our interest focuses on the stationary joint distribution of the number of customers in the system and the content of the fluid reservoir, from which various performance measures such as the steady-state sojourn time distribution of a customer may be obtained. We study two variants of the system. For the first, in which the fluid reservoir is infinitely large, we present an exact analysis. The variant in which the fluid reservoir is finite is analysed approximatively through a discretization technique. The system may serve as a mathematical model for a traffic regulation mechanism - a two-level traffic shaper - at the edge of an ATM network, regulating a very bursty source. We present some numerical results showing the effect of the mechanism. This revised version was published online in June 2006 with corrections to the Cover Date.     

Exponential decay for a viscoelastic problem with a singular kernel

In this paper we consider a problem which arises in viscoelasticity. We prove exponential decay of solutions for the problem with a memory term involving a kernel which is singular at zero. This is established by introducing an appropriate Lyapunov type functional and using the energy method. This work extends earlier results.      

On surfaces with a rectilinear geodesic circle

Summary We say that a surface has a “rectilinear geodesic circle“ if it contains a straight line segment AB and a point F whose geodesic distance from a variable point of AB is a constant. The problem of generating such surfaces is solved here by constructing families of cones which behave locally (along a curce) like solutions, and then taking their envelopes. This method generates a class of solutions which depend on an arbitrary curve. This is an excerpt from a thesis presented in partial fulfillment of the Ph. D. Requirements of the Mathematics Department of Stanford University. It was supported in part by the Ballistics Research Laboratory of the Ordnance Department, U. S. Army, under Contract No. DA-04-200-ORD-294.     

The expected likelihood of transitivity for a probabilistic chooser

May [18] developed an algebraic choice model of pairwise preference comparison in which subjects respond precisely to ordinal information on attributes of comparison. This study considers a probabilistic choice model variation of May's model, in which subjects respond with various degrees of precision in comparison to May's model. This precision can be viewed as an indirect measure of the subject's level of perception of the attributes of comparison. The purpose of the study is to examine the expected likelihood with which subjects will have transitive responses, as the degree of precision is varied. Closed form representations are obtained for the expected likelihood of transitivity for three alternatives for each different level of precision. Results indicate that a relatively small change in this precision can lead to substantial changes in the expected likelihood of transitivity.This research was supported through a fellowship from the Center for Advanced Study of the University of Delaware. Helpful comments from Sven Berg on a draft version of this paper are gratefully acknowledged.