k-Arbiter: A Safe and General Scheme for h-out of-k Mutual Exclusion

Mutual exclusion is a well-known problem that arise when multiple processes compete, in an uncoordinated way, for the acquisition of shared resources over a distributed system. In particular, k-mutual exclusion allows at most k processes to get one unit of the same resource simultaneously. These paradigms do not cover all the cases in which resource accesses must be serialized over a distributed system. There exist cases (e.g. the bandwidth of communication lines) where the amount of shared resource might diier from request to request (for example, audio and video communications). In this paper, we formalize this problem as the h-out of-k mutual exclusion problem, in which each request concerns some number h (1 h k) of units of shared resource and no unit is allocated to multiple processes at the same time. We present a general scheme for a quorum-based h-out of-k mutual exclusion algorithm that relies on a collection of quorums called k-arbiter. Several examples of k-arbiters are discussed, two particular classes of k-arbiters are investigated and a metric to evaluate the resiliency with respect to failures of k-arbiters is also given. Le concept de k-arbitre: un m ecanisme g en eral pour l'exclusion mutuelle du type "h parmi k" R esum e : Cet article etudie l'exclusion mutuelle g en eralis ee du type h parmi k. Il existe k ressources identiques et chaque processus peut en demander, a tout instant, un nombre quelconque; de plus, chaque exemplaire de la ressource ne peut ^ etre utilis e que par un processus a la fois. Une solution simple a ce probl eme fond ee sur un nouveau concept (k-arbitre) est propos ee. Un k-arbitre g en eralise la notion de coterie habituellement utilis ee pour r esoudre l'exclusion mutuelle simple. Des propri et es g en erales des k-arbitres sont etablies et plusieurs familles de k-arbitres sont propos ees et evalu ees.