Modified Bernoulli vacation batch arrival and retrial clients in a single server queuing model with server utilization
Authors :
V. Rajam 1 * and S. Uma 2
Author Address :
1 Department of Mathematics, Rajah Serfoji Government College, Affiliated to Bharathidasan University, Thanjavur-613005, Tamil Nadu, India.
2 Department of Mathematics, Dharmapuram Gannambigai Government Women’s College, Mayilduthurai-609001, Tamil Nadu, India.
*Corresponding author.
Abstract :
This paper investigates a batch arrival feedback retrial queue with two types of service under modified Bernoulli vacation where each type consists of an optional re-service where the busy server is subjected to starting failures In Poisson form, the consumer comes to the system in batches but can also baulk at certain specific times. Customers may re-service the same type without joining the orbit after the completion of each type of service or may leave the system. The server either goes on vacation at the completion stage of each service or can wait for the next client to serve. The model is analysed during the supplementary variable technique and the probability generating function of system size, the server utilization and the probability that the system is empty are found. Stochastic decomposition law is shown to hold good for this model also when there is no bulking permitted along with other performance measures to predict the behaviour of the system are derived. Further, we carry out some special cases for the proposed model.
Keywords :
Modified Bernoulli Vacation, Retrial Queue, Single server Queue, Server Utilization.
DOI :
Article Info :
Received : September 14, 2020; Accepted : December 11, 2020.
