In this thesis, we proposed a delay limited routing scheme in wireless ad hoc networks. When nodes transmit packets in wireless ad hoc networks, most people think the one-hop way is better than the multi-hop way in reducing the delay time. Since most cases in wireless ad hoc networks are not single sources, we should consider at least two sources transmitting packets at the same time and then use the multi-hop way in order to reduce the energy consumption. We want to maximize the throughput with limited delay. Our contribution is to transform the optimal scheduling problem in wireless ad hoc networks to the classic maximum flow problem. The maximum flow approach does maximize the throughput and can get the optimal solution.

Delay is an important quality-of-service measure for the design of next-generation wireless networks. This dissertation considers the problem of delay-limited communication over block-fading channels, where the channel state information is available at the receiver but not at the transmitter. For this communication scenario, the difference between the ergodic capacity and the maximum achievable expected rate (the expected capacity) for coding over a finite number of coherent blocks represents a fundamental measure of the penalty incurred by the delay constraint. This dissertation introduces a notion of worst-case expected-capacity loss. Focusing on the slow-fading scenario (one-block delay), the worst-case additive and multiplicative expected-capacity losses are precisely characterized for the point-to- point fading channel. Extension to the problem of writing on fading paper is also considered, where both the ergodic capacity and the additive expected-capacity loss over one-block delay are characterized to within one bit per channel use. The problem with multiple-block delay is considerably more challenging. This dissertation presents two partial results. First, the expected capacity is precisely characterized for the point-to-point two-state fading channel with two-block delay. Second, the optimality of Gaussian superposition coding with indirect decoding is established for a two-parallel Gaussian broadcast channel with three receivers. Both results reveal some intrinsic complexity in characterizing the expected capacity with multiple-block delay.

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