• R. Kalyanaraman
• R. Shanthi

We consider an M/G/1 queue with K-phase of vacation and with second optional service. The service policy is after completion of essential service, the customer chooses an optional service with probability p or leaves the system with probability (1-p). Both the essential service and optional service follows general distributions. In addition, after completion of essential service or second optional service, if there are no customers in the system, the server takes vacation consisting of K-phases. After completing the Kth phase of vacation, the server enters into the service station independent of the number of customers in the system. The vacation periods follows general distribution. For this model the supplementary variable technique has been applied to obtain the probability generating functions of number of customers in the queue at different server states. Some particular models are obtained, and a numerical study is also carried out.

Vacation queue, Supplementary variable, Probability generating function, Performance measures.

"An M/G/1 Queue with K Phases of Vacation and with Second Optional Service and with State Dependent Arrival Rate", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.4, Issue 10, page no.678-700, October-2017, Available :http://www.jetir.org/papers/JETIR1710107.pdf

"An M/G/1 Queue with K Phases of Vacation and with Second Optional Service and with State Dependent Arrival Rate", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.4, Issue 10, page no. pp678-700, October-2017, Available at : http://www.jetir.org/papers/JETIR1710107.pdf