A Delay-Optimal Group Mutual Exclusion Algorithm for a Tree Network

The group mutual exclusion problem is an extension of the traditional mutual exclusion problem in which every critical section is associated with a type or a group. 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 an efficient distributed algorithm for solving the group mutual exclusion problem when processes are arranged in the form of a tree. Our algorithm is derived from Beauquier et al.’s group mutual exclusion algorithm for a tree network. The message complexity of our algorithm is at most 3hmax, where hmax is the maximum height of the tree when rooted at any process. Its waiting time and synchronization delay, measured in terms of number of message hops, are at most 2hmax and hmax, respectively. Our algorithm has optimal synchronization delay for the class of tree network based algorithms for group mutual exclusion in which messages are only exchanged over the edges in the tree. Our simulation experiments indicate that our algorithm outperforms Beauquier et al.’s group mutual exclusion algorithm by as much as 70% in some cases.