Not Just Age but Age and Quality of Information

A versatile scheduling problem to model a three-way tradeoff between delay/age, distortion, and energy is considered. The considered problem called the age and quality of information (AQI) is to select which packets to transmit at each time slot to minimize a linear combination of the distortion cost, the age/delay cost and the energy transmission cost in an online fashion. AQI generalizes multiple important problems such as age of information (AoI), the remote estimation problem with sampling constraint, the classical speed scaling problem among others. The worst case input model is considered, where the performance metric is the competitive ratio. A greedy algorithm is proposed that is shown to be 2-competitive, independent of all parameters of the problem. For the special case of AQI problem, a greedy online maximum weight matching based algorithm is also shown to be 2-competitive.