MAP/M/1 queue with M-policy of transfer of customers from pool to buffer
Downloads
DOI:
https://doi.org/10.26637/MJM0802/0046Abstract
In this paper we describe an MAP/M/1 queuing system. The customers arrive according to Markovian Arrival Process and are served in first in first out order with exponential service time distribution. The arrived customers wait in a buffer of finite capacity and postponed customers or postponed work can either join pool of infinite capacity or balk. The customers waiting in the pool are transferred to buffer according to an M- Policy. The probabilistic behaviour of the system in steady state is analyzed with the help of Quasi- Birth-Death process(QBD) and matrix geometric method in continuous time Markov chain. We perform numerical calculations to evaluate some queuing measures and this queuing system can thus be analysed.
Keywords:
Matrix Geometric method, Quasi- Birth Death Process, M-policy, buffer, pool, Markovian arrival processMathematics Subject Classification:
Mathematics- Pages: 588-592
- Date Published: 01-04-2020
- Vol. 8 No. 02 (2020): Malaya Journal of Matematik (MJM)
T. G. Deepak, V.C.Joshua, A. Krishnamoorthy, Queues with postponed work, Sociedad de Estadistica e Investigation Operativa, 2(12)(2004), 375-398.
D. Gross, John F Shortle, James M Thompson, Carl M Harris, Fundamentals of Queueing Theory, Fourth Edition, Wiley series in Probability and Statistics, (1988).
B. Hendrik, W. Sandman, Numerical solution of level dependent quasi-birth- and - death processes, Procedia Computer Science, (2010), 1561-1569.
A Krishnamoorthy A,S. Dhanya and B. Lakshmy GI/M/1 Type Queueing -Inventory systems with postponed work, reservation, cancellation and common life time, Indian Journal of Pure and Applied Mathematics, 47(2)(2016), 357-388.
A. Krishnamoorthy, C. B. Ajayakumar, Ph D thesis suubmitted at Cochin Universty of Science and Technology, (2011).
G. Latouche, V.Ramaswami Introduction to Matrix Analytic Methods in Stochastic Modelling, SIAM, (1999).
- NA
Similar Articles
- Santosh M. Popade, Rajkumar N. Ingle, P. Thirupati Reddy, On a certain subclass of analytic functions defined by a differential operator , Malaya Journal of Matematik: Vol. 8 No. 02 (2020): Malaya Journal of Matematik (MJM)
- Rasheed Olawale Ayinla, Ayotunde Olajide Lasode, Some coefficient properties of a certain family of regular functions associated with lemniscate of Bernoulli and Opoola differential operator , Malaya Journal of Matematik: Vol. 12 No. 02 (2024): Malaya Journal of Matematik (MJM)
- TIMOTHY OLOYEDE OPOOLA, EZEKIEL ABIODUN OYEKAN, SEYI DEBORAH OLUWASEGUN, PETER OLUWAFEMI ADEPOJU, New subfamilies of univalent functions defined by Opoola differential operator and connected with modified Sigmoid function , Malaya Journal of Matematik: Vol. 11 No. S (2023): Malaya Journal of Matematik (MJM): Special Issue Dedicated to Professor Gaston M. N'Guérékata’s 70th Birthday
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.
