Average waiting time profiles of uniform DQDB model

We consider a simple and uniform abstraction of the Distributed Queue Dual Bus (DQDB) system of N nodes to highlight the fairness issues in terms of average waiting time. For the uniform DQDB with equal distance between adjacent nodes, we show that the system operates under three basic behavior profiles and a finite number of their combinations that depend on the load of the network. Consequently, the system is not fair at any load in terms of the average waiting times. In the vicinity of a critical load of 1 - 4/N, the uniform network runs into a state akin to chaos, where its behavior fluctuates from one extreme to the other with a load variation of 2/N. Our analysis is supported by simulation results. We also show that the main theme of the analysis carries over to the general (non-uniform) DQDB.