Delay Distributions for Simple Trunk Groups with Recurrent Input and Exponential Service Times

In the theory of telephone traffic, the following process is of considerable interest. In the time interval 0 ^ t , calls appear before a simple t r u n k group with m lines at instants r t , r 2 , · · ·, r,, , · · · where the interarrival times r n + l -- r n ( n = 1 , 2 , · · ·) are identically distributed, mutually independent, positive random variables with distribution function P r n + i - r,, ^ ar} = F(x) (» = 1, 2, · · · ). (1)