Multiple feedback at a single-server station

A single server facility is equipped to perform a collection of operations. The service rendered to a customer is a branching process of operations. While the performance of an operation may not be interrupted before its completion, once completed, the required follow-up work may be delayed, at a cost per unit time of waiting that depends on the type and load of work being delayed. Under some probabilistic assumptions on the nature of the required service and on the stream of customers, the problem is to find service schedules that minimize expected costs. The authors generalize results of Bruno [2], Chazan, Konheim and B. Weiss [4], Harrison [8], Klimov [10], Konheim [11], and Meilijson and G. Weiss [13], using a dynamic programming approach.