Some Equilibrium Results for the Queueing Process EK/M/1

Summary A queueing process is studied in which the inter-arrival time of customers is proportional to a variate distributed as χ2, the service time distribution is negative exponential and a single server serves customers in order of arrival. Using Erlang’s method, the steady state equations are obtained and the generating function for state probabilities evaluated. Limiting distributions are found and the case of a “regular” input is derived. The solutions are made to depend upon the real positive root of a certain equation. This root is easily obtained by the usual numerical methods and the solutions are easily computed functions of this root.