A c-server Poisson queue with customer impatience due to a slow-phase service. (9th September 2021)
- Record Type:
- Journal Article
- Title:
- A c-server Poisson queue with customer impatience due to a slow-phase service. (9th September 2021)
- Main Title:
- A c-server Poisson queue with customer impatience due to a slow-phase service
- Authors:
- Sivasamy, R.
Peter, Peter O. - 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 λj, and are served according to an exponential distribution with rate μj where μS < μF . 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 ( λ 0 )/ M ( μ 0 + α )/ c queue with customer impatience (CI) and of another M ( λ )/ M ( μ )/ c facility without CI.
- Is Part Of:
- International journal of mathematics in operational research. Volume 20:Number 1(2021)
- Journal:
- International journal of mathematics in operational research
- Issue:
- Volume 20:Number 1(2021)
- Issue Display:
- Volume 20, Issue 1 (2021)
- Year:
- 2021
- Volume:
- 20
- Issue:
- 1
- Issue Sort Value:
- 2021-0020-0001-0000
- Page Start:
- 85
- Page End:
- 98
- Publication Date:
- 2021-09-09
- Subjects:
- two-phase service? fast-service? slow-service? stationary? probability distribution
Operations research -- Mathematical models -- Periodicals
Operations research -- Mathematics -- Periodicals
Decision making -- Mathematical models -- Periodicals
658.4033 - Journal URLs:
- http://www.inderscience.com/ ↗
http://www.inderscience.com/jhome.php?jcode=ijmor ↗ - Languages:
- English
- ISSNs:
- 1757-5850
- Deposit Type:
- Legaldeposit
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