A stabilizing /-exclusion algorithm in arbitrary rooted networks

In this paper, we present the first stabilizing solution to the /-exclusion problem in arbitrary networks. The /-exclusion problem is a generalization of the mutual exclusion problem to / (/ ≥ 1) processes, where / processes instead of 1, are free to use a shared resource simultaneously. The algorithm is semi-uniform, and its space requirement is (/ + 3)σr, states (or[log((/+ 3)Δr])) bits) for the root r and 4 xσ²px D states (or [4log(σpx D)]) bits) for each non root process p, where σp is the degree of process p and D is the diameter of the communication network. This is the first /-exclusion algorithm on arbitrary networks with the property that the space requirement is independent of the size of the network for any process, and is independent of / for all processes except the root. The proposed protocol is distributed, deterministic, and does not use a preconstructed spanning tree. Since our algorithm is self-stabilizing, it does not require initialization and withstands transient faults. The stabilization time of the algorithm is O ([n/l] x (/ + D)) rounds, where n is the size of network.