Offline scheduling is attractive when the traffic profile is known a priori since the complexity of online scheduling is largely removed. Given any admissible rate matrix = (ij), Birkhoff-von Neumann decomposition offers a quasi-offline scheduling strategy that can provide a service rate of at least ij for each flow (i, j) without internal speedup. This paper extends the Birkhoff-von Neumann switching strategy to consider traffic profiles in which the traffic demands are specified as statistical distributions rather than fixed rates. Key words: Birkhoff-von Neumann, utility max-min fair, statistical optimization, rate guarantees, high-performance switches.