We investigate an optimal scheduling problem in a discrete-time system of L parallel queues that are served by K identical servers. This model has been widely used in studies of emerging 3G/4G wireless systems. We introduce the class of Most Balancing (MB) policies and provide their mathematical characterization. We prove that MB policies are optimal among all work conserving policies; we define optimality as minimization, in stochastic ordering sense, of a range of cost functions of the queue lengths, including the process of total number of packets in the system. We use dynamic coupling arguments for our proof. We also introduce the Least Connected Server First/Longest Connected Queue (LCSF/LCQ) policy as an approximate implementation of MB policies. We conduct a simulation study to compare the performance of several work conserving policies to that of the optimal one. In the simulations we relax some of the mathematical assumptions we required for the analytical proofs. The simulation results show that: (a) in all cases, MB policies outperform the other policies, (b) randomized policies perform fairly close to the optimal one, and, (c) the performance advantage of the optimal policy over the other work conserving policies increases as the channel connectivity decreases.
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