Power-Law and Exponential Tails in a Stochastic, Priority-Based, Model Queue

We derive exact asymptotic results for a stochastic queueing model in which tasks are executed according to a continuous-valued priority. The distribution, , of the waiting times  of executed tasks for this model is shown to behave asymptotically as a power law, , when the average rates of task arrival and execution satisfy (as was earlier noted empirically). For .