September 1997 We study Bayesian models and methods for analysing network traffic counts in problems of inference about the traffic intensity between directed pairs of origins and destinations in networks. This is a class of problems very recently discussed by Vardi in a 1996 JASA article, and of interest in both communication and transportation network studies. The current paper develops the theoretical framework of variants of the origin-destination flow problem, and introduces Bayesian approaches to analysis and inference. In the first, the so-called fixed routing problem, traffic or messages pass between nodes in a network, with each message originating at a specific source node, and ultimately moving through the network to a predetermined destination node.
All nodes are candidate origin and destination points.
The framework assumes no travel time complications, considering only the number of messages passing between pairs of nodes in a specified time interval. The route count, or route flow, problem is to infer the set of actual number of messages passed between each directed origin-destination pair in the time interval, based on the observed counts flowing between all directed pairs of adjacent nodes. Based on some development of the theoretical structure of the problem and assumptions about prior distributional forms, we develop posterior distributions for inference on actual origin-destination counts and associated flow rates. We discuss issues of convergence and related practical matters, and illustrate the approach in a network previously studied in Vardi's 1996 article. We explore both methodological and applied aspects much further in a concrete problem of a road network in North Carolina, studied in transportation flow assessment contexts by civil engineers.