Point Processes Competing for Runs: A New Tool for their Investigation

Marcel F. Neuts () and Jian-Min Li ()
Additional contact information
Marcel F. Neuts: The University of Arizona
Jian-Min Li: The University of Adelaide

Methodology and Computing in Applied Probability, 1999, vol. 1, issue 1, 29-53

Abstract: Abstract As part of a broader search for statistical descriptors of the burstiness of stationary point processes including teletraffic streams, we consider a stationary point process with two types of labeled events. With two positive integers r 1 and r 2 specified beforehand, an event of type 2 is the end of a 1-run if it is preceded by at least r 1 events of type 1 for which there are no intervening events of type 2. Similarly, the end of a 2-run is an event of type 1 preceded by at least r 2 events of type 2 without intervening events of type 1. By working with the tractable and versatile Markovian arrival process (MAP) we are able to derive descriptors that can shed light on its behavior. Examples and illustrative figures are included.

Keywords: point processes; runs; burstiness; Markovian arrival processes; matrix-analytic methods; algorithmic probability (search for similar items in EconPapers)
Date: 1999
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1023/A:1010008123195 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:1:y:1999:i:1:d:10.1023_a:1010008123195

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1023/A:1010008123195

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().