Research Reports from the Department of Operations
Document Type
Dissertation
Publication Date
1-1-1985
Abstract
This dissertation addresses the areas of thinning and superposition of point and marked point processes. Specifically, we examine the dependencies between the thinned processes obtained when an original point process is thinned to produce two or more point processes. These dependencies have been examined at the level of cross-covariances under certain assumptions about the original point process as well as the thinning rule. In particular, the following independent thinning of point processes models are studied: 1) Bernoulli thinning of delayed renewal processes, exponential moving-average processes of order 1 and doubly stochastic; 2) Poisson processes; 3) Multinomial thinning of point processes; 4) Markov chain thinning of renewal processes; 5) Position dependent thinning of renewal processes. Further, we relax the “independence” assumption about the thinning process and the original point process. We examine the covariance structure between the thinned processes obtained by mark dependent thinning of marked point processes. Specifically, we investigate mark dependent thinning of an alternating renewal process and a Bernoulli oriented Markov process. Also, on a M/G/1/0 system with instantaneous Bernoulli feedback, due to the Markov renewal characteristic of the output process, we examine the covariance structure of the departure and feedback processes. Finally, we study the problems of superposition of dependent point processes in the context of thinning. We obtain the joint distribution function of the component processes wherein the superposed process is a renewal and/or a Markov renewal process.
Keywords
Operations research, Point processes, Stochastic processes, Renewal theory, Markov processes, Poisson processes, Queueing theory, Mathematical models
Publication Title
Dissertation, Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 562 ; Submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy.
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Liang, Lung-kuang, "Some Generalizations and Applications of Thinning of Point Processes-Covariance Analysis" (1985). Research Reports from the Department of Operations. 538.
https://commons.case.edu/wsom-ops-reports/538