Grid computing is a state-of-the-art parallel computing technology which enables worldwide computers to dynamically share their computing powers and resource to each other. The grid takes advantage of Internet as a universal communication platform to carry messages. Basically, Internet doesn't guarantee loss-free and ordered transmission, hence, the grid should keep the cause and effect of events by itself to ensure the correct ordering of command invocations at the remote hosts. The ordering issue arises when the messages travel across the networks with unpredictable delay. Recent research has studied the security and resource control issues, but failed to address the requirements of transport layer on the grid communication platform. In this paper, we propose the Causal Ordered Grid (COG) architecture and implement it to study the transport performance issues when the grid is built over worldwide networks. The COG provides a novel service model to the applications with time-sensitive and causal-ordered transportation. From our experiments, the design of the grid middleware should use a causal-ordered, time-sensitive transportation rather than TCP. Our research will be beneficial to the improvement of the grid computing and can provide wealthy empirical results for the designer.