Superposition of renewal processes and an application to multi-server queues
The vector-valued forward recurrence time process of a superposition of independent renewal processes at arrival epochs of the superposed (marked point) process is studied. Stationary distribution and a SLLN are deduced for the process. As an application, the departure process of a multi-server queue without idleness is considered. As a specific case, the identical servers with Erlang service time distribution are considered in detail.
scientific article; zbMATH DE number 5072679