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In multi-access wireless networks, transmission scheduling is a key component that determines the efficiency and fairness of wireless spectrum allocation. At one extreme, greedy opportunistic scheduling that allocates airtime to the user with the largest instantaneous channel gain achieves the optimal spectrum efficiency and transmission reliability but the poorest user-level fairness. At the other extreme, fixed TDMA scheduling achieves the fairest airtime allocation but the lowest spectrum efficiency and transmission reliability. To balance the two competing objectives, extensive research efforts have been spent on designing opportunistic scheduling schemes to reach certain tradeoff points between the two extremes by tuning the greediness in scheduling policy. In this paper and in contrast to the conventional wisdom, we find that in relay-assisted MIMO cellular networks, being greedy in user scheduling is unnecessary since it does not directly translate to larger diversity gain. When each mobile user has no less antennas than the base station, even fixed TDMA achieves the optimal diversity gain that is otherwise achievable by greedy opportunistic scheduling. In addition, by incorporating very limited opportunism, a simple TDMA-based scheme, named relaxed-TDMA, asymptotically achieves the same optimal system reliability in terms of outage probability as greedy opportunistic scheduling. This reveals a surprising fact: transmission reliability and user fairness are not necessarily contradicting each other in relay-assisted systems. They can be both achieved by the simple TDMA schemes. For practical implementations, we further propose a fully distributed algorithm to implement the relaxed-TDMA scheme. Our results here may find applications in the design of next-generation wireless communication systems with relay architectures such as LTE-advanced and WiMAX.