Equipped with the results that we have derived for our fundamental birthand-death model, we shall now review a problem whose many variations will help illustrate several of the best-known and most widely used models of queueing systems.
    Many cities have by now instituted the use of the telephone number 911 for all types of emergency calls. At the "other end" of the 911 number there is usually a center for emergency calls employing a number of trained operators. The sophistication of equipment and operational setup in these centers varies widely from city to city. Some cities (e.g., New York City) employ quite elaborate schemes for screening calls and determining their priorities, schemes backed up by special-purpose computers and communications equipment. Other centers consist of little more than a switchboard and a number of telephone operators who either process telephone calls themselves (in cooperation with a number of dispatchers) or transfer calls to the most appropriate city department (e.g., fire department, emergency medical services department, etc.). It is interesting to compare, at least in an approximate way, the characteristics of these centers as a function of different levels of manpower and under various organizational schemes. Queueing theory offers us a good opportunity to do so.
    Throughout the following discussion it will be assumed that the arrival of calls at a center constitutes a Poisson process (whose mean rate may vary). This assumption is reasonable, with the possible exception of the occurrence of major incidents which can be expected to trigger bursts of telephone calls-all reporting the same event and its repercussions.