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(τ), decreases for large times τ as P(τ)~τ^-3/2 or as P(τ)~τ^-5/2exp(-τ/τ₀) 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(τ).