## On Quorum Systems for Group Resources with Bounded Capacity

### Authors

- Yuh-Jzer Joung, National Taiwan University

### Abstract

We present a problem called
(m,1,k)-resource allocation to model group mutual exclusion with
bounded capacity. Specifically, the problem concerns the scheduling
of a resource among m groups of processes. The resource can be used
by at most k processes of the same group at a time, but no two
processes of different groups can use the resource simultaneously.
The problem reduces to group mutual exclusion when k is equal to the
group size. We then generalize quorum systems for mutual exclusion to
the problem. We show that the study of quorum systems for
(m,1,k)-resource allocation is closely related to some classical
problems in combinatorics and in finite projective geometries. By
applying the results there, we are able to obtain some
optimal/near-optimal quorum systems. We also exploit the properties
of these systems pertaining to distributed computing.