Stochastic analysis of a slotted FIFO communication channel

Messages arrive randomly at one end of a slotted communication channel. They are assigned to (packed in) packets of fixed duration which queue up for transmission in first-in-first-out order; the packets are sent one per time slot. In a stochastic setting, where message durations are also random, we analyze a model which yields statistics on message delays and the number of waiting messages, assuming that the assignment protocol is the well-known next-fit rule of one-dimensional bin packing. A stability condition is obtained as a function of general discrete message-length distributions. As a by-product, we contribute a new result to the literature on the probabilistic analysis of the static next-fit bin-packing rule, viz. the limiting expected bin occupancy for general discrete distributions. Specializations of the results to constant message lengths and to uniform message-length distributions are worked out in detail