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

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 constraints. Their validity is checked for some known results. Furthermore, the conjectured decay rates are shown to be useful to see how the decay rates are changed according to modeling parameters and the direction to decrease in a two node tandem queue.