A Quorum-Based Group Mutual Exclusion Algorithm for a Distributed System with Dynamic Group Set

Abstract

The group mutual exclusion problem extends the traditional mutual exclusion problem by associating a type (or a group) with each critical section. In this problem, processes requesting critical sections of the same type can execute their critical sections concurrently. However, processes requesting critical sections of different types must execute their critical sections in a mutually exclusive manner. We present a distributed algorithm for solving the group mutual exclusion problem based on the notion of surrogate-quorum. Intuitively, our algorithm uses the quorum that has been successfully locked by a request as a surrogate to service other compatible requests for the same type of critical section. Unlike the existing quorum-based algorithms for group mutual exclusion, our algorithm achieves a low message complexity of OðqÞ and a low (amortized) bit-message complexity of OðbqrÞ, where q is the maximum size of a quorum, b is the maximum number of processes from which a node can receive critical section requests, and r is the maximum size of a request while maintaining both synchronization delay and waiting time at two message hops. As opposed to some existing quorum-based algorithms, our algorithm can adapt without performance penalties to dynamic changes in the set of groups. Our simulation results indicate that our algorithm outperforms the existing quorum-based algorithms for group mutual exclusion by as much as 45 percent in some cases. We also discuss how our algorithm can be extended to satisfy certain desirable properties such as concurrent entry and unnecessary blocking freedom.Index Terms-Message-passing system, resource management, mutual exclusion, group mutual exclusion, quorum-based algorithm.

On quorum systems for group resources allocation

“…However, since a permission may be preempted to avoid deadlock, this method may result in high message complexity [29]. Another approach is presented in [2]. Processes compete for quorums as usual, i.e., only one quorum can be acquired at a time.…”

“…The difference between the compositions in the above two lemmas is that in Lemma 3, every quorum S in C u i is formed by r sub-quorums, one from C 1 u [1] , one from C 2 u [2] , . .…”

A priority-based distributed group mutual exclusion algorithm when group access is non-uniform

“…However, unlike Maekawa_M which uses surficial quorum system, the algorithm by Toyomura et al [28] uses a traditional quorum system. In [2], Atreya and Mittal proposed another quorumbased group mutual exclusion algorithm based on the notion of surrogate quorum. Their algorithm has low message complexity of O(q).…”

“…Note that, in our algorithm, the relationship between a primary token holder and a secondary token holder of the same session is different from that of a leader and its follower in RA2 [13,2]. Specifically, in our algorithm, it is possible for a secondary token holder to enter the critical section and perhaps even leave it before the primary token holder is able to enter the critical section.…”

“…Most algorithms for solving the group mutual exclusion problem that have been developed so far treat all groups in the same manner [12,29,4,3,14,2]. This is quite acceptable, if a process, at the time of making a request for critical section, selects the group for the critical section uniformly.…”