  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 a 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 $a_c$ 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.
