Non Markovian Queue with Two Types service Optional Re-service and General Vacation Distribution

Authors

K. Sathiya, Rajiv Gandhi Arts and Science College
G. Ayyappan, Pondicherry Engineering College

Abstract

We consider a single server batch arrival queueing system, where the server provides two types of heterogeneous service. A customer has the option of choosing either type 1 service with probability p1 or type 2 service with probability p2 with the service times follow general distribution. After the completion of either type 1 or type 2 service a customer has the option to repeat or not to repeat the type 1 or type 2 service. As soon as the customer service is completed, the server will take a vacation with probability θ or may continue staying in the system with probability 1 -θ: The re-service periods and vacation periods are assumed to be general. Using supplementary variable technique, the Laplace transforms of time dependent probabilities of system state are derived and thus we deduce the steady state results. We obtain the average queue size and average waiting time. Some system performance measures and numerical illustrations are discussed.

Recommended Citation

Sathiya, K. and Ayyappan, G. (2016). Non Markovian Queue with Two Types service Optional Re-service and General Vacation Distribution, Applications and Applied Mathematics: An International Journal (AAM), Vol. 11, Iss. 2, Article 2.
Available at: https://digitalcommons.pvamu.edu/aam/vol11/iss2/2