An Efficient Method to Compute the Rate Matrix for Multi-Server Retrial Queues with Cloud Computing Systems

Abstract

This study presents the usage of retrial queues with cloud computing systems in which the operating unit (the server) and the storing unit (buffer) are independently considered. In fact, the tasks cannot occupy the server to the system. Instead, they are stored in the buffer and sent back to the server after a random time. Upon a service completion, the server does not always get to work while waiting for a new task or a task from the buffer. After the idle time, the server instantly starts searching for a task from the buffer. The analysis model proposed in this study refers to a retrial queue system searching for tasks from theorbit with limited size under a multi-server context, and the model is modelized into the 3-dimension Markov chain. The solution is based on building an algorithm under the analytical methodology of the quasi birthdeath (QBD) process that utilizes the Q-matrix to calculate the probability of states toward the proposed model.