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This paper considers the design of multiuser opportunistic packet schedulers for users sharing a time-varying wireless channel from performance and robustness points of view. For a simplified model falling in the classical Markov decision process framework, we numerically compute and characterize mean-delay-optimal scheduling policies. The computed policies exhibit radial sum-rate monotonicity: As users' queues grow linearly, the scheduler allocates service in a manner that deemphasizes the balancing of unequal queues in favor of maximizing current system throughput (being opportunistic). This is in sharp contrast to previously proposed throughput-optimal policies, e.g., Exp rule and MaxWeight (with any positive exponent of queue length). In order to meet performance and robustness objectives, we propose a new class of policies, called the Log rule, that are radial sum-rate monotone (RSM) and provably …