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Busy Period Analysis for the Discrete-time GI/Geo/1 Queue with Multiple Vacations

Kim Sung-Jin, Lim Dae-Eun
<span title="2015-07-09">2015</span> <i title="Indian Society for Education and Environment"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wffwpj3q45g5zfjzfeyagk5uea" style="color: black;">Indian Journal of Science and Technology</a> </i> &nbsp;
We consider the discrete-time GI/Geo/1 queue with multiple geometric vacations.  ...  We derive the joint probability generating function of the length of a busy period, the number of customers served during the busy period, and the residual interarrival time at the instant the busy period  ...  Introduction We consider the discrete-time GI/Geo/1 queue with multiple geometric vacations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.17485/ijst/2015/v8i15/73367">doi:10.17485/ijst/2015/v8i15/73367</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/myufg2pzibeo3g6pbho6drzfyu">fatcat:myufg2pzibeo3g6pbho6drzfyu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190428131708/http://www.indjst.org/index.php/indjst/article/download/73367/65650" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.17485/ijst/2015/v8i15/73367"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Analysis of finite capacity discrete-time GI/Geo/1 queueing system with multiple vacations

S K Samanta, U C Gupta, R K Sharma
<span title="">2007</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fq4jrflj6zesjk7f4nb4otuwwy" style="color: black;">Journal of the Operational Research Society</a> </i> &nbsp;
SK Samanta et a/—Gi/Geo/1 queueing system with multiple vacations 377 Gravey A and Hebuterne G (1992). Simultaneity in discrete time single server queues with Bernoulli inputs.  ...  SK Samanta et a/—Gi/Geo/1 queueing system with multiple vacations 375 It may be noted that to obtain the average waiting-time in tional stage even for high values of parameters of the the queue (W,) of  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1057/palgrave.jors.2602148">doi:10.1057/palgrave.jors.2602148</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2x56wkfrcrd4bkyhvbxde5u2oy">fatcat:2x56wkfrcrd4bkyhvbxde5u2oy</a> </span>
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The discrete-time GI/Geo/1 queue with working vacations and vacation interruption

Ji-hong Li, Nai-shuo Tian
<span title="">2007</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xkk23xlywfez5l246cnmlit4qq" style="color: black;">Applied Mathematics and Computation</a> </i> &nbsp;
In this paper, we consider a GI/Geo/1 queue with working vacations and vacation interruption.  ...  Meanwhile, we explain the stochastic decomposition properties of queue length and waiting time.  ...  Acknowledgements The authors would like to thank the support from National Natural Science Foundation of China #10271102.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.amc.2006.07.008">doi:10.1016/j.amc.2006.07.008</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zhmxkwazajhwhcq34axfzgnmei">fatcat:zhmxkwazajhwhcq34axfzgnmei</a> </span>
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M/M/1 Multiple Vacation Queueing Systems with Differentiated Vacations

Oliver C. Ibe, Olubukola A. Isijola
<span title="">2014</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/vuxtivm3engnvjeetvpgeep2um" style="color: black;">Modelling and Simulation in Engineering</a> </i> &nbsp;
For ease of analysis it is assumed that the service times are exponentially distributed and the two vacation types are also exponentially distributed but with different means.  ...  We consider a multiple vacation queueing system in which a vacation following a busy period has a different distribution from a vacation that is taken without serving at least one customer.  ...  They also want to thank the reviewers for their comments on the application of the model to practical systems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2014/158247">doi:10.1155/2014/158247</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wshssgfuy5cqnfxegmt3dyuinq">fatcat:wshssgfuy5cqnfxegmt3dyuinq</a> </span>
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Analysis of the equilibrium strategies in the Geo/Geo/1 queue with multiple working vacations [article]

Yang Bixuan, Hou Zhenting, Wu Jinbiao, Liu Zaiming
<span title="2014-04-27">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This paper studies the equilibrium behavior of customers in the Geo/Geo/1 queueing system with multiple working vacations.  ...  The arriving customers decide whether to join or to balk the queueing systems based on the information of the queue length and the states of the server.  ...  Acknowledgements This research is partially supported by the National Natural Science Foundation of China (11201489, 11271373, 11371374) .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1404.6758v1">arXiv:1404.6758v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/52uy2xfbfvfpxjan6n2eum63i4">fatcat:52uy2xfbfvfpxjan6n2eum63i4</a> </span>
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Performance analysis and optimization of a pseudo-fault Geo/Geo/1 repairable queueing system with $N$-policy, setup time and multiple working vacations

Wuyi Yue, Pengcheng Wang, Zhanyou Ma
<span title="">2016</span> <i title="American Institute of Mathematical Sciences (AIMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/s5irg25l6bbd7hbii2cthj7k3m" style="color: black;">Journal of Industrial and Management Optimization</a> </i> &nbsp;
In this paper, we consider a discrete time Geo/Geo/1 repairable queueing system with a pseudo-fault, setup time, N -policy and multiple working vacations.  ...  If the pseudo-fault occurs, the server will enter into a vacation period instead of a busy period.  ...  This work was supported by the National Natural Science  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3934/jimo.2017002">doi:10.3934/jimo.2017002</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fwa7m33cw5etfa4zzdjseujqay">fatcat:fwa7m33cw5etfa4zzdjseujqay</a> </span>
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Discrete-time GeoX/G/1 queue with unreliable server and multiple adaptive delayed vacations

Yinghui Tang, Xi Yun, Shujuan Huang
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/av75skmu6neednu63f27tpk7qu" style="color: black;">Journal of Computational and Applied Mathematics</a> </i> &nbsp;
In this paper we consider a discrete-time Geo X /G/1 queue with unreliable server and multiple adaptive delayed vacations policy in which the vacation time, service time, repair time and the delayed time  ...  Several common vacation policies are special cases of the vacation policy presented in this study.  ...  Acknowledgment The authors wish to thank the anonymous referees for their valuable comments and suggestions for the improvement of this paper and the supports from Natural Science Foundation of the Education  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cam.2007.08.019">doi:10.1016/j.cam.2007.08.019</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ykokgnzewbf6pee25kn47btlgi">fatcat:ykokgnzewbf6pee25kn47btlgi</a> </span>
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Analyzing discrete-time D-BMAP/G/1/N queue with single and multiple vacations

S.K. Samanta, U.C. Gupta, R.K. Sharma
<span title="">2007</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2fqqu5s6wbgk5gcucpt3wqm3gy" style="color: black;">European Journal of Operational Research</a> </i> &nbsp;
This paper analyzes a single-server finite-buffer vacation (single and multiple) queue wherein the input process follows a discrete-time batch Markovian arrival process (D-BMAP).  ...  The service and vacation times are generally distributed and their durations are integral multiples of a slot duration.  ...  Acknowledgement The authors are thankful to the referees for their valuable comments and suggestions which have led to the presentation of this paper in its present form.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ejor.2006.09.031">doi:10.1016/j.ejor.2006.09.031</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/enqssxmwcfcfbmj5axoizwbnyy">fatcat:enqssxmwcfcfbmj5axoizwbnyy</a> </span>
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On the Two-Moment Approximation of the Discrete-Time GI/G/1 Queue with a Single Vacation

Doo Ho Lee
<span title="">2016</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3s4wom7forhp3klujcroiocrpi" style="color: black;">Discrete Dynamics in Nature and Society</a> </i> &nbsp;
We consider a discrete-time GI/G/1 queue in which the server takes exactly one vacation each time the system becomes empty.  ...  The interarrival times of arriving customers, the service times, and the vacation times are all generic discrete random variables.  ...  For a discrete-time 2 Discrete Dynamics in Nature and Society GI/Geo/1/GSV, where GSV stands for geometric single vacation, Chae et al.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2016/5345374">doi:10.1155/2016/5345374</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iyi6av3epbcahljtmvgoxx7kga">fatcat:iyi6av3epbcahljtmvgoxx7kga</a> </span>
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Analysis of the discrete-time Geo/G/1 working vacation queue and its application to network scheduling

Ji-hong Li
<span title="">2013</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4k6bj3yn4rcg5ffssuooy6efde" style="color: black;">Computers &amp; industrial engineering</a> </i> &nbsp;
In this paper we present an exact steady-state analysis of a discrete-time Geo/G/1 queueing system with working vacations, where the server can keep on working, but at a slower speed during the vacation  ...  To understand the stationary queue length better, by applying the stochastic decomposition theory of the standard M/G/1 queue with general vacations, another equivalent expression for the PGF is derived  ...  Acknowledgements The authors thank editors and referees for their valuable comments and suggestions, which are very helpful to improve the manuscript.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cie.2013.04.009">doi:10.1016/j.cie.2013.04.009</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pdjghgubznczrawap2emuufbmq">fatcat:pdjghgubznczrawap2emuufbmq</a> </span>
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Synchronized abandonment in discrete-time renewal input queues with vacations

Veena Goswami, Gopinath Panda
<span title="">2021</span> <i title="American Institute of Mathematical Sciences (AIMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/s5irg25l6bbd7hbii2cthj7k3m" style="color: black;">Journal of Industrial and Management Optimization</a> </i> &nbsp;
<p style='text-indent:20px;'>We consider a discrete-time infinite buffer renewal input queue with multiple vacations and synchronized abandonment.  ...  Waiting customers get impatient during the server's vacation and decide whether to take service or abandon simultaneously at the vacation completion instants.  ...  GI/Geo/1 queue with multiple vacations. Taking p = 0, the model reduces to GI/Geo/1 queue with multiple vacations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3934/jimo.2021163">doi:10.3934/jimo.2021163</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zlim7r3s4fer7act2xu5r6prfi">fatcat:zlim7r3s4fer7act2xu5r6prfi</a> </span>
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Page 377 of The Journal of the Operational Research Society Vol. 58, Issue 3 [page]

<span title="">2007</span> <i title="Palgrave Macmillan"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_journal-of-the-operational-research-society" style="color: black;">The Journal of the Operational Research Society</a> </i> &nbsp;
SK Samanta et a/—Gi/Geo/1 queueing system with multiple vacations 377 Gravey A and Hebuterne G (1992). Simultaneity in discrete time single server queues with Bernoulli inputs.  ...  The discrete-time G//Geo/1 queue with multiple vacations. Queueing Systems 40: 283-294. Woodward ME (1994). Communication and Computer Networks: Modelling with Discrete-Time Queues.  ... 
<span class="external-identifiers"> </span>
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Performance Analysis Of A Discrete-Time Geox/G/1 Queue With Single Working Vacation

Shan Gao, Zaiming Liu
<span title="2011-08-20">2011</span> <i title="Zenodo"> Zenodo </i> &nbsp;
This paper treats a discrete-time batch arrival queue with single working vacation.  ...  For this purpose, we first analyze the Markov chain underlying the queueing system and obtain its ergodicity condition.  ...  [5] respectively discussed a continuous-time GI/M/1 and a discrete-time GI/Geo/1 queue with working vacations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5281/zenodo.1080278">doi:10.5281/zenodo.1080278</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wtotp4jdwjhwvew2vgbaz4rtfy">fatcat:wtotp4jdwjhwvew2vgbaz4rtfy</a> </span>
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Performance analysis of GI/M/1 queue with working vacations and vacation interruption

Ji-Hong Li, Nai-Shuo Tian, Zhan-You Ma
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gtpvsgujvfb5fjb2m4xzlxum6a" style="color: black;">Applied Mathematical Modelling</a> </i> &nbsp;
The GI/M/1 queue with such two policies is described and by the matrix analysis method, we obtain various performance measures such as mean queue length and waiting time.  ...  In this paper, we analyze a single-server vacation queue with a general arrival process. Two policies, working vacation and vacation interruption, are connected to model some practical problems.  ...  Meanwhile, the authors also thank the support from National Natural Science Foundation of China #10671170, and the work is also supported by the Science Foundation of Yanshan University for the Excellent  ... 
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A note on the sojourn time distribution of an M/G/1 queue with a single working vacation and vacation interruption

Doo Ho Lee, Bo Keun Kim
<span title="">2015</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/57sxpgdcmnch3nzb556bdheuhu" style="color: black;">Operations Research Perspectives</a> </i> &nbsp;
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.  ...  [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. Lately, Xu et al.  ... 
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