The integration of ad hoc device-to-device (D2D) communications and open-access small cells can result in a networking paradigm called hybrid the ad hoc network, which is particularly promising in delivering delay-tolerant data. The capacity-delay performance of hybrid ad hoc networks has been studied extensively under a popular framework called scaling law analysis. These studies, however, do not take into account aspects of interference accumulation and queueing delay and, therefore, may lead to over-optimistic results. Moreover, focusing on the average measures, existing works fail to give finer-grained insights into the distribution of delays. This paper proposes an alternative analytical framework based on queueing theoretic models and physical interference models. We apply this framework to study the capacity-delay performance of a collaborative cellular D2D network with coverage sensing and two-hop relay. The new framework allows us to fully characterize the delay distribution in the transform domain and pinpoint the impacts of coverage sensing, user and base station densities, transmit power, user mobility and packet size on the capacity-delay trade-off. We show that under the condition of queueing equilibrium, the maximum throughput capacity per device saturates to an upper bound of 0.7239 λ b / λ u bits/s/Hz, where λ b and λ u are the densities of base stations and mobile users, respectively.
Keywords: ad hoc network; capacity-delay trade-off; device-to-device.