Delay-aware Scheduling in Wireless Coding Networks: To Wait or Not to Wait

Wireless technology has become an increasingly popular way to gain network access. Wireless networks are expected to provide efficient and reliable service and support a broad range of emerging applications, such as multimedia streaming and video conferencing. However, limited wireless spectrum together with interference and fading pose signi cant challenges for network designers. The novel technique of network coding has a significant potential for improving the throughput and reliability of wireless networks by taking advantage of the broadcast nature of wireless medium. Reverse carpooling is one of the main techniques used to realize the benefits of network coding in wireless networks. With reverse carpooling, two flows are traveling in opposite directions, sharing a common path. The network coding is performed in the intermediate (relay) nodes, which saves up to 50% of transmissions. In this thesis, we focus on the scheduling at the relay nodes in wireless networks with reverse carpooling. When two packets traveling in opposite directions are available at the relay node, the relay node combines them and broadcasts the resulting packet. This event is referred to as a coding opportunity. When only one packet is available, the relay node needs to decide whether to wait for future coding opportunities, or to transmit them without coding. Though the choice of holding packets exploits the positive aspects of network coding, without a proper policy in place that controls how long the packets should wait, it will have an adverse impact on delays and thus the overall network performance. Accordingly, our goal is to find an optimal control strategy that delicately balances the tradeoff between the number of transmissions and delays incurred by the packets. We also address the fundamental question of what local information we should keep track of and use in making the decision of of whether to transmit uncoded packet or wait for the next coding opportunity. The available information consists of queue length and time stamps indicating the arrival time of packets in the queue. We could also store history of all previous states and actions. However, using all this information makes the control very complex and so we try to find if the overhead in collecting waiting times and historical information is worth it. A major contribution of this thesis is a stochastic control framework that uses state information based on what can be observed and prescribes an optimal action. For that, we formulate and solve a stochastic dynamic program with the objective of minimizing the long run average cost per unit time incurred due to transmissions and delays. Subsequently, we show that a stationary policy based on queue lengths is optimal, and the optimal policy is of threshold-type. Then, we describe a non-linear optimization procedure to obtain the optimal thresholds. Further, we substantiate our analytical ndings by performing numerical experiments under varied settings. We compare systems that use only queue length with those where more information is available, and we show that optimal control that uses only the queue length is as good as any optimal control that relies on knowing the entire history.