Multicast group communication protocols provide a foundation on which distributed systems can be built. The performance of these protocols is, however, not easy to characterize or to analyze. This research determines probability density functions for the latency to message delivery for the Totem multicast protocols, which provide reliable totally ordered delivery of multicast messages across single and multiple local-area networks (LANs). Totem uses a logical token-passing ring on each LAN with gateways that forward messages selectively between LANs. Comparing the performance of single-ring, two-ring and four-ring networks shows that, with message filtering in the gateways, multiple-ring networks can achieve lower mean latency, less variability in the latency, and shorter tails of the latency distribution than an equivalent single-ring network.