Matstat seminarium fredagen 16 november 2001 i MH:227


Conjectures on decay rates of tail probabilities in generalized Jackson and 
batch movement networks

Masakiyo Miyazawa
Science University of Tokyo
 
Asymptotic decay rates are considered for the stationary joint 
distributions of customer populations in a generalized Jackson network and 
a batch movement network. We first define an asymptotic decay rate for a 
multi-dimensional distribution concerning a tail set and a direction to 
decrease. Then, for the stationary joint distributions of customer 
populations, the decay rates are conjectured to be obtained through max-min 
linear optimizations with convex constrains. The existence results are 
shown to be consistent with those conjectures. Some examples are considered 
to see how the decay rates are changed according to modeling parameters and 
the direction to decrease.