In this paper, the problem of token ring networks interconnected by a backbone ring is considered. The token ring networks connect each other through bridges. The bridge nodes themselves form the “backbone” ring. Each bridge node is modeled as two queues, one is for the local ring to send messages to the backbone ring and the other is for the backbone ring to send packets to the local ring. With the assumptions that the packet length distribution is exponential, the token walk time is constant, and the service discipline is exhaustive, we find that the interarrival time distribution of the bridge queues is close to exponential when the inter‐ring traffic is small. The Kolmogorov‐Smirnov test is used to determine the distribution of the interarrival time at the bridge queues. When exponential distribution of interarrival time at bridge queues is accepted, the arrival processes of the two queues are Poisson.