A Generalization of Erlang's Loss System to State Dependent Arrival and Service Rates

An Erlang Loss System with state dependent arrival and service rates is examined. This model includes Processor Shared Systems and birth-death processes. The state of the system is the number of occupied servers, the time until the next arrival, and the amounts of work remaining for the customers being served. Stationary probability distributions and conditions for their existence are determined for the continuous time process observed at arrivals and departures. The average delay of a customer is also computed.