Fluctuations of telephone traffic
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The number of calls in progress in a simple telephone exchange model characterized by unlimited call capacity, a general probability density of holding-time, and randomly arriving calls is defined as N(t). A formula, due to Riordan, for the generating function of the transition probabilities of N(t) is proved. From this generating function, expressions for the co-variance function of N(t) and for the spectral density of N(t) are determined. It is noted that the distributions of N(t) are completely specified by the co-variance function.
[1] S. Rice. Mathematical analysis of random noise , 1944 .
[2] John Riordan,et al. Telephone traffic time averages , 1951 .