On Optional Deterministic Server Vacations in a Batch Arrival Queueing System with a Single Server Providing First Essential Service Followed by One of the Two Types of Additional Optional Service<
Authors :
Kailash C. Madan
Author Address :
Ahlia University, PO Box 10878, GOSI Complex, Kingdom of Bahrain.
Abstract :
We analyze a batch arrival queue with a single server providing first essential service (FES) followed by one of the two types of additional optional service (AOS). After completion of the FES, a customer has the option to leave the system or to choose one of the two types of AOS and as soon as a customer leaves (either after the FES or after completing one of the chosen AOS, the server may take a vacation or may continue staying in the system. The vacation times are assumed to be deterministic and the server vacations are based on Bernoulli schedules under a single vacation policy. We obtain explicit queue size distribution at a random epoch under the steady state. In addition, some important performance measures such as the steady state expected queue size and the expected waiting time of a customer at a random epoch are obtained. Further, some interesting particular cases are also discussed.
Keywords :
Batch arrivals, compound Poisson process, first essential service (FES), additional optional service (AOS), deterministic server vacation, queue size distribution.
DOI :
Article Info :
Received : June 26, 2015; Accepted : August 23, 2015.
