Future wireless networks are expected to be a convergence of many diverse network technologies and architectures, such as cellular networks, wireless local area networks, sensor networks, and device to device communications. Through cooperation between dissimilar wireless devices, this new combined network topology promises to unlock ever larger data rates and provide truly ubiquitous coverage for end users, as well as enabling higher spectral efficiency. However, it also increases the risk of co-channel interference and introduces the possibility of correlation in the aggregated interference that not only impacts the communication performance, but also makes the associated mathematical analysis much more complex. To address this problem and evaluate the communication performance of cooperative relay networks, we adopt a stochastic geometry based approach by assuming that the interfering nodes are randomly distributed according to a Poisson point process (PPP). We also use a random medium access protocol to counteract the effects of interference correlation. Using this approach, we derive novel closed-form expressions for the successful transmission probability and local delay of a relay network with correlated interference. As well as this, we find the optimal transmission probability $p$ that jointly maximizes the successful transmission probability and minimizes the local delay. Finally numerical results are provided to confirm that the proposed joint optimization strategy achieves a significant performance gain compared to a conventional scheme.