Optimal Operating Policies for a Stochastic Clearing System with Bounded Waiting Times

This paper is a continuation of a previous paper where we investigated the steady-state behaviour of a stochastic clearing system with Poisson input operated under the following clearing policy : all the quantity is instantaneously removed from the system whenever there are at least M items in the queue, or every t time units since the first arrival after the last clearing, whichever occurs first. This type of policy was termed a bounded M-policy. The objective of this paper is to examine the behaviour of the expected average cost per unit time in the class of bounded M-policies and in the class of T-policies that clear the system every T time units. We find optimal policies in both classes by comparing the associated expected average costs, and present some computational results

The Steady-State Behaviour of a Stochastic Clearing System with Bounded Waiting Times

The stochastic clearing system considered in this paper is characterized by an uncontrollable Poisson input process and bounded customers' wating times. We assume that all the quantity currently present in the system is instantaneously removed whenever there are at least M items in the queue, or ev0ery t time units since the first arrival after the last clearing, whichever occurs first. The objective is to study the steady-state behaviour of this system. Knowledge of this steady-state behaviour can be used for the evaluation of the system performance as a function of the system's parameters. We present explicit expressions for the queue length and waiting time distribution, the average queue length, and the average waiting time under steady-state conditions. This work is related to dispatching in transportation systems with stationary Poisson arrivals

A Stochastic Theory of the Diffusion of Traffic Flow

This paper presents a study of the diffusion of traffic flow and an observation by a moving observer, that is, a Doppler's effect. First we introduce a time process and a space process, and we show they are composed Poisson processes under the suitable assumptions. Secondly, we derive transformation formulae between these processes, interpreting velocity as the measure preserving transformation. Moreover, we analyze a Doppler's effect occurring in an observation by a moving observer, and finally we demonstrate, in a simple case that the time process is a homogeneous Poisson process

Preventive Maintenance of a Two-Unit Standby Redundant System with a Good State

A preventive maintenance policy is proposed for a two-unit standby redundant system, each of which has good, degraded and failed states. The maen time to first system down is derived by the theory of Semi-Markov process. Further, the condition under which the policy is effective is obtained

An Algorithm for Solving the Weighted Distribution Linear Programs with Zero-One Variables

Recently, very considerable efforts have been devoted to integer programming. In practical point of view, zero-one integer programming is important for solving the actual integer programming problems. For these problems, various approaches have been proposed by many researchers in this field. However, the fundamental idea for solving these problems is based on the additive algorithm for solving linear programs with zero-one variables proposed by Egon Balas in 1965. In this paper, we propose an algorithm for solving the weighted distribution linear programming problem with zero-one variables. This algorithm is also an extension of the additive algorithm, but is more powerful than that of Egon Balas for the structured problem as the weighted distribution linear programming problem with zero-one variables

Some Remarks on Optimality Conditions for Markovian Decision Process

This paper is concerned with a discrete time parameter Markovian decision problem. The expected total returns for infinite horizon are considered as the power series of discount factor. Some optimality criterions, for example, β-optimal, 1-optimal and so on, are discussed from the view point of the theory of infinite series. And a new optimality criterion is introduced. This criterion is valuable to construct an intuitive optimal policy theoretically

A New Rounding Algorithm for Integer Linear Programming

An algorithm is given for optimizing a linear function subject to integer linear constraints by a rounding method which is an extension of Gomory's. The range of computation to obtain the optimal solution to the integer linear problem by this algorithm is less than that of Gomory's. In particular, this algorithm is very effective in the case where the value of the product of the pivots is much larger than the number of nonbasic variables

A Method of Determining Characteristic Functions for Cooperative Differential Games without Side Payment

Many person games are treated as non-cooperative games or cooperative games. Cooperative games are divided into games with side payment and without side payment. It is known that cooperative games without side payment can be analyzed and solved in the form of characteristic functions. It is necessary to determine the characteristic functions for differential games which are not described in the form of the characteristic functions. In this paper, a method of determining the characteristic functions is presented. Two kinds of characteristic functions are obtained according to the α-effectiveness and β-effectiveness, respectively. Determining the characteristic functions is reduced to solving the parametric minimax and maximin problems, two person differential games. The necessary conditions for the solutions of the problems are obtained

Stress-Strain Relation of Polyvinyl Chloride Sheath Used for Electrical Cords

In general, polyvinyl chloride compounds are widely used as a sheath material of electrical cords for indoor use. In this paper, a stress-strain relation of the polyvinyl chloride sheath is analyzed by the experimental data derived from a number of tensile tests. As a result, the stress-strain relation can be numerically expressed by a hyperbola which is based on the two parallel element Vigot model