Switching scheduling policies and their balanceabililty

The generalized switched server (GSS) system, a discretely controlled continuous time system model, and some switching scheduling policies, such as FRR, FMM, aMM, and FSS policy, have been proposed for resolving a cluster of task balancing problems. This paper studies the switching scheduling policies for the generalized switched server systems, with an emphasis on their balanceabililty. It is shown that the GSS system would have a smaller maximum load difference (MLD) under the FMM policy than under the FRR policy, and further, for a given GSS system, the FMM policy is balanceable if the FRR policy is. A general case where the number of the parallel units is arbitrary is investigated, and a sufficient condition for the balanceability of the FMM policy in the case where the system consists of three units is obtained.