A c -server Poisson queue with customer impatience due to a slow-phase service

R. Sivasamy and Peter O. Peter

International Journal of Mathematics in Operational Research, 2021, vol. 20, issue 1, 85-98

Abstract: In this paper, we investigate a queue with c-servers in a Markovian environment (ME) under two phases (S - slow and F - fast). We assume that the sojourn times follow an exponential distribution at states S and F with parameters ν and η respectively. Each customer chooses a random relative deadline duration (RDD), which follows an exponential law with parameter α under S-phase but abandons the system as soon as its RDD expires and never returns. When the environment remains under phase j (= S, F), customers arrive according to a Poisson process with rate λ_j, and are served according to an exponential distribution with rate μ_j where μ_S < μ_F. We formulate the queue length process Y_(j,n)(t), representing the number of customers n(t), waiting in the phase j at time t as level dependent quasi birth-death (LDQBD) process in a 2-dimensional space. We apply matrix analytic methods on computational procedures and iterative methods to obtain scalar types of explicit expressions for the stationary probability distributions of Y_(j,n)(t) as t tends to infinity. We present comparable charts to highlight the variations between the steady state measures of an M(λ₀)/M(μ₀ + α)/c queue with customer impatience (CI) and of another M(λ)/M(μ)/c facility without CI.

Keywords: two-phase; service?; fast-service?; slow-service?; stationary?; probability; distribution. (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.inderscience.com/link.php?id=117632 (text/html)
Access to full text is restricted to subscribers.

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:ids:ijmore:v:20:y:2021:i:1:p:85-98

Access Statistics for this article

More articles in International Journal of Mathematics in Operational Research from Inderscience Enterprises Ltd
Bibliographic data for series maintained by Sarah Parker ().