In distributed applications, a group of multiple processes are cooperating with one another by exchanging messages in networks. Information systems like cloud computing systems are getting scalable, which are composed of a huge number of processes. We assume a physical clock which each process reads is synchronized with a time sever, i.e. maximum offset of each clock to UTC time is bounded by some value. Furthermore, processes are interconnected in various types of networks. In this paper, we consider a scalable group composed of subgroups. Processes in each subgroup are interconnected in a local network (LN) and each pair of subgroups are interconnected in a global network (GN). We assume each network supports every pair of processes with reliable and synchronous communication. That is, no message is lost and maximum delay time between every pair of nodes is bounded by some value. An LN and GN support shorter and longer maximum delay time than the maximum clock offset, respectively. Messages are causally delivered by taking usage of both linear clock and physical clock. In the linear clock, some pair of messages which are not required to be causally delivered may be unnecessarily ordered. In order to reduce the number of pairs of unnecessarily ordered messages in the linear clock, the physical clock is additionally used. We evaluate the protocol and show the number of pairs of unnecessarily ordered messages can be reduced compared with the linear clock protocol.