Multiclass batch arrival retrial queues analyzed as branching processes with immigration
At an \(M/G/1\) queue without waiting room customers arrive in batches which possibly consist of customers of different classes. If the server is free according to some probabilistic rule one of the customer is served immediately. Customers finding the server occupied wait for an exponential time with class-dependent mean and after that try to enter service again, and so on. It is shown that the time development of that system can be described by means of multitype branching processes. The theory developed for these processes is applied to obtain usual performance characteristics of queueing systems.
scientific article; zbMATH DE number 149032
scientific article