Investigation on the Lu-Kumar queueing network

Abstract

Multi-class re-entrant networks are common in semiconductor, communication and other complex manufacturing systems. The project seeks to investigate the Lu-Kumar re-entrant queueing network through simulation. The Lu-Kumar network is a simple re-entrant system used as a starting point in examining multi-class queueing networks. Insights gained through simulation can have potential application in improving manufacturing systems.

It is common to find literature that discusses the stability of such systems using fluid models. This project takes on a different approach by examining the stability of such systems using a deterministic model through simulation.

The experimental results show that the stability conditions of the Lu-Kumar network in a deterministic model is different from those proved using fluid models. The stability conditions established using fluid models do not apply in a deterministic case. The deterministic model have discrete regions of stability, the author conjectures that it is most likely achieved through synchronization.

Further exploration on the intrinsic properties of the model is conducted through simulation using Poisson arrivals and exponential service times. It is found that the network has a linear relationship with M/M/1 queue times, with the virtual station showing the strongest linearity. The results support the author’s belief that the Lu-Kumar re-entrant network can be approximated to a G/G/k queue model if the coefficient of variation can be determined.

In addition, recommendations are provided for future work to further develop the understanding of multi-class re-entrant queueing networks.