Delay and Energy Efficiency Tradeoff for Information Pushing System

We study the optimum designs of a unicast push-based information delivery system, where information is sent from a server to a user by using server-initiated pushing actions. Information arrives at the server at random and the server adopts a 'hold-then-serve' strategy, where new information is temporarily stored in a queue for a later one-time transmission. At any given time instant the server decides whether to stop waiting and push all information in the queue to the user, or to keep waiting based on the current queue status and the long-term design objective. A shorter waiting time can preserve the 'freshness' or timeliness of the information, which can be measured by using various delay penalty functions. However, frequent pushing actions will increase the power consumption of user devices by frequently waking up the client. The objective is to identify the optimum stopping rule that can optimize the tradeoff between the delay penalty and energy consumption. Motivated by the fact that different applications have different delay requirements, we adopt three different types of delay penalty functions, including linear, exponential, and logarithmic penalty functions. Using optimum stopping theories, optimum stopping rules are developed to minimize a weighted combination of delay penalty and energy efficiency. Different Pareto-optimum tradeoffs between delay and energy efficiency can be achieved by tuning the weight coefficient in the objective function. In particular, if the delay penalty function is convex, it is proved that the one-step look ahead stopping rule is optimum.