Waiting in concurrent algorithms

Between the two extremes, lock-based algorithms, which involve “a lot of waiting”, and wait-free algorithms, which are “free of locking and waiting”, there is an interesting spectrum of different levels of waiting. This unexplored spectrum is formally defined and its properties are investigated. New progress conditions, called k-waiting, for k ≥ 0, which are intended to capture the “amount of waiting” of processes in asynchronous concurrent algorithms, are introduced. To illustrate the utility of the new conditions, they are used to derive new lower and upper bounds, and impossibility results for well-known basic problems such as consensus, election, renaming and mutual exclusion. Furthermore, the relation between waiting and fairness is explored.