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. Here, the following two-step arbitration is carried out, thereby determining one high-rank apparatus. Namely, at first, a shared/exclusive control using an already-existing shared volume is performed based on an in-site arbitration within the site. Next, a shared/exclusive control based on an inter-sites arbitration is performed by high-rank apparatuses each of which has won the arbitration within each site.