Optimum energy efficiency and age-of-information tradeoff in multicast scheduling

We study the optimum scheduling of a multicast system, where a server transmits information to multiple users via multicasting based on requests from the users. To improve energy efficiency, the server can queue and bundle the requests from different users based on the requested contents, and serve all users requesting the same contents in a later one-time transmission. A longer waiting time can increase the average number of users served in each multicasting transmission, thus improve the energy efficiency. The higher energy efficiency is achieved at the cost of the timeliness of the information, which can be measured by using age-of-information (AoI). The goal of this paper is to identify the multicast scheduling strategy that can optimize the tradeoff between energy efficiency and AoI. Using optimum stopping theories, we develop optimum stopping rules that can minimize a cost function expressed as a weighted combination of AoI penalty function and energy efficiency, where the weight coefficient is used to adjust the tradeoff between the two. Specifically, we consider the case that the AoI penalty grows exponentially with time, and show that the optimum scheduling can be formulated as a simple threshold test with a low complexity one-step look ahead stopping rule. The proposed multicast scheduling strategy can achieve the optimum tradeoff between energy efficiency and AoI penalty.