Dynamical Systems Seminar

Jamol PenderCornell University
Queues with Information Updates: A Functional Dynamical System Perspective

Friday, February 8, 2019 - 1:30pm
Malott 206

Many queueing systems provide real-time information to their customers with the goal of reducing the customers’ anxiety of the unknown. However, in reality, the information might be given in the form of an update. To understand the impact of updates, we prove fluid limit theorems for a state dependent queueing model where customers choose which queue to join by a generalized customer choice model. In the choice model, the information about the queue length is updated periodically in increments of size ∆. We show that the fluid limit is given by a system of functional differential equations with a non-stationary time delay and the diffusion limit is a system of stochastic functional differential equations with a non-stationary time delay. Using the fluid limit, we derive an exact formula for the critical updating size that partitions the system in stable and unstable regions. In the case of multiple updates, we uncover a novel connection between our updating queueing model and Auto-Regressive (AR) time series models. To this end, we show that the stability of our updating queueing model is equivalent to analyzing the stationarity of a subsequent AR time series model.