A decomposition result for single server discrete-time queues with generalized vacations
Pages 38 - 43
Abstract
For several specific discrete-time queueing models with a vacation policy, the stationary system occupancy at the beginning of a random slot is distributed as the sum of two independent random variables. One of these variables is the stationary number of customers in an equivalent queueing system with no vacations. This paper aims to show that this decomposition can be applied to for a large class of discrete-time queueing systems with vacations. The analysis builds on results obtained by Fuhrmann and Cooper concerning continuous-time queueing systems with Poissonian arrivals. Through some examples we show that the queueing analysis can be considerably simplified using this decomposition property.
References
[1]
S. C. Borst, O. J. Boxma Polling Models with annd without Switchover Times, Operations Research, 45 (1997), 536--543.
[2]
H. Bruneel Performance of Discrete-Time Queueing Systems, Computers Operations Research, 20 (1993), 303--320.
[3]
R. B. Cooper "Introduction to Queueing Theory, Ed.2", North-Holland (Elsevier), New York (1981).
[4]
S. De Clercq, B. Steyaert and H. Bruneel Analysis of a Multi-Class Discrete-time Queueing System under the Slot-Bound Priority rule, Proceedings of the 6th St. Petersburg Workshop on Simulation, (2009), 827--832.
[5]
S. W. Fuhrmann, R. B. Cooper Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations, Operations Research, 33 (1985), 1117--1129.
[6]
S. Halfin Batch Delays Versus Customer Delays, The Bell System Technical Journal, 62 (1983), 2011--2015.
[7]
L. Kleinrock "Queueing Systems, Volume I: Theory", Wiley, New York (1975)
[8]
Z. Liang, S. Xiao Performance Evaluation of Single-Wavelength Fiber Delay Line Buffer With Finite Waiting Places, Journal of Lightwave Technology, 26 (2008), 520--527.
[9]
J. Loris-Teghem On a Decomposition Result for a Class of Vacation Queueing Systems, Journal of Applied Probability, 27 (1990), 227--231.
[10]
W. Rogiest, J. Lambert, D. Fiems, B. Van Houdt, H. Bruneel, C. Blondia A unified model for synchronous and asynchronous FDL buffers allowing closed-form solution, Performance Evaluation, 66 (2009), 343--355.
[11]
H. Takagi "Queueing Analysis, Volume 3: Discrete-Time Systems", North-Holland (Elsevier), Amsterdam (1991)
[12]
H. Takagi "Analysis of Polling Systems", The MIT Press, Cambridge (Massachusetts 1986)
[13]
J. Walraevens, B. Steyaert, H. Bruneel Performance analysis of the system contents in a discrete-time non-preemptive priority queue with general service times, Belgian Journal of Operations Research (JORBEL), 40 (2001), 91--103.
Index Terms
- A decomposition result for single server discrete-time queues with generalized vacations
Recommendations
Discrete-time single-server finite-buffer queues under discrete Markovian arrival process with vacations
This paper treats a discrete-time single-server finite-buffer exhaustive (single- and multiple-) vacation queueing system with discrete-time Markovian arrival process (D-MAP). The service and vacation times are generally distributed random variables and ...
New fluctuation analysis of D-policy bulk queues with multiple vacations
This paper offers new studies of the queueing process in D-policy models with Poisson bulk input, general service time, and multiple vacations. The D-policy applies when the system, after being exhausted, suspends service until the total workload ...
Discrete-time GeoX/G(a,b)/1/N queues with single and multiple vacations
In this paper, we consider a discrete-time single-server finite-buffer batch arrival queue in which customers are served in batches according to a general bulk-service rule, that is, at least 'a' customers are needed to start a service with a maximum ...
Comments
Information & Contributors
Information
Published In
August 2011
234 pages
ISBN:9781450307581
DOI:10.1145/2021216
- Conference Chairs:
- Bara Kim,
- Ho Woo Lee,
- Program Chairs:
- Gang Uk Hwang,
- Yang Woo Shin
Copyright © 2011 ACM.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]
Sponsors
- Korea University
In-Cooperation
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 23 August 2011
Check for updates
Author Tags
Qualifiers
- Research-article
Conference
QTNA '11
Sponsor:
QTNA '11: 6th International Conference on Queueing Theory and Network Applications
August 23 - 26, 2011
Seoul, Korea
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 75Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 08 Mar 2025
Other Metrics
Citations
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in