Analysis of the GI/Geo/1 queue with N -policy

Lim, Dae-Eun; Lee, Doo-Ho; Yang, Won Seok; Chae, Kyung-Chul

doi:10.1016/j.apm.2012.09.037

Cited by 23 publications

(15 citation statements)

References 14 publications

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“…Luo, et al [10] obtained the recursive solution of queue length for Geo/G/1 queue with N -policy, and the important relations between the steady state queue length distributions at different time epochs n − , n and n + are discovered. Moreover, under the renewal input process, Lim, et al [11] studied the GI/Geo/1 queue with N -policy and obtained the steady state queue length and the waiting time distributions.…”

Section: Introductionmentioning

confidence: 99%

Queue size distribution of Geo/G/1 queue under the Min(N,D)-policy

Ying-yuan

Tang

et al. 2016

J Syst Sci Complex

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This paper considers a discrete-time Geo/G/1 queue under the Min(N, D)-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D, whichever occurs first (Min(N, D)-policy). By using renewal process theory and total probability decomposition technique, the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state, and obtain both the recursive expression of the z-transformation of the transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n + . Meanwhile, the authors obtain the explicit expressions of the additional queue length distribution. Furthermore, the important relations between the steady state queue length distributions at different time epochs n − , n and n + are also reported. Finally, the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution, and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.

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Section: Introductionmentioning

confidence: 99%

Queue size distribution of Geo/G/1 queue under the Min(N,D)-policy

Ying-yuan

Tang

et al. 2016

J Syst Sci Complex

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“…Since the introduction of the N-policy, there has been considerable attention on this topic. For more literature on N-policy queues, we may refer interested readers to the works of Moreno (2007), Ke (2003), Ke and Wang (2002), Zhang and Tian (2004), Lim et al (2013), Lee and Yang (2013), and others.…”

Section: Introductionmentioning

confidence: 99%

“…Meanwhile, the system may suffer from disasters while the server is idle. Following the idea presented by Lim et al (2013), who used a trial solution approach in dealing with the N-policy queue, we derive the stationary queue length distribution at arrival epochs. Furthermore, we give the stationary queue length distribution at arbitrary epochs by using the method of the semi-Markov process.…”

Section: Introductionmentioning

confidence: 99%

Analysis of an N–Policy GI/M/1 Queue in a Multi–Phase Service Environmentwith Disasters

Jiang

Ammar

Chang

et al. 2018

International Journal of Applied Mathematics and Computer Science

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This paper investigates an N-policy GI/M/1 queue in a multi-phase service environment with disasters, where the system tends to suffer from disastrous failures while it is in operative service environments, making all present customers leave the system simultaneously and the server stop working completely. As soon as the number of customers in the queue reaches a threshold value, the server resumes its service and moves to the appropriate operative service environment immediately with some probability. We derive the stationary queue length distribution, which is then used for the computation of the Laplace-Stieltjes transform of the sojourn time of an arbitrary customer and the server’s working time in a cycle. In addition, some numerical examples are provided to illustrate the impact of several model parameters on the performance measures.

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“…As special cases, the Geo / /1 queues with multiple vacations, single vacation, and -policy are also considered. Until recently, numerous studies have been reported regarding variations of queueing systems with -policy and vacations including Markovian queues (Choudhury [9], Ke et al [10], and Wang 2 Journal of Applied Mathematics [11]), general input queues (Lim et al [12]), and combination with other control policies (Ke et al [13] and Feyaerts et al [14]). Also, reported works are well summarized by Tian and Zhang [15].…”

Section: Introductionmentioning

confidence: 99%

On the Discrete-TimeGeoX/G/1Queues underN-Policy with Single and Multiple Vacations

Kim

Park

et al. 2013

Journal of Applied Mathematics

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We consider the discrete-time Geo / /1 queue under N-policy with single and multiple vacations. In this queueing system, the server takes multiple vacations and a single vacation whenever the system becomes empty and begins to serve customers only if the queue length is at least a predetermined threshold value N. Using the well-known property of stochastic decomposition, we derive the stationary queue-length distributions for both vacation models in a simple and unified manner. In addition, we derive their busy as well as idle-period distributions. Some classical vacation models are considered as special cases.

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Analysis of the GI/Geo/1 queue with N -policy

Cited by 23 publications

References 14 publications

Queue size distribution of Geo/G/1 queue under the Min(N,D)-policy

Queue size distribution of Geo/G/1 queue under the Min(N,D)-policy

Analysis of an N–Policy GI/M/1 Queue in a Multi–Phase Service Environmentwith Disasters

On the Discrete-TimeGeoX/G/1Queues underN-Policy with Single and Multiple Vacations

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