
Accession Number : AD0693980
Title : STOCHASTIC STORAGE PROCESSES WITH MULTIPLE SLOPE LINEAR INPUTS AND OUTPUTS.
Descriptive Note : Technical rept.,
Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS
Personal Author(s) : Weldon,K. L. M.
Report Date : AUG 1969
Pagination or Media Count : 74
Abstract : Let X(t) be the level of the storage process at time t; X(0) = 0. Starting at time 0, the level X(t) increases linearly with slope s sub i for a random length of time (the input period) after which it decreases linearly with slope g sub j for a random time (the output period). Subsequently, the process continues to alternate between periods of input and output where the inputoutput transitions are governed by a transition matrix P, and the outputinput transitions by Q. For each input slope i and output slope j, there corresponds an input period distribution F sub i and an output period distribution M sub j which is exponential. When the zero level is a positive recurrent state, the steady state joint distributions of the level of the process and the slope is obtained. The means of these distributions are determined. The mean nonempty period is also determined. When the zero level is a transient state, the limiting distribution of the storage level is obtained.
Descriptors : (*STOCHASTIC PROCESSES, *DISTRIBUTION THEORY), INVENTORY CONTROL, MATHEMATICAL MODELS, QUEUEING THEORY, PROBABILITY DENSITY FUNCTIONS, BOUNDARY VALUE PROBLEMS
Subject Categories : Statistics and Probability
Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE