A Fluid Model for Data Communication

Example 1 (A Multiple Source Data Handling System). There are N sources of messages, which may be on or off from time to time. A switch receives these messages at a unit rate from each source and transmits them at a fixed maximum rate c (1 ≤ N < ∞, 0 < c < ∞), storing messages it cannot transmit in a buffer of infinite capacity. The sources act independently, the durations of on and off times being independent random variables with exponential densities. Denoting by J(t) the number of on sources at time t, these assumptions amount to the statement that J = {J(t), t ≥ 0} is a birth and death process on the state space {0, 1, 2, …, N}.