Nonstationary Blocking in Telephone Traffic

The main purpose of this paper is to present a discussion of the time behavior of blocking in a fully available iV-trunk group for anyinitial state with exponential servers and with Poisson-offered load whose rate parameter a(t) itself may be considered to vary with time; that is, the probability of j calls arriving in a time interval (0, t) is assumed given by The service rate is taken equal to 1, so that a(t) is measured in erlangs. The problem of blocking with time-variable offered load was considered by Palm 1 for finite trunk groups and by Khintchine 2 for infinite 625 trunk groups. The impetus for this is the need felt for more accurate computation of blocking probabilities and correlation information 3 than can be obtained by quasi-stationary analyses, that is, by the use of equilibrium formulas in which the offered load parameter is replaced by its instantaneous value. Lack of statistical equilibrium renders this approach inaccurate. The time-variable aspect of the input stream should be carefully distinguished from other statistical descriptions such as peakedness,4 since the effects on the system are separately identifiable. It has been reported, for example, that offered load and peakedness determinations from carried usage, peg count attempts offered to a group, and overflows are misled by the time variability of the offered load. P a l m h a d proposed an interesting m e t h o d of accounting for t h e t i m e