A Simple and Complete Computational Analysis of MAP/R/1 Queue Using Roots
M. L. Chaudhry (),
Gagandeep Singh () and
U. C. Gupta ()
Additional contact information
M. L. Chaudhry: Royal Military College of Canada
Gagandeep Singh: Indian Institute of Technology
U. C. Gupta: Indian Institute of Technology
Methodology and Computing in Applied Probability, 2013, vol. 15, issue 3, 563-582
Abstract In this paper, we present (in terms of roots) a simple closed-form analysis for evaluating system-length distribution at three epochs of time (arbitrary, pre-arrival, and post-departure) and queueing-time distribution (virtual and actual) of the MAP/R/1 queue, where R represents the class of distributions whose Laplace–Stieltjes transforms are rational functions. Our analysis is based on roots of the associated characteristic equations of the (i) vector-generating function of system-length distribution and (ii) Laplace–Stieltjes transform of the virtual queueing-time distribution. The proposed method for evaluating boundary probabilities is an alternative to the matrix-analytic method as well as spectral method. Numerical aspects have been tested for a variety of arrival and service-time (including matrix-exponential (ME)) distributions and a sample of numerical outputs is presented. The method is analytically quite simple and easy to implement. It is hoped that the results obtained would prove to be beneficial to both theoreticians and practitioners.
Keywords: Queueing; Markovian arrival process (MAP); Queueing-time; Roots; System-length; Rational Laplace–Stieltjes transform; Matrix-exponential (ME); Phase-type (PH); Primary 60K25; Secondary 90B25 (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2) Track citations by RSS feed
Downloads: (external link)
http://link.springer.com/10.1007/s11009-011-9266-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:15:y:2013:i:3:d:10.1007_s11009-011-9266-3
Ordering information: This journal article can be ordered from
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 ().