Transform-Domain Solutions of Poisson’s Equation with Applications to the Asymptotic Variance

Dispatching to parallel servers

“…Recent studies on size-aware dispatching renewed the interest in explicit Poisson solutions, extending their class in [21] to the fixed-deadline cost functions f (u) = 1 [τ,∞) (u), and to exponential costs in [22], with views on polynomials. In the discrete space setting, the forms f [u] = u n a −u and f [u] = δ[u − a] were identified in [12] as candidates for closed-form relative value function, via transform-domain analysis (based on generating functions) of the general solution of Poisson's equation-a methodology in spirit similar to the approach we will use in this study.…”