Contention for a resource in a multi-resource system is resolved by separately resolving contention for each resource. In some cases where two or more entities contending for a resource are associated with equal priorities, lexicographic ordering is used to resolve contention between these entities. In some cases where two or more entities contending for a resource are associated with equal priorities, a random probability-based scheme is used to resolve contention between these entities. Also, different types of schemes may be used to resolve contention for different resources.