Abstract

We introduce Queueing and Markov Chain Decomposition (QMCD)  for the exact analysis of Queues and Markov Chains.  QMCD includes four steps: Decompose the system to smaller subsystems, Tie the subsystems together –transition rates and other effects, Solve each subsystem while considering the relevant effects, and Normalize the solution. We focus on applications of QMCD where the subsystems are single stage systems, such as the Mn/Gn/1 with state-dependent arrivals and services. We also discuss QMCD with more complicated subsystems such as for the M/M/C with preemptive priority and different service rates, and a threshold based allocation of Blood units to patients.  QMCD allows us to provide exact analysis of these, previously well studied but unsolved, models. We will discuss current and future research.

Opher Baron is a Professor of Operations Management and the area coordinator for Operations Management and Statistics at the Rotman School of Management, the University of Toronto.  He has a PhD in Operations Management from the Sloan school at the Massachusetts Institute of Technology along with an MBA and BSc in Industrial Engineering and Management from the Technion.  On the teaching front, Opher is especially proud of the "The Art of Modeling with Spreadsheet" MBA elective course he introduced and teach at Rotman. His research interest include queuing, applied probability, facility location, service operations (such as healthcare and call centers), inventory planning, and revenue management.  Opher's published at leading journals such as Operations Research, and Manufacturing & Service Operations Management, and he has won several research awards and grants.  Opher is active in the operations research and operations management community.  He has chaired several conferences, clusters, and sessions and currently serves on the editorial board of both the Mathematical Methods of Operations Research, the Manufacturing & Service Operations Management, and Information System and Operational Research journals.