Transient and steady state analysis of M/M^([b])/1 queue with second optional service

References

• Templeton JGC, Sim SH. Computational procedure for steady state characteristics of unscheduled multi carrier shuttle system. Eur J Oper Res. 1983;12(2):190–202.
   Web of Science ®Google Scholar
• Ayyappan G, Karpagam S. Analysis of a bulk queue with unreliable server, immediate feedback, N-Policy, Bernoulli schedule multiple vacation and stand by server. Ain Shams Eng J. 2019;10(4):873–880.
   Web of Science ®Google Scholar
• Carmen A, David C. Bayesian hierarchical models in manufacturing bulk service queues. J Stat Plan Infer. 2004;136(2):335–354.
   Web of Science ®Google Scholar
• Ayyappan G, Devipriya G, Muthu A. Analysis of single server fixed batch service queueing system under multiple vacation with catastrophe. Math Theory Model. 2013a;3(11):35–41.
   Google Scholar
• Ayyappan G, Devipriya G, Muthu A. Analysis of single server fixed batch service queueing system under multiple vacation with gated service. Int J Comput Appl. 2014a;89(5):15–19.
   Google Scholar
• Ommeren VKJ, Baer N, Mishra N, et al. Batch service systems with heterogeneous servers. Queueing Syst. 2020;95(3–4):251–269.
   Web of Science ®Google Scholar
• Madan CK. An M/G/1 queue with second optional service. Queueing Syst. 2000;34(1/4):37–46.
   Web of Science ®Google Scholar
• Medhi J. A single server poison input queue with a second optional channel. Queueing Syst. 2002;42(3):239–242.
   Web of Science ®Google Scholar
• Maraghi FA, Madan KC, Dowman KD. Batch arrival vacation queue with second optional service and random system breakdowns. J Stat Theory Pract. 2010;4(1):137–153.
   Google Scholar
• Yang DY, Chen YH. Computation and optimization of a working breakdown queue with second optional servic. J Ind Prod Eng. 2018;35(3):181–188.
   Web of Science ®Google Scholar
• Jau CK, Chia HW, Wen LP. Analysis of an infinite multi server queue with an optional service. Comput Ind Eng. 2013;65(2):216–225.
   Web of Science ®Google Scholar
• Ayyappan G, Devipriya G, Muthu A. Analysis of single server batch service queueing system under multiple vacations with second optional service. Int J Math Archive. 2014b;5(2):126–144.
   Google Scholar
• Uma S, Punniyamoorthy K. Single server bulk queue with second optional service, balking and compulsory vacation. Int J Eng Res Appl. 2016;6:15–20.
   Google Scholar
• Ayyappan G, Devipriya G, Muthu A. Transient analysis of single server queueing system with batch service under catastrophe. Int J Math Archive. 2013b;4(5):26–32.
   Google Scholar
• Oduol VK, Ardil C. Transient analysis of a single server queue with fixed size batch arrival. Int J Electr Comput Eng. 2012;6(2):253–258.
   Google Scholar
• Ayyappan G, Shyamala S. Time dependent solution of Mx/G/1 queueing model with second optional service, Bernoulli K-Optional vacation and balking. Int J Sci Res Publ. 2013c;3(9):1–13.
   Google Scholar
• Ayyappan G, Shyamala S. Transient solution of Mx/G/1 with second optional service, Bernoulli schedule server vacation and random break downs. Int J Manag Infor Techn. 2013d;3(3):45–55.
   Google Scholar
• Choudhury G, Paul M. A batch arrival queueing with a second optional service channel under N-Policy. Stochastic Anal Appl. 2007;24(1):1–21.
   Web of Science ®Google Scholar
• Singh S, Srivastava KR. Markovian queueing system with bulk arrival and three types of essential and optional services. Int J Math Appl. 2020;8(4):103–112.
   Google Scholar
• Shyamala S, Vijayaraj R. Time dependent solution of two stages Mx/G/1 queue model server vacation random setup time and balking with Bernoulli schedule. AIP Conference Proceedings 2261, 030005. 2020.
   Google Scholar
• Devi RNV, AnkammaRao A, Chandan K. Analysis of a M/M/1 queueing system with two-phase, N- Policy, server failure and second optional batch service with customers impatient behaviour, IOP Conf. Series; J Phys: Conf. Series 1344. 2019.
   Google Scholar
• Kalyanaraman R, Murugan SPB. A single service queue with additional optional service in batches and server vacation. Appl Math Sci. 2008;2(56):2765–2776.
   Google Scholar
• Laxmi VP, George AA. Transient analysis of batch service queue with second optional service and reneging. Int J Adva Sci Hub. 2020;2(10):29–38.
   Google Scholar
• Medhi J. Stochastic models in queueing theory. 2nd ed. California (USA): Academic Press; 2003.
   Google Scholar
• Al-Jararha J, Madan CK. An M/G/1 queueing with second optional service with general service time distribution. Inform and Manag Sci. 2003;14(2):47–56.
   Google Scholar