The telephone, communications, and computer industries have long used queuing models to estimate the performance of a service system in the face of random demand. The two most frequently used models are the Erlang loss and Erlang waiting models. In both cases, customers arrive randomly at a number of identical servers. In the Erlang loss model, there is no queue, so any customer finding all servers busy is lost. In the Erlang waiting model, there is an infinite queue space, so any customer finding all servers busy waits until a server is free. In either case, the major measure of performance is the fraction of customers that find all servers busy.

To compute a system's performance, we must know the load placed on the system per unit of time and the number of servers. The load is a unitless measure of the amount of work arriving per unit of time. For example, if 20 customers arrive each hour and each requires ½ hour of work, then the arriving load is 10 (20 customers per hour multiplied by ½ hour per customer).

The most crucial probabilistic assumption in both cases is that the number of arrivals per unit of time is Poisson distributed with a constant mean. The held case (with a queue) further requires that service times be exponentially distributed. If the arriving load is denoted AL and the number of servers by NS, then the expected fraction finding all servers busy is given in the loss case by @PEL( AL, NS) and in the held case by @PEB( AL, NS).