# Abstract of Talk by Dr. William A. Massey

## Rethinking Queueing Theory to
Model Time-Varying Behavior

Dr. William A. Massey
AT&T Bell Laboratories
600 Mountain Avenue, Office 2C-120
Murray Hill, NJ 07974

## Office Telephone Number:

(908)-582-3225
## Fax Number:

## Electronic Mail Address:

will@research.att.com

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.

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