Dynamical queueing systems

Saturday, November 4, 2006 - 4:15pm - 5:00pm
EE/CS 3-180
William Massey (Princeton University)
Technological innovations are creating new types of communication systems such as call centers, electronic
commerce, and wireless communications. Communication services managers must make important business decisions
to stay competitive and profitable. They have to maximize the communication resources that they are making
available to the customer. However, managers must also minimize their costs for providing these resources,
which results in maximizing profits for their companies.

The mathematical field of queueing theory was successfully introduced in the first half of the 20th century
to model voice communication networks. It has traditionally provided managers with a useful set of decision
making formulas, algorithms and policies for designing communication systems and services.
Another major triumph for queueing theory happened in the second half of the 20th century when it
was applied to data communication systems and contributed to the design of the first prototype for the Internet.
Both types of voice and data queueing models made significant use of the steady state theory for continuous time
Markov chains.

Given the new types of communication systems and services available in the 21st century, it is no longer possible
to make many of the simplifying assumptions of classical queueing theory. One major theme of my research has been
to move away from the static steady state analysis of the past and develop a theory of queues that captures more
of the true dynamic behavior that is found in real communications operations. My talk will discuss the types of
mathematical tools needed to create a dynamical queueing theory.

This involves new types of perturbation analysis applied to the differential equations of the transition
probabilities for the underlying, time-inhomogeneous Markov chain, queueing model. Moreover, we also use the theory
of strong approximations to apply this asymptotic analysis directly to the random sample paths of these stochastic
processes. We can also relax these Markovian assumptions by using the theory of Poisson random measures.
Finally, we can establish fundamental limit theorems that approximate many of these random processes by dynamical
systems. From these results, we can then apply the dynamic optimization techniques of variational calculus and
classical mechanics to the efficient design of these queueing models.