We consider the P/sub i/-persistent protocol and we derive approximate analytical results for the unfinished work distribution at each node on the bus under the assumption that the arrival process at each node follows a discrete time Gaussian process. A deterministic version of the protocol, which reduces the variance of the service process and therefore improves queueing performance, is also considered. The solution is simple and fast to compute and is not overly sensitive to the number of nodes. Simulation results indicate that the results are accurate so long as the performance can be accurately approximated based on the dominant effect of an exponential tail in the distribution of queued load. The results are also applicable to a single server Gaussian queue with priorities.