On the optimality of LEPT and .c rules for parallel processors and dependent arrival processes

In this paper we study scheduling problems of multiclass customers on identical parallel processors. A new type of arrival process, called a Markov decision arrival process, is introduced. This arrival process can be controlled and allows for an indirect dependence on the numbers of customers in the queues. As a special case we show the optimality of LEPT and the µc-rule in the last node of a controlled tandem network for various cost structures. A unifying proof using dynamic programming is given.