Internet evolved from a world communication network with restricted information transmission capabilities into an entertainment and information network with many broadband clients and more multimedia-rich applications. In particular, video (streaming) applications are gaining in popularity and usage, but those are also notorious for their high resources demand. A study of the popularity evolution of videos in different online video content systems can give insight and have implications for adequate network dimensioning. In this paper we study and model the popularity evolution of some video traces from YouTube, one Dutch catch-up TV online portal, and historical data on DVD rentals in the US. The model we put forward can degenerate into either a power-law distribution or an exponential distribution depending on its form-determining parameter. We find out that not all traces have a power-law decay as suggested in other works, but also a significant part of those expose an exponential popularity evolution.

This paper aims at investigating the tradeoff between ergodic energy efficiency (EE) and spectral efficiency (SE) for device-to-device (D2D) communications underlaying cellular networks. Assuming average-based resource allocation, we propose a multiobjective optimization problem (MOOP) approach to deal with the EE and SE maximization problem. Specifically, the formulated MOOP results in the maximization of the total ergodic sum rate of the D2D users and the minimization of the total average transmit power of the D2D transmitters. Two practical scenarios are considered, i.e., a limited interference scenario, which includes the sparsely deployed scenario, and a densely deployed scenario, where for each scenario the maximum achievable EE and SE are derived. Specifically, considering the limited interference scenario, an upper bound is imposed on the received interference across different D2D communications, and closed-form expressions for the optimal power allocation, ergodic sum rate, and maximum EE are obtained. In the general, densely deployed scenario, however, the cross D2D network interference needs to be taken into account. We provide an optimal solution for the power control based on sequential fractional programming to tradeoff between complexity and performance gain. Simulation results unveil an interesting tradeoff to strike a balance between EE and SE.