The wakeup problem in synchronous broadcast systems

This paper studies the differences between two levels of synchronization in a distributed broadcast system (or a multiple-access channel). In the glob ally synchronous model, all processors have access to a global clock. In th e locally synchronous model, processors have local clocks ticking at the sa me rate, but each clock starts individually when the processor wakes up. We consider the fundamental problem of waking up all n processors of a comp letely connected broadcast system. Some processors wake up spontaneously, w hile others have to be woken up. Only awake processors can send messages; a sleeping processor is woken up upon hearing a message. The processors hear a message in a given round if and only if exactly one processor sends a me ssage in that round. Our goal is to wake up all processors as fast as possi ble in the worst case, assuming an adversary controls which processors wake up and when. We analyze the problem in both the globally synchronous and l ocally synchronous models with or without the assumption that n is known to the processors. We propose randomized and deterministic algorithms for the problem, as well as lower bounds in some of the cases. These bounds establ ish a gap between the globally synchronous and locally synchronous models.