To operate the automatic devices of manufacturing process more effectively and to solve the needs of the resource sharing, network technology is applied to the control devices located in common manufacturing zone and operated by connecting them. In this paper, functional standard of the network layers are set as physical and data link layer of IEEE 802.2, 802.4, and VMD application layer and ISO-CIM reference model. Then, they are divided as minimized architecture, designed as group objects which perform group management and service objects which organizes and operates the group. For the stability in this network, this paper measures the variation of data packet length and node number and analyzes the variated value of the waiting time for the network operation. For the method of the analysis, non-exhausted service method are selected, and the arrival rates of the each data packet to the nodes that are assumed to form a Poission distribution. Then, queue model is set as M/G/1, and the analysis equation for waiting time is found. For the evalution of the performance, the length of the data packet varies from 10 bytes to 100 bytes in the operation of the group management network, the variation of the wating time is less than 10 msec. Since the waiting time in this case is less than 10 msec, response time is fast enough. Furthermore, to evaluate the real time processing of the group management network, it shows if the number of nodes is less than 40, and the average arrival time is less than 40 packet/sec, it can perform stable operation even taking the overhead such as software delay time, indicated packet service, and transmissin safety margin.