Analysis on a non-Markovian batch arrival queuing model with phases of service and multi vacations in cloud computing services

Abstract

We investigate a new variant of the M[X]/G/1 queue model with three levels of service and a single server in this study. The initial phase of service includes two types of service. Following that, the server provides the second level of service. During the service period, service interruption is unavoidable. This system also assumes that an interruption will occur during the second phase of service. As a result, it enters the repair process without delay. In addition, a vacation concept is introduced to carry out server maintenance work. A preprocessing work is performed in the setup time stage prior to the vacation stages. This model includes additional parameters such as reneging, setup time, and standby server. We find the stationary queue length of various system states using a probability generating function and derive various performance measures. Furthermore, some numerical examples are provided to investigate the impact of system parameters.