Calculus

In this chapter, we consider a discrete-time system with time indexed by t = 0, 1, 2,… We describe a discrete-time arrival process of a traffic source by a sequence of variables A≡{A(t),t = 0, 1, 2,…, where A(t) is the cumulative number of arrivals by time t. We assume that there is no arrival at time 0, i.e., A(0) = 0, and that A(t) is increasing, i.e., A(s) < A(t), for all s < t. Following the terminology in communication networks, we sometimes call an arrival a packet. Packets are assumed to be of the same size unless otherwise specified.