LAUSR

ABSTRACT In this study, we introduce the Heine process, {Xq(t), t > 0}, 0 < q < 1, where the random variable Xq(t), for every t > 0, represents the number of events (occurrences or arrivals) during a time interval (0, t]. The Heine process is introduced as a q-analog of the basic Poisson process. Also, in this study, we prove that the distribution of the waiting time Wν, q,  ν ⩾ 1, up to the νth arrival, is a q-Erlang distribution and the interarrival times Tk, q = Wk, q − Wk − 1, q, k = 1, 2, …, ν with W0, q = 0 are independent and equidistributed with a q-Exponential distribution.