A Single-Server Queue with Feedback

Although the problems discussed in this paper arose in the theory of telephone traffic, we use the terminology of queues. Thus instead of calls and holding times we shall speak about customers and service times respectively. Let us suppose that in the time interval (0, ) customers arrive at a counter in accordance with a Poisson process of density X. Denote by r,, (n = 1,2, · · ·) the arrival time of the nth customer. Then the interarrival times r H+ i -- r,, (n = 0, 1, · · · ; r0 = 0) are identically distributed, mutually independent random variables with distribution function if .r ^ 0, if £