Congestion in blocking systems — a simple approximation technique

In the study of congestion in complex stochastic server systems, it is often desirable to have simple techniques available for obtaining approximations to important quantities of interest. This is particularly true in the early stages of the systems analysis and in cases where the only “solution” will be via a simulation. In this paper, we present an extremely simple, but surprisingly useful, technique for the approximate analysis of some such systems. Beginning with an approximation for the blocking of overflow traffic that was originally proposed by W. S. Hayward, we develop a natural extension to the approximation of blocking in a more general system as well as the determination of other (than blocking) quantities of interest. For the special, but important, case of renewal input to exponential servers, we give an explicit asymptotic (for heavy traffic) representation of the error introduced by this approximation.