Remark on a Service System with Mixed Input Streams

In a paper published in Opns. Res. 14, 145–156 (1966) J. P. Young discusses multiple-channel queuing systems with exponential service-time distribution, no waiting space, and two parallel input streams (Poisson input mixed with an L-phase Erlang input). This note discusses the consequences of an additional assumption introduced by Young to obtain steady-state probabilities of having n channels occupied. Since the assumption is justified only for the pure Poisson input in the case of mixed input, the Erlang formula (4), proposed by Young, gives only an approximation to the exact probabilities.