We consider discrete-time dynamic scheduling problems of the following three types of G/G/1 queue with K different customer classes: (i) a G/DFR/1 queue with K classes under preemptive resume service discipline, (ii) a G/IFR/1 queue with two classes under preemptive resume service discipline, and (iii) a G/G/1 queue with two classes under non-preemptive service discipline. Interchange arguments are used to show that simple index policies of different type minimize the total holding cost of customers in a finite-horizon scheduling period for the three cases. Our results extend the result for a G/M/1 queue by Buyukkoc et al. (1985) to general queues.
