The GI/M/1 queue and the GI/Geo/1 queue both with single working vacation

In this paper, we study a finite buffer renewal input N-policy queue with state dependent services and working vacations. The amount of service demanded by a customer is conditioned by the queue length at the moment service is begun for that customer. We provide a recursive algorithm using the supplementary variable technique to compute the stationary queue length distribution of the system. Some queueing models discussed in the literature are derived as special cases. Finally, using some numerical results, we present the parameter effect on various performance measures.

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“…As K ! 1 our model reduces to a GI=M=1=1 queue with SWV and the results are in conformity with those of Chae et al (2009).…”

Section: Special Casessupporting

confidence: 84%

“…The analysis of a GI=M=1 queue with MWV was carried out by Baba (2005) and Banik, Gupta, and Pathak (2007) and, for SWV, see Banik (2010) and Li and Tian (2011). Recent studies related to the GI=M=1 queue together with the GI=Geo=1 queue with SWV are to be found in Chae, Lim, and Yang (2009).…”

Section: Introductionmentioning

confidence: 99%

Analysis of state dependent N-policy queue with working vacations

Laxmi

Suchitra

2013

International Journal of Management Science and Engineering Man

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“…Many fruitful theoretical results and interesting applications are presented in this area (see, e.g. [25][26][27][28][29][30][31][32][33][34][35][36][37]). On the other hand, in both single and multiple working vacation policies, server resumes fast service rate only when the system is non-empty at the end of a vacation.…”

Section: Introductionmentioning

confidence: 99%

Strategic queueing behavior for individual and social optimization in managing discrete time working vacation queue with Bernoulli interruption schedule

Alfa

2016

Computers & Operations Research

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In this paper, we consider a discrete time working vacation queue with a utility function for the reward of receiving the service and the cost of waiting in the system. A more flexible switching mechanism between low and regular service states is introduced to enhance the practical value of the working vacation queue. Under different precision levels of the system information, namely observable, almost unobservable and fully unobservable cases, the utility function is studied from both the individual customer's and the system administrator's points of view. By analyzing the steady-state behavior of the system, the associated optimal joining decisions under different information scenarios are obtained. We find that for the fully observable queue, the joining threshold for individual optimization may be less than the one for social optimization in working vacation period. A similar situation also appears in almost unobservable case. Such phenomenon is not possible for the classic first come first served queue due to the fact that there is no vacation time and thus will not cause large fluctuations in customers' conditional waiting time. Additionally, we also conduct some numerical comparisons to demonstrate the effect of the information levels as well as system parameters on customer joining behavior.

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“…Gao and Liu [11] investigated an M/G/1/SWV queue. Chae et al [12] discussed a GI/M/1/SWV queue and a discretetime GI/Geo/1/SWV queue. Banik [13] extended the system to a finite buffer GI/M/1/N/SWV queue.…”

Section: Introductionmentioning

confidence: 99%

A note on the sojourn time distribution of an M/G/1 queue with a single working vacation and vacation interruption

Lee

Kim

2015

Operations Research Perspectives

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a b s t r a c tWe study the paper of Gao and Liu (2013). In the paper, the authors pay little attention to the customer's sojourn time in their model although both the queue length and the busy cycle are seriously analyzed. The objective of this note is to derive the sojourn time distribution of Gao and Liu's model without considering Bernoulli schedule. A simple numerical example is also given to demonstrate our result.

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The GI/M/1 queue and the GI/Geo/1 queue both with single working vacation

Cited by 35 publications

References 14 publications

Analysis of state dependent N-policy queue with working vacations

Analysis of state dependent N-policy queue with working vacations

Strategic queueing behavior for individual and social optimization in managing discrete time working vacation queue with Bernoulli interruption schedule

A note on the sojourn time distribution of an M/G/1 queue with a single working vacation and vacation interruption

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