Biased diffusion and universality in model queues

We study the structure and robustness of universality classes for queueing, deriving analytic results for priority-based models with continuous-valued priorities. By mapping one model onto the problem of biased diffusion, we show that its distribution of waiting times, P(tau), decreases for large times tau as P(tau) approximately tau;{-3/2} or as P(tau) approximately tau;{-5/2}exp(-tau/tau_{0}) in different parameter regimes. In a second model, introducing a cost for switching between different classes of tasks substantially changes the asymptotic behavior of P(tau).