Multi-Server Batch Service Queueing Model With Variable Service Rates

In this paper, we study the batch queueing model, where multi-servers are used to provide the service. Arrival follows a Poisson distribution and service time is exponentially distributed. If there are less than the batch of
customers, they are served individually. However, if there are the batch of
customers, all the customers are served together. We calculate the probability distribution and the performance measures of queue length and waiting time for both conditions: having less than the batch of
customers and having more than the batch of
customers using recursive method. Finally, we verify the results with some numerical illustrations presenting some applications in the real life situation.