Robustness of the avalanche dynamics in data-packet transport on scale-free networks

We study the avalanche dynamics in the data-packet transport on scale-free networks through a simple model. In the model, each vertex is assigned a capacity proportional to the load with the proportionality constant 1+a. When the system is perturbed by a single vertex removal, the load of each vertex is redistributed, followed by subsequent failures of overloaded vertices. The avalanche size depends on the parameter a as well as which vertex triggers it. We find that there exists a critical value ac at which the avalanche size distribution follows a power law. The critical exponent associated with it appears to be robust as long as the degree exponent is between 2 and 3 and is close in value to that of the distribution of the diameter changes by single vertex removal.