Jackson’s Conjecture on Earliest Due Date Scheduling

We discuss Jackson's conjecture on the optimality of the earliest due date scheduling rule in queueing systems. We investigate a single server queueing system with two due date classes of customers scheduled by an earliest due date rule allowing preemption. Using results from Goldberg’s analysis of EDD scheduling (Goldberg, H. M. 1977. Analysis of the earliest due date scheduling rule in queueing systems. Math. Oper. Res.2 145–154.), we analytically describe relations for the distribution functions of virtual waiting time and their inverses, in transient as well as steady state. This leads to a proof of a more accurate statement than the conjecture for the model described.