Traffic flow in an exponential delay system with priority categories

The mathematical solution to the problem of traffic flow in a simple delay system when the distribution of message lengths is exponential was first established by Erlang in 1917 and is now well known. The paper presents an extension to this theory, covering a case where the traffic is divided into priority categories. Expressions are obtained which describe the behaviour of a general system of this kind and which include that of the homogeneous system investigated by Erlang as a special case. This extension was developed to assist in the study of the effect of using priority categories, including the special category of ¿deferred¿ traffic, in automatic and semi-automatic tape-relay systems.