Performance analysis of a discrete-time Geo/G/1 queue with randomized vacations and at most J vacations

Luo, Chuanyi; Tang, Yinghui; Chao, Baoshan; Xiang, Kaili

doi:10.1016/j.apm.2013.01.033

Cited by 8 publications

(6 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Such a modified vacation discipline has potentially applications in practical systems [13], for example, in some stochastic production and inventory control systems such as production to orders. This is a continuation of work by Wang et al(2011) [16] and Luo et al (2013) [17] where they study the queue size distribution for / /1 with randomized vacation and at most vacations by using different methods, respectively. Instead of studying the queue size distribution studied in [16,17], this paper considers another theme-the departure process in that discrete-time model.…”

Section: Introductionmentioning

confidence: 57%

“…This is a continuation of work by Wang et al(2011) [16] and Luo et al (2013) [17] where they study the queue size distribution for / /1 with randomized vacation and at most vacations by using different methods, respectively. Instead of studying the queue size distribution studied in [16,17], this paper considers another theme-the departure process in that discrete-time model. The investigation of departure process in a queueing system is primarily motivated by the need to analyze queueing network models, in which the departure process of an upstream queue is the arrival process of the downstream queue.…”

Section: Introductionmentioning

confidence: 57%

See 1 more Smart Citation

Study on the Departure Process of Discrete-TimeGeo/G/1Queue with Randomized Vacations

Luo

Huang

Ding

2014

Discrete Dynamics in Nature and Society

Self Cite

View full text Add to dashboard Cite

This paper presents an analysis of the departure process of a discrete-timeGeo/G/1queue with randomized vacations. By using probability decomposition techniques and renewal process, the expression of expected number of departures during time interval(0+,n+]is derived. The relation among departure process, server state process, and service renewal process is obtained. The relation displays the decomposition characteristic of the departure process. Furthermore, the approximate expansion of the expected number of departures is gained. Since the departure process also often corresponds to an arrival process for a downstream queue in queueing network, it is hoped that the results obtained in this paper may provide useful information for queueing network.

show abstract

Section: Introductionmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 57%

Study on the Departure Process of Discrete-TimeGeo/G/1Queue with Randomized Vacations

Luo

Huang

Ding

2014

Discrete Dynamics in Nature and Society

Self Cite

View full text Add to dashboard Cite

show abstract

“…Over the past decades, Geo/G/1 queues and Geo/G/1 retrial queues with a variety of vacation policies have been well developed, such as Takagi [2], Zhang and Tian [16], Gao and Wang [17], Wang [18], Wang et al [19], Yue and Zhang [20], Luo et al [21], and Wang [22,23] (not exhaustive list). However, most of these vacation queues deal with the case of single waiting queues; i.e., there is only a waiting queue in the service area in the Geo/G/1 queue or an orbit waiting queue in the Geo/G/1 retrial queue.…”

Section: Related Workmentioning

confidence: 99%

Analysis of a Single Server Retrial Queue with Server Vacation and Two Waiting Buffers Based on ATM Networks

Gao

Wang

2019

Mathematical Problems in Engineering

View full text Add to dashboard Cite

is paper presents a discrete-time Geo/G/1 retrial queue with two waiting buffers to model an ATM network, in which the server begins a single vacation in cases where the system is empty at the instant of a service completion. New arriving customer who finds the server being on vacation can decide to either enter the retrial buffer with some probability p or leave the system with complementary probability 1 − p. But the new arriving customer can begin its service immediately if he finds the server idle and join the original buffer if he finds the server busy. We first carry out an extensive analysis of the model by using the supplementary variable method and the generating function approach, and give some performance measures, such as server's state probabilities and mean queue lengths in the original buffer, retrial buffer, and in the system. Secondly, we give the generating function of the sojourn time of a customer in the system and prove that Little's law still holds in our model. Sensitivity analysis and cost optimization are finally given for illustrative purposes.

show abstract

“…Recently, Cai et al [5] considered an M/G/1 repairable queueing system with warm standby failure and Min(N, V )-policy based on single vacation, Jiang et al [11] analyzed a GI/M/1 queue in multi-phase service environment with N -policy and disasters. In addition, some important research works on discrete-time queues with the threshold policies and vacation policies can be refer to the references behind (see [12], [14], [15], [16], [22], [28]). With the fast development of the information era, there has been an increasing interest in investigating some queueing systems with the joint control policy.…”

mentioning

confidence: 99%

Analysis of $ {{M}^{({{\lambda }_{1}}, {{\lambda }_{2}})}}/G/1 $ queue with uninterrupted single vacation and server's workload controlled <i>D</i>-policy

Liu

Tang

et al. 2023

JIMO

Self Cite

View full text Add to dashboard Cite

<p style='text-indent:20px;'>This paper studies an <inline-formula><tex-math id="M1">\begin{document}$ {{M}^{({{\lambda }_{1}}, {{\lambda }_{2}})}}/G/1 $\end{document}</tex-math></inline-formula> queueing system with uninterrupted single vacation under the control of <inline-formula><tex-math id="M2">\begin{document}$ D $\end{document}</tex-math></inline-formula>-policy based on server's workload, in which customers arrive at the system in variable input rates according to the states of the server. Employing the renewal process, the total probability decomposition technique and the Laplace transform, we discuss the transient queue length distribution at any time <inline-formula><tex-math id="M3">\begin{document}$ t $\end{document}</tex-math></inline-formula> under any initial state, and derive the expressions of the Laplace transform of the transient queue length distribution with respect to time <inline-formula><tex-math id="M4">\begin{document}$ t $\end{document}</tex-math></inline-formula>. Based on the transient analysis, the explicit recursive formulas of the steady-state queue length distribution are obtained by using L'Hospital's rule. Also, the expressions of its probability generating function of the steady-state queue length distribution and the expected queue size are presented. Meanwhile, some special cases are also discussed. Furthermore, numerical experiments are provided to investigate the sensitivity of the system performance measures and the system capacity optimization design. Finally, applying the renewal reward theorem, the explicit expression of the long-run expected cost per unit time of the system is derived. To demonstrate the model's application, we consider a practical situation related to a production system. Numerical examples are provided to determine the optimal control policy <inline-formula><tex-math id="M5">\begin{document}$ {{D}^{*}} $\end{document}</tex-math></inline-formula> for economizing the system cost as well as the optimal two-dimensional control policy <inline-formula><tex-math id="M6">\begin{document}$ ({{D}^{*}}, {{T}^{*}}) $\end{document}</tex-math></inline-formula> when the vacation time is a fixed length <inline-formula><tex-math id="M7">\begin{document}$ T $\end{document}</tex-math></inline-formula>.</p>

show abstract

Performance analysis of a discrete-time Geo/G/1 queue with randomized vacations and at most J vacations

Cited by 8 publications

References 17 publications

Study on the Departure Process of Discrete-TimeGeo/G/1Queue with Randomized Vacations

Study on the Departure Process of Discrete-TimeGeo/G/1Queue with Randomized Vacations

Analysis of a Single Server Retrial Queue with Server Vacation and Two Waiting Buffers Based on ATM Networks

Analysis of $ {{M}^{({{\lambda }_{1}}, {{\lambda }_{2}})}}/G/1 $ queue with uninterrupted single vacation and server's workload controlled <i>D</i>-policy

Contact Info

Product

Resources

About