In a computer system where a site including a storage device system connected to high-rank apparatuses, via a network such as a SAN, and a site including a storage device system similarly connected to high-rank apparatuses via a network are connected to each other via an inter-high-rank-apparatuses network, arbitration-emulation software is installed in each of the high-rank apparatuses. A two-step arbitration is performed, thereby determining one high-rank apparatus. At first, a shared/exclusive control using an already-existing shared volume is performed based on an arbitration conducted within the site. Next, a shared/exclusive control based on an arbitration conducted between the sites is performed by high-rank apparatuses each of which has won the arbitration within each site.