Bayesian Inference on Network Traffic Using Link Count Data

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to Journal of the American Statistical Association.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 is of interest in both communication and transportation network studies. The current article 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. This involves iterative simulation methods, or Markov chain Monte Carlo (MCMC), that combine Metropolis-Hastings steps within an overall Gibbs sampling framework. We discuss issues of convergence and related practical matters, and illustrate the approach in a network previously studied in Vardi's 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. This investigation generates critical insight into limitations of statistical analysis, and particularly of non-Bayesian approaches, due to inherent structural features of the problem. A truly Bayesian approach, imposing partial stochastic constraints through informed prior distributions, offers a way of resolving these problems and is consistent with prevailing trends in updating traffic flow intensities in this field. Following this, we explore a second version of the problem that introduces elements of uncertainty about routes taken by individual messages in terms of Markov selection of outgoing links for messages at ...

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