Analysis of Queueing Networks with Geo/Geo/1 Clients and Batch Service Queue

Currently, the knowledge of queueing network is an important tool for modeling many complex communication systems. In this work, we consider a tandem open queueing network consisting of multiple Geo/Geo/1 clients, and a server with batch service queue. All of queues are finite-buffer discrete-time. The main purpose of this work is to analyze the average delay and the overflow probability of messages from each client through the system. To solve the problem, we firstly transform the model with plenty of clients and one server into one client and one server according to the coupling clients with independent arrivals. Next, we calculate the stationary distribution of queue lengths of all nodes by the knowledge of Bivariate Discrete Time Markov Chains. Then, we analyze the performance metrics of messages from each client through the queueing network. Finally, simulation results verify the effectiveness of the analytical method and draw some constructive conclusions.