This paper presents an analytical study of average delay and throughput in a two-way relay network exploiting network coding to exchange source packets, where arrival and departure of packets are stochastic. In this case, a fundamental problem for the relay node is whether to wait in order to obtain a coding opportunity, leading to reduction of the number of transmissions, or sending a packet (coded/uncoded) whenever it has a transmission opportunity, leading to reduction of the packet delay. In order to address the fundamental trade-off between packet delay and transmission power, we develop three network coding schemes based on power-delay constraint of the application. We devise a theoretical framework to compute the average delay and stability region for each proposed scheme and compare the performance of network coding and traditional routing. Our results reveal that network coding may deliver packets with either larger or lower delay compared to traditional routing, depending on the selected scheme. Unlike the previous works in this area, in order to include channel loss due to noise, interference, etc., we consider probabilistic transmission for all packets. The transmission probabilities depend on the nature (coded/uncoded) and destination of packets, which are generally different for coded and uncoded packets. We carry out simulations to confirm our theoretical analysis.
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