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In this paper we study the flow of traffic on roads for which passing is not permitted. Such traffic conditions exist in rural areas, hilly or mountainous regions, tunnels, etc. The traffic flow process is considered as taking place in a one directional road of infinite length, with passing not permitted. This paper studies measures of traffic flow in a road where vehicles have one of two free speeds. Measures of traffic flow are obtained for general vehicle entrance processes and derived explicitly for the homogeneous Poisson case.

Almost all the analytical models in the literature for traffic flow on two-lane roads are concerned with steady state situations, assuming that passing is possible at any point along the road. In this paper we study the steady state situation, assuming that passing is possible only at passing points, which are located at equal distances along the road. The mathematical model, presented in this paper, shows how expected velocities, expected driver loss time and platoon length are affected by such characteristics as speeds of fast and slow vehicles, rates at which fast and show vehicles enter the road, spacing of passing opportunities, and probability of a vehicle being able to pass given a passing opportunity.

A number of writers have observed that the particle size distributions obtained from some breakage processes appear to be logarithmico-normal. There have been virtually no attempts to explain this phenomenon. In this paper a statistical model is constructed for a breakage mechanism which will generate size distributions which are asymptotically logarithmico-normal. In this model, Fn(x), the distribution function of the particle sizes, after n steps of the breakage process, is the distribution function of the product of (n + 1) independent random variables and hence, by the central limit theorem, is asymptotically logarithmico-normal.