JSSM  Vol.5 No.3 , September 2012
On an M/G/1 Queueing Model with k-Phase Optional Services and Bernoulli Feedback
Abstract: In this article an M/G/1 queueing model with single server, Poisson input, k-phases of heterogeneous services and Bernoulli feedback design has been considered. For this model, we derive the steady-state probability generating function (PGF) of queue size at the random epoch and at the service completion epoch. Then, we derive the Laplace-Stieltjes Transform (LST) of the distribution of response time, the means of response time, number of customers in the system and busy period.
Cite this paper: S. Abdollahi and M. Rad, "On an M/G/1 Queueing Model with k-Phase Optional Services and Bernoulli Feedback," Journal of Service Science and Management, Vol. 5 No. 3, 2012, pp. 280-288. doi: 10.4236/jssm.2012.53033.

[1]   D. Bertsimas and X. Papaconstantinou, “On the Steady State Solution of the M/C2(a;b)/S Queueing System,” Transportation Sciences, Vol. 22, No. 2, 1988, pp. 125138. doi:10.1287/trsc.22.2.125

[2]   O. J. Boxma and U. Yechiali, “An M/G/1 Queue with Multiple Type of Feedback and Gated Vacations,” Journal of Applied Probability, Vol. 34, No. 3, 1997, pp. 773784. doi:10.2307/3215102

[3]   G. Choudhury, “A Batch Arrival Queueing System with an Additional Service Channel,” International Journal of Information and Management Sciences, Vol. 14, No. 2, 2003, pp. 17-30.

[4]   G. Choudhury and P. Madhuchanda, “A Two Phase Queueing System with Bernolli Feedback,” Information and Management Sciences, Vol. 16, No. 1, 2005, pp. 35-52.

[5]   B. D. Choi, B. Kim and S. H. Choi, “An M/G/1 Queue with Multiple Types of Feedback, Gated Vacations and FCFS Policy,” Computers and Operations Research, Vol. 30, No. 9, 2003, pp. 1289-1309. doi:10.1016/S0305-0548(02)00071-0

[6]   R. L. Disney, “A Note on sojourn Times in M/G/1 Queue with Instantaneous Bernoulli Feed-Back,” Naval Research Logistics Quarterly, Vol. 28, No. 4, 1981, pp. 679-684. doi:10.1002/nav.3800280415

[7]   B. Krishna Kumar, A. Vijaykumar and D. Arivudainambi, “An M/G/1 Retrial Queueing System with two Phase Service and Preemptive Resume,” Annals of Operations Research, Vol. 113, No. 1-4, 2002, pp. 61-79. doi:10.1023/A:1020901710087

[8]   K. C. Madan, “An M/G/1 Queue with Second Optional Service,” Queueing Systems, Vol. 34, No. 1-4, 2000, pp. 37-46. doi:10.1023/A:1019144716929

[9]   J. Medhi, “A Single Server Poisson Input Queue with a Second Optional Channel,” Queueing Systems, Vol. 42, No. 3, 2002, pp. 239-242. doi:10.1023/A:1020519830116

[10]   G. H. Shahkar and A. Badamchizadeh, “A Single Server Queue with k-Phase of Heterogeneous Service under Bernoulli Schedule and a General Vacation Time,” Journal of Theoretical Statistic, Vol. 20, No. 2, 2006, pp. 151-162.

[11]   H. Takagi, “A Note on the Response Time in M/G/1 Queue with Service in Random Order and Bernoulli Feedback,” Journal of Operational Research Society of Japan, Vol. 39, No. 4, 1996, pp. 486-500.