Analysis of a discrete-time queueing system with time-limited service

Takagi, Hideaki; Leung, Kin K.

doi:10.1007/bf01158781

Cited by 27 publications

(25 citation statements)

References 14 publications

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“…Based on the work write as Hunter [4] , references [5][6][7] have studied M/G/1 queue with feedback, Geom/G/1 queue with server vacations, Geom/G/1 queue with time-limited service by using embedded Markov Chains and obtained the Probability Generating Function (P. G. F.) of equilibrium queue size distribution at departure epoch. But the above papers did not study the transient distribution of the queue size at any epoch n and no authors obtained expression of the equilibrium probability distribution for queue size yet.…”

Section: Introductionmentioning

confidence: 99%

Transient Queue Size Distribution Solution of Geom / G / 1 Queue with Feedback-A Recursive Method

2009

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This paper considers the Geom/G/1 queueing model with feedback according to a late arrival system with delayed access (LASDA). Using recursive method, this paper studies the transient property of the queue size from the initial state N (0 + ) = i. Some new results about the recursive expression of the transient queue size distribution at any epoch n + and the recursive formulae of the equilibrium distribution are obtained. Furthermore, the recursive formulae of the equilibrium queue size distribution at epoch n − , and n are obtained, too. The important relations between stationary queue size distributions at different epochs are discovered (being different from the relations given in M/G/1 queueing system). The model discussed in this paper can be widely applied in all kinds of communications and computer network.

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Section: Introductionmentioning

confidence: 99%

Transient Queue Size Distribution Solution of Geom / G / 1 Queue with Feedback-A Recursive Method

2009

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“…For the PRD discipline, we obtain (7) using (19). Here, note that we have used the independence of successive vacation times to derive (25) and (29). Therefore, we get the statement of this theorem.…”

Section: Waiting Time Analysis For Exhaustive Servicementioning

confidence: 99%

“…Leung and Lucantoni [18] analyzed nonpreemptive time-limited service vacation models using the matrix-analytical method and exponential time stages to approximate constant time limits. Several discrete-time vacation models have been analyzed by Takagi and Leung [25], Chiarawongse, Srinivasan, and Teorey [3], and Alfa [1]; e.g., Takagi and Leung [25] analyzed an exhaustive time-limited service vacation model with preemptive-resume discipline using the technique of discrete Fourier transforms. The related queueing models to the time-limited service vacation model have been studied in some articles: Sengupta [22] analyzed a single-queue model with alternating on/off-service periods and preemptive-resume discipline.…”

Section: Introductionmentioning

confidence: 99%

Waiting time analysis for a queueing system with time‐limited service and exponential timer

Katayama

2001

Naval Research Logistics

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Abstract:We consider a single-queue with exhaustive or gated time-limited services and server vacations, in which the length of each service period at the queue is controlled by a timer, i.e., the server serves customers until the timer expires or the queue becomes empty, whichever occurs first, and then takes vacations. The customer whose service is interrupted due to the timer expiration may be attended according to nonpreemptive or preemptive service disciplines. For the M/G/1 exhaustive/gated time-limited service queueing system with an exponential timer and four typical preemptive/nonpreemptive service disciplines, we derive the Laplace-Stieltjes transforms and the moment formulas for waiting times and sojourn times through a unified approach, and provide some new results for these time-limited service disciplines.

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“…In theory, it had produced a large number of research results [1][2][3][4]. These results were widely used in practice [5][6][7][8][9] (especially in the digital communications network performance analysis). In recent years, driven by the gateway router modeling analysis of optical fiber communications, Servi and Finn [4] led in the introduction of service rate and vacation-related variable service rate queue to working vacation queue.…”

Section: Introductionmentioning

confidence: 99%

Recursive solution of queue length distribution for Geo/G/1 queue with single server vacation and variable input rate

Luo

Xiang

et al. 2011

Computers & Mathematics with Applications

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a b s t r a c tIn this paper we consider discrete time Geo/G/1 queue with single server vacation and variable input rate. Using renewal process, probability decomposition technique and u-transform, we derive the recursive expressions of the queue length distributions at epochs n − , n + , and n. The results obtained in this paper indicate that the equilibrium queue length distribution no longer follows the stochastic decomposition discipline. Furthermore we derive the important relations between equilibrium queue length distributions at different epochs (n − , n + , n).

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Analysis of a discrete-time queueing system with time-limited service

Cited by 27 publications

References 14 publications

Transient Queue Size Distribution Solution of Geom / G / 1 Queue with Feedback-A Recursive Method

Transient Queue Size Distribution Solution of Geom / G / 1 Queue with Feedback-A Recursive Method

Waiting time analysis for a queueing system with time‐limited service and exponential timer

Recursive solution of queue length distribution for Geo/G/1 queue with single server vacation and variable input rate

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