2021 | 1 | 123-146
Article title

Discussion on the transient behavior of single server Markovian multiple variant vacation queues

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We consider an M/M/1 queue where beneficiary visits occur singly. Once the beneficiary level in the system becomes zero, the server takes a vacation at once. If the server finds no beneficiaries in the system, then the server can take another vacation after the return from the vacation. This process continues until the server has exhaustively taken all the J vacations. The closed form transient solution of the considered model and some important time-dependent performance measures are obtained. Further, the steady state system size distribution is obtained from the time-dependent solution. A stochastic decomposition structure of waiting time distribution and expression for the additional waiting time due to the presence of server vacations are studied. Numerical assessments are presented.
Physical description
  • Department of Mathematics, Karpagam Academy of Higher Education, Coimbatore 641 021, Tamil Nadu, India
  • Department of Mathematics, Karpagam Academy of Higher Education, Coimbatore 641 021, Tamil Nadu, India
  • AMMAR S.I., Transient analysis of an M/M/1 queue with impatient behavior and multiple vacations, Appl. Math. Comp., 2015, 260 (1), 97–105.
  • AMMAR S.I., Transient solution of an M/M/1 vacation queue with a waiting server and impatient customers, J. Egypt. Math. Soc., 2017, 25 (3), 337–342.
  • BANIK A.D., The infinite-buffer single server queue with a variant of multiple vacation policy and batch Markovian arrival process, Appl. Math. Model., 2009, 33 (7), 3025–3039.
  • CHANDRASEKARAN V.M., INDHIRA K., SARAVANARAJAN M.C., RAJADURAI P., A survey on working vacation queueing models, Int. J. Pure Appl. Math., 2016, 106 (6), 33–41.
  • DOSHI B.T., Queueing systems with vacations. A survey, Queueing Syst., 1986, 1, 29–66.
  • IBE O.C., ISIJOLA O.A., M/M/1 multiple vacation queueing systems with differentiated vacations, Model. Sim. Eng., 2014, 3, 1–6.
  • KALIDASS K., GNANARAJ J., GOPINATH S., KASTURI R., Transient analysis of an M/M/1 queue with a repairable server and multiple vacations, Int. J. Math. Oper. Res., 2014, 6 (2), 193–216.
  • KALIDASS K., KASTURI R., Time dependent analysis of M/M/1 queue with server vacations and a waiting server, QTNA 2011, Proc. 6th International Conference on Queueing Theory and Network Applications, 2011, 77–83.
  • KE J.C., Operating characteristic analysis on the M/M/1 system with a variant vacation policy and balking, Appl. Math. Model., 2007, 31 (7), 1321–1337.
  • KE J.C., WU C.H., ZHANG G., Recent developments in vacation queueing models: A short survey, Int. J. Oper. Res., 2010, 7 (4), 3–8.
  • KE J.C., HUANG H.I., CHU Y.K., Batch arrival queue with 𝑁-policy and at most 𝐽 vacations, Appl. Math. Model., 2010, 34 (2), 451–466.
  • LEVY Y., YECHIALI U., An M/M/1 queues with servers’ vacations, INFOR., 1976, 14 (2), 153–163.
  • LORIS-TEGHEM J., Analysis of single server queueing systems with vacation periods, Belg. J. Oper. Res. Stat. Comp. Sci., 1985, 25, 47–54.
  • LIU W., XU X., TIAN N., Some results on the M/M/1 queue with working vacations, Oper. Res. Lett., 2002, 50, 41–52.
  • PIKKALA V.L., PILLA R., Transient Solution of M/M/1 variant working vacation queue with balking, Int. J. Math. Model. Comp., 2018, 8, 17–27.
  • [16] SERVI L.D., FINN S.G., M/M/1 queues with working vacations (M/M/1/WV), Perform. Eval., 2002, 50 (1), 41–52.
  • SUDHESH R., AZHAGAPPAN A., Transient analysis of an M/M/1 queue with variant impatient behavior and working vacations, Opsearch, 2018, 55 (1), 787–806.
  • SUDHESH R., AZHAGAPPAN A., DHARMARAJA S., Transient analysis of M/M/1 queue with working vacation, heterogeneous service and customers’ impatience, RAIRO-Oper. Res., 2017, 51 (3), 591–606.
  • SUDHESH R., FRANCIS RAJ L., Computational analysis of stationary and transient distribution of single server queue with working vacation, International Conference on Computing and Communication Systems, 2012, 480–489.
  • SURANGA SAMPATH M.I.G., JICHENG LIU, Impact of customers impatience on an M/M/1 queueing system subject to differentiated vacations with a waiting server, Qual. Technol. Quant. Manage., 2018, 17 (2), 125–148.
  • SURANGA SAMPATH M.I.G., KALIDASS K., Transient analysis of a repairable single server queue with working vacations and system disasters, Springer, 2019, 258–272.
  • SURANGA SAMPATH M.I.G., KALIDASS K., JICHENG LIU., Transient analysis of an M/M/1 queueing system subjected to multiple differentiated vacations, impatient customers and a waiting server with application to IEEE 802.16E power saving mechanism, Indian145-146 J. Pure Appl. Math., 2020, 51 (1), 297–320.
  • TAKAGI H., Queueing analysis. A foundation of performance evaluation, Vol. I. Vacation and priority systems, North-Holland, Amsterdam 1991.
  • TIAN N., ZHANG Z.G., Vacation queueing models, Springer, 2006.
  • UPADHYAYA S., Queueing systems with vacation. An overview, Int. J. Math. Oper. Res., 2016, 9 (2), 167–213.
  • VIJAYASHREE K.V., JANANI B., Transient analysis of an M/M/1 queueing system subject to differentiated vacations, Qual. Technol. Quant. Manage., 2017, 15 (6), 730–748.
  • YUE D., YUE W., SAFFER Z.,CHEN X., Analysis of an M/M/1 queueing system with impatient customers and a variant of multiple vacation policy, J. Ind. Manage. Optim., 2014, 10 (1), 89–112.
  • ZHANG Z.G., TIAN N., Discrete time Geo/G/1 queue with multiple adaptive vacations, Queueing Syst., 2001, 38, 419–429.
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