\magnification=1200
\baselineskip=20pt
\nopagenumbers
\font\big=cmr12 scaled \magstep2

\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\bf JOINT PROBABILITY AND STATISTICS SEMINAR}
\bigskip

\baselineskip=12pt
\centerline{4:15 p.m., Tuesday, February 20, 2001}
\centerline{Sequoia Hall Rm. 200}

\bigskip
\baselineskip=15pt
\centerline{\sl Peter W. Glynn}
\centerline{\sl Dept. of Management Science and Engineering}
\centerline{\sl Stanford University}
\bigskip
\centerline{\bf Limit Theorems for Queues with Scheduled Arrivals}

\bigskip

Taditional queueing theory assumes that customers arrive according to a
renewal-like point process. In recent years, a number of efforts have been
made to extend the theory to cover queues in which the arrival process
exhibits heavy ( marginal ) tails or long-range dependence. Such efforts
have been motivated by the modeling needs that arise in the context of
modern telecommunications networks, and the resulting analysis suggests
that the performance of such queues can be substantially degraded relative
to what is observed in traditional renewal-like models. In this talk, we
discuss a class of queueing models that exists at the opposite end of the
traffic modeling spectrum. In particular, we introduce a class of traffic
models that exhibit more order than that observed in the renewal setting.
This class of models, which we refer to as a " scheduled arrival process ",
arises naturally in many applications settings ( e.g. arrivals of aircraft
to an air traffic control region, arrivals of patients to a doctor's
office, etc. ). We discuss the basic properties of such traffic models and
describe the implications of such traffic for performance of the
corresponding queueing models. As expected, such queues behave much better
than do queues fed by renewal-like traffic. This work is joint with Hong
Chen and Yijuan Zhao.

\bye