The data broadcast problem with non-uniform transmission times

The Data Broadcast Problem consists of finding an infinite schedule to broadcast a given set of messages so as to minimize a linear combination of the average service time to clients requesting messages, and of the cost of the broadcast. This problem also models the Maintenance Scheduling Problem and the Multi-Item Replenishment Problem. Previous work concentrated on a discrete-time restriction where all messages have transmission time equal to 1. Here, we study a generalization of the model to a setting of continuous time and messages of non-uniform transmission times. We prove that the Data Broadcast Problem is strongly NP-hard, even if the broadcast costs are all zero, and give 3-approximation algorithms.