HEAVY-TRAFFIC ANALYSIS OF A DATA-HANDLING SYSTEM WITH MANY SOURCES

A model is considered in which a buffer receives messages from N independent and identical information sources that asynchronously alternate between exponentially distributed periods in the "on" and "off" states. While on, a source transmits at unit rate. The buffer depletes through an output channel with a given maximum transmission rate c < N. This model is useful for a data-handling switch in a computer network. Anick, Mitra, and Sondhi [Bell System Tech. J., 61 (1982), pp. 1871-1894] have derived an explicit expression for the equilibrium probability G(x) that the buffer content exceeds x, which is convenient for numerical calculations for moderate values of N. In this paper, the heavy traffic case, in which N is large and the system is close to instability, is investigated. Important scalings are introduced, and a two-term asymptotic approximation to G(x) is derived, with the help of function theoretic techniques. Numerical comparisons are given that show the quality of the approximation.