Dynamical Systems Seminar

Elizabeth Wesson
Stability of queues with delayed information

Monday, October 30, 2017 - 3:30pm
Malott 224

A discussion of joint work with Jamol Pender (ORIE) and Richard Rand.

Information about queue length can influence service users' decisions about
which queue to join; however, in many situations the information available
to customers is delayed. We consider a deterministic fluid model in which
customers join queues according to a multinomial logit model, with two
types of delayed information. This gives systems of delay differential
equations. In the case of a constant arrival rate, we identify the critical
delay for a Hopf bifurcation, above which the equilibrium queue length is
unstable. When the arrival rate is time-varying, we use two-variable
expansion to analyze the change in the critical delay.