Dr. William A. Massey AT&T Bell Laboratories 600 Mountain Avenue, Office 2C-120 Murray Hill, NJ 07974
Queueing theory has its origins in the performance modelling of telecommunication systems, starting with the Erlang loss model developed in 1917. This led to the classical Erlang blocking formula which is used to this very day to estimate the frequency with which all circuits are busy in a telephone trunk group for a given average call arrival rate, average conversation rate, and fixed number of telephone trunklines. Such formulas were obtained through the then emerging probabilistic theory of Markov chains. Although queueing theory has evolved considerably over the decades, relatively little work has been done in the area of queueing systems whose average arrival and service rates vary over time. Whereas it is clear that systems with time-varying rates are more realistic, analyzing the resulting mathematical model is considerably more difficult.
In this talk, we will introduce both the classical Erlang queueing model and its time-varying analogue. First we will show how we must reassess what are the most appropriate mathematical techniques for analyzing this time-varying model and formulate new approaches. In addition, we will see how we must also rethink what are the most appropriate performance metrics for the underlying telephone system that is being modelled. Finally, we will highlight the intimate relationship between modelling and estimation assumptions with the creation of a mathematical framework of theorems for a time-varying queueing theory.