This paper studies the time-dependent analysis of an M/M/1 queueing model with single, multiple working vacation, balking and vacation interruptions. Whenever the system becomes empty, the server commences working vacation. During the working vacation period, if the queue length reaches a positive threshold value ‘k’, the working vacation of the server is interrupted and it immediately starts the service in an exhaustive manner. During working vacations, the customers become discouraged due to the slow service and possess balking behavior. The transient system size probabilities of the proposed model are derived explicitly using the method of generating function and continued fraction. The performance indices such as average and variance of system size are also obtained. Further, numerical simulations are presented to analyze the impact of system parameters.
Arumugam Azhagappan, Thirunavukkarasu Deepa
. Transient Behavior of a Single-Server Markovian Queue with Balking and Working Vacation Interruptions[J]. Journal of the Operations Research Society of China, 2021
, 9(2)
: 322
-341
.
DOI: 10.1007/s40305-019-00288-3
[1] Servi, L.D., Finn, S.G.: M/M/1 queue with working vacations (M/M/1/WV). Perform. Eval. 50, 41–52(2002)
[2] Sudhesh, R., Azhagappan, A., Dharmaraja, S.: Transient analysis of M/M/1 queue with working vacation heterogeneous service and customers’ impatience. RAIRO Oper. Res. 51(3), 591–606(2017)
[3] Sudhesh, R., Azhagappan, A.: Transient analysis of an M/M/1 queue with variant impatient behavior and working vacations. Opsearch 55(3–4), 787–806(2018)
[4] Tian, N., Zhao, X., Wang, K.: The M/M/1 queue with single working vacation. Int. J. Inf. Manag. Sci. 19, 621–634(2008)
[5] Vijayalaxmi, P., Jyothsna, K.: Analysis of finite buffer renewal input queue with balking and multiple working vacations. Opsearch 50, 548–565(2013)
[6] Haight, F.A.: Queueing with balking. Biometrika 44, 360–369(1957)
[7] Kumar, B.K., Parthasarthy, P.R., Sharafali, M.: Transient solution of an M/M/1 queue with balking. Queueing Syst. 13(4), 441–447(1993)
[8] Baba, Y.: The M/PH/1 queue with working vacations and vacation interruption. J. Syst. Sci. Syst. Eng. 19(4), 496–503(2010)
[9] Gao, S., Liu, Z.: An M/G/1 queue with single working vacation and vacation interruption under Bernoulli schedule. Appl. Math. Model. 37(3), 1564–1579(2013)
[10] Goswami, C., Selvaraju, N.: A working vacation queue with priority customers and vacation interruptions. Int. J. Oper. Res. 17(3), 311–332(2013)
[11] Isijola-Adakeja, O.A., Ibe, O.C.: M/M/1 multiple vacation queueing systems with differentiated vacations and vacation interruptions. IEEE Access 2, 1384–1395(2014)
[12] Li, J., Tian, N.: The M/M/1 queue with working vacations and vacation interruptions. J. Syst. Sci. Syst. Eng. 16, 121–127(2007)
[13] Zhao, G., Du, X., Tian, N.: GI/M/1 queue with set-up period and working vacation and vacation interruption. Int. J. Inf. Manag. Sci. 20, 351–363(2009)
