Recent advancement in distributed scheduling algorithms mainly focuses on designing CSMA-type protocols to achieve maximum network throughput in a fully distributive manner. However, it is inherently difficult for distributed scheduling algorithms to promise hard deadlines and a good performance in the presence of heavy-tailed traffic. To encounter this, there are two distributed throughput optimal scheduling to be proposed, which is timely-throughput optimal scheduling and throughput optimal scheduling with heavy-tailed traffic. The timely-throughput optimal scheduling distributed determines the optimal transmission times for network users so that the largest set of traffic rates of network users can be supported, while ensuring timely data delivery within hard deadlines. Then, the distributed throughput optimal scheduling with heavy-tailed traffic is proposed, which makes the scheduling decision based on the queue lengths raised to the ?-th power. It is demonstrated that DMWS-? is throughput optimal with respect to moment stability in the sense that if the traffic arrivals rates are within the network stability region, all network users with light-tailed traffic arrivals always have bounded queueing delay with finite mean and variance.