Fixed points for multiclass queues, via interchangeability.
(Joint work with Balaji Prabhakar)
Burke's
theorem tells us (among other things) that a Poisson process is a
"fixed point" for an ./M/1 queue; if the arrivals have this
distribution then so do the departures. I'll talk about extensions to
priority queues with two or more classes of customers. The fixed points
can be related to equilibria of multiclass exclusion processes. I'll
emphasise the role played by ideas of interchangeability of queues (for
example, if a sequence of independent ./M/1 queues in tandem, with
different service rates, are fed by an arbitrary arrival process, then
the law of the departure process does not depend on the order of the
queues).