M/M/1 queues with working vacations (M/M/1/WV)
TL;DR: The classical single server vacation model is generalized to consider a server which works at a different rate rather than completely stops during the vacation period, which approximates a multi-queue system whose service rate is one of the two speeds for which the fast speed mode cyclically moves from queue to queue with an exhaustive schedule.
About: This article is published in Performance Evaluation.The article was published on 2002-10-01. It has received 388 citations till now. The article focuses on the topics: M/M/c queue & M/M/1 queue.
Citations
More filters
TL;DR: In this article, the authors studied an M/G/1 queue with multiple vacations and exhaustive service discipline such that the server works with different service times rather than completely stopping service during a vacation.
216 citations
TL;DR: The steady-state distributions for the number of customers in the system both at arrival and arbitrary epochs, and for the sojourn time for an arbitrary customer are derived.
204 citations
01 Jan 2006
TL;DR: An M/G/1 queue with multiple vacations and exhaustive service discipline such that the server works with different service times rather than completely stopping service during a vacation.
173 citations
01 Jan 2010
TL;DR: In this paper, the authors provide a brief summary of the most recent research works on vacation queueing systems in the past 10 years, including a survey of server's vacation models.
Abstract: Queueing systems with server vacations (server's performing non-queueing jobs) have been studied extensively since the late 70's. A considerable number of works in this area were completed in the early 80's and surveyed by Doshi in 1986. As an extension to the classical queueing system, allowing idle servers to work on non-queueing jobs makes the vacation models more applicable in a variety of systems including flexible manufacturing or service and computer communication systems. Motivated by these applications, more studies on vacation models have been done during the late 80's and 90's and surveyed in the book by Takagi in 1991 and the book by Tian and Zhang in 2006. This paper intends to provide a brief summary of the most recent research works on vacation queueing systems in the past 10 years. Keywords server's vacation, batch arrivals, modified vacation policy, working vacations, multi-server vacation models.
136 citations
Cites background from "M/M/1 queues with working vacations..."
...Working vacation policy (WV): Servi and Finn (2002) first introduced the concept of working vacation in a single server system....
[...]
TL;DR: Stochastic decomposition structures of the queue length and waiting time in an M/M/1/WV queue are demonstrated, and the distributions of the additional queuelength and additional delay are obtained.
130 citations
References
More filters
Book•
25 Aug 2011TL;DR: For many system contexts for which Little's Law is valid a distributional form of the law is also valid as discussed by the authors, and this paper establishes the prevalence of such system contexts and makes clear the value of the distributional forms.
Abstract: For many system contexts for which Little's Law is valid a distributional form of the law is also valid. This paper establishes the prevalence of such system contexts and makes clear the value of the distributional form.
111 citations
TL;DR: The Laplace Transform (and the first two moments) of the busy period of the recently introduced M/G/1 vacation model with a Bernoulli schedule is completed exactly and this expression makes it possible to estimate the average waiting time of each queue for the Bernouelli schedule cyclic service queue.
Abstract: The Laplace Transform (and the first two moments) of the busy period of the recently introduced M/G/1 vacation model with a Bernoulli schedule is completed exactly. This expression makes it possible to estimate the average waiting time of each queue for the Bernoulli schedule cyclic service queue. Consequently, the weighted average of the mean waiting time can be minimized over the class of Bernoulli schedules. The Bernoulli schedule has the advantage over exhaustive schedules (or classical priority schedules) in that the performance of one class of traffic is somewhat insulated from the adverse effects of high utilization in a different class of traffic. The analysis of cyclic service queues can be applied to processor schedules and token ring local area networks as well as components of other data communication systems.
93 citations
01 Jan 1945
38 citations
17 Mar 2001
TL;DR: A queuing model for a reconfigurable network is developed that allows us to directly quantify the benefits and costs of reconfiguration as the resulting average packet delay.
Abstract: The benefit/cost tradeoff of reconfiguration in IP/WDM networks is evaluated as the resulting reduction in average packet delay. We compare, analytically and through simulations, the performance of several reconfiguration policies to fixed topology systems. We develop a queuing model for a reconfigurable network that allows us to directly quantify the benefits and costs of reconfiguration as the resulting average packet delay. This simple model allows us to compare, both analytically and via simulations, appropriate reconfiguration policies and to determine the network reconfiguration downtime that can be tolerated.
15 citations
"M/M/1 queues with working vacations..." refers background or methods in this paper
...A previous study [2] examined a variation of an exhaustive schedule, i....
[...]
...The results are compared to a simulation using a modification of a simulator developed for [2]....
[...]
...The latter assumption, called the continuous bandwidth mode, is discussed in [2]....
[...]
...Consider an Internet Protocol (IP) access network, where n access routers are connected via an optical network to the global IP network through a gateway router [2]....
[...]
...The former strategy is best only when the reconfiguration time (relative to the service time of the queues) is very long [2]....
[...]
Dissertation•
01 Jan 1994
6 citations
"M/M/1 queues with working vacations..." refers methods in this paper
...Below we examine a generalization of this strategy which was first proposed and examined by simulation in [5] for a related reconfiguration access problem applied to satellites....
[...]