ABSTRACT
This chapter contains an analysis of the transient behavior of Erlang's model, the basic model of circuit-switched traffic. In the parlance of queueing theory, the system just described is an M/M/n/n queue: Poisson arrivals, a capacity–n queue, n exponential servers. There are obviously several deficiencies in this model. Once the chapter has a handle on the transient behavior of Erlang's basic model, it extend the results in several ways. It discusses whether the process z n (t) satisfies a large deviations principle. The chapter provides a justification of the large deviations principle for Erlang's model and constructs processes for which the theorems are known to hold, and uses them to prove the theorems for Erlang's model by approximation arguments.
