Queuing System of Bulk Arrival Model With Optional Services in Third Stage and Two Different Vacation Policies

Abstract

This paper presents an introduction into the most important queueing theory concepts used for modeling computer performance. In this paper, customers arrive in batches to the queuing system. Arrival of customers follows a poisson process. The service to the customers is given in three stages in which the first two stages are compulsory and the third stage is optional. Server can avail vacation of short or long period after the completion of service. Moreover, the server may breakdown at random which leads to a repair process immediately. By means of supplementary variable technique and generating function approach the probability generating function of the cloud computing user queue size is determined. The other performance measures of the model are derived by means of Little's law. A trade-off between the Quality of service and queue length is observed.