Letter to the Editor—A Doubled-Ended Queuing Problem of Kendall

The distribution of the difference between two independent Poisson variables has been obtained by Irwin (Irwin, J. O. 1937. The frequency-distribution of the difference between two independent variates following the same Poisson distribution. J. Roy. Stat. Soc.100(Part 3) 415–416.), when the means are equal, and by Skellam (Skellam, J. G. 1946. The frequency-distribution of the difference between two Poisson variates belonging to different populations. J. Roy. Stat. Soc.109(Part 3) 296.), when the means are unequal. The purpose of this note is to point out that the Irwin-Skellam distribution still applies when α and β are time-dependent.