A class of deadlock-free Maekawa-type algorithms for mutual exclusion in distributed systems

Abstract

Maekawa-type mutual exclusion algorithms use locking of a set of sites to achieve mutual exclusion. These algorithms are prone to deadlocks because a site is locked by other sites in exclusive mode and the timestamp of requests is not used to order requests while granting locks. These algorithms require additional rounds of message exchanges, like INQUIRE and FAILED, to recover from a possible deadlock. In this paper we present a class of Maekawa-type mutual exclusion algorithms which are free from deadlocks and do not exchange additional messages to resolve deadlocks. We systematically point out the reasons for deadlocks in Maekawa-type algorithms and eliminate them one by one to give a class of Maekawa-type algorithms which are free from deadlocks. It turns out that to prevent deadlocks in Maekawa-type algorithms, locks on sites must be mutable, timestamps must be used judiciously, and communication among sites must be increased. A deadlock-free Maekawa-type algorithm is optimal when the request sets of sites are the smallest possible such that a correctness condition is satisfied. We state the condition of optimality and present a method to construct optimal request sets. We also give a swap operation which allows us to derive an optimal configuration of request sets from another optimal configuration. There are large number of optimal configurations of request sets, which define a class of optimal deadlock-free Maekawa-type algorithms. Freedom from deadlocks is a desirable property because it dispenses with the need of cumbersome deadlock recovery scheme (e.g., exchange of INQUIRE, FAILED, and YIELD messages). Freedom from deadlock has another benefit: simplicity of the implementation.