A Single-Server Queue with Markov Modulated Service Times

Yong-Pin Zhou and Noah Gans

Center for Financial Institutions Working Papers from Wharton School Center for Financial Institutions, University of Pennsylvania

Abstract: We study an M/MMPP/1 queuing system, where the arrival process is Poisson and service requirements are Markov modulated. When the Markov Chain modulating service times has two states, we show that the distribution of the number-in-system is a superposition of two matrix-geometric series and provide a simple algorithm for computing the rate and coefficient matrices. These results hold for both finite and infinite waiting space systems and extend results obtained in Neuts [5] and Naoumov [4].

Numerical comparisons between the performance of the M/MMPP/1 system and its M/G/1 analogue lead us to make the conjecture that the M/MMPP/1 system performs better if and only if the total switching probabilities between the two states satisfy a simple condition. We give an intuitive argument to support this conjecture.

Date: 1999-10
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://fic.wharton.upenn.edu/fic/papers/99/9940.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (http://fic.wharton.upenn.edu/fic/papers/99/9940.pdf [301 Moved Permanently]--> https://wifpr.wharton.upenn.edu/fic/papers/99/9940.pdf)

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:wop:pennin:99-40

Access Statistics for this paper

More papers in Center for Financial Institutions Working Papers from Wharton School Center for Financial Institutions, University of Pennsylvania Contact information at EDIRC.
Bibliographic data for series maintained by Thomas Krichel ().