Analyzing Scheduling Performance for Real-time Traffic in Wireless Networks

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This paper is a sequel to an earlier study on scheduling real-time traffic in wireless TDMA channels. In particular, we develop mathematical analysis to model the system behavior of the equal-delay scheme and its extension of the multi-class scheme, both of which were proposed previously. The main usefulness of the proposed scheduling mechanisms is the improvement on the worst-case delay, and consequently the reduction in probability of delay violation or loss. We achieve the analytical solution by evaluating the corresponding cumulative distribution of delay. The derivation of the distribution function is based on a well-known method of solving a set of first order differential equations and eliminating all unstable modes. However, the existence of channel variations generate unique difficulties which renders the original method unsuitable. To solve this problem, we devise novel transformation techniques and an algorithm to recursively estimate the state probabilities in steady-state, so the original method can be applied in an alternative manner. Furthermore, we develop a reduced state model for homogeneous systems to alleviate the requirement on computational complexity of the full model. On the other hand, an additional challenge to extend the mathematical model to support the multi-class system is to overcome the varying progression rates of individual transmissions. To tackle this problem, we model the system aggregate delay value and recalculate the scaled statistics for each class of flows according to their pre-assigned weights. Finally, numerical results and computational complexity analysis are presented.
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