A Fluid Model for an Overloaded Queueing System with Scoring-Based Priority Rules

SCAIM Seminar
March 12, 2013 7:30 pm

Speaker:  Daniel Y. Ding, Sauder School of Business, UBC

URL for Speaker:  http://www.sauder.ubc.ca/Faculty/People/Faculty_Members/Ding_Yichuan

Location:  ESB 4133

Intended Audience:  Public

We consider a queueing system with multitype customers and servers. When a server is available, each customer is assigned a score which depends on the customer’s waiting time, type, and the server’s type. The service is then provided to the customer with the highest score. We develop a fluid limit process to approximate the behavior of such a system, Our model has two important features: (1) the service rate in the transient state coincides with the max-flow of a parameterized network; (2) the service rate at the steady state coincides with the the minimal-cost max-flow of a capacitated network. Thanks to these properties, we may solve the transient and stationary behavior of the fluid limit process efficiently by combinatorial methods, and predict the performance of the system when a scoring policy has been implemented. By properly defining the performance metrics, we may solve the scoring formula that leads to the optimal efficiency-fairness tradeoff. We illustrate the application of our fluid model in the context of kidney allocation policy design. In particular, the fluid model we developed can be used to predict the steady-state allocation outcome of the scoring policy proposed by the United Network of Organ Sharing (UNOS) in 2008.