Biased diffusion and universality in model queues

Abstract

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-5/2(-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). © 2006 The American Physical Society.