Research Reports from the Department of Operations
Document Type
Report
Publication Date
1-1-1970
Abstract
This study investigates the limiting behavior of stochastic processes in systems with two types of inputs of differing statistical nature and linear continuous output. Type 1 input points are modeled as a time-homogeneous Poisson process, while Type 2 input points follow a recurrent process, both with magnitudes that are mutually independent, identically distributed, positive random variables. Conditions for the existence of limiting distributions are established, yielding practical results for queueing theory, storage theory, and insurance risk theory. Using a vector-Markov process, the problem is reduced to solving an integral equation via Wiener-Hopf factorization. Closed-form results for Laplace transforms of limiting distributions and approximate expressions for expected system states are provided for cases with complex or intractable computations.
Keywords
Stochastic processes--Evaluation, Operations research, Poisson processes
Publication Title
Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 171
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Sahin, Izzet, "Some Stochastic Systems with Secondary Inputs" (1970). Research Reports from the Department of Operations. 547.
https://commons.case.edu/wsom-ops-reports/547