On Lattice Path Counting and the Random Product Representation, with Applications to the Er/M/1 Queue and the M/Er/1 Queue

Xiaoyuan Liu () and Brian Fralix ()
Additional contact information
Xiaoyuan Liu: Clemson University
Brian Fralix: Clemson University

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 4, 1119-1149

Abstract: Abstract We explain how lattice-path counting techniques can be used in conjunction with the random-product representations from Buckingham and Fralix (Markov Process Related Field 21:339–368 2015) to study both the stationary and time-dependent behavior of Markovian queueing systems, and continuous-time Markov chains in general. We illustrate how the approach works by applying it to both the Er/M/1 queue, and the M/Er/1 queue. Interestingly, through this approach we show that the stationary distributions, as well as the Laplace transforms of the transition functions associated with both the Er/M/1 queue and the M/Er/1 queue, can be expressed explicitly in terms of generalized binomial series from Chapter 5 of the text Concrete Mathematics of Graham, Knuth, and Patashnik.

Keywords: Er/M/1 queue; Generalized binomial series; Lattice path counting; M/Er/1 queue; Markovian queues; 60J27; 60J28; 60K25; 90B22 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-018-9658-8 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:21:y:2019:i:4:d:10.1007_s11009-018-9658-8

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

DOI: 10.1007/s11009-018-9658-8

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 ().