A Stochastic Analysis of a Tandem Delay System

A basic model is proposed for traffic on a two-way, two-lane road which allows that successive queues of fast vehicles traveling behind slow vehicles in one lane may see the same pattern of overtaking opportunities as the opposing stream moves past. A general process of overtaking in bunches is incorporated in the model. We also allow that queues may coalesce when the finite space between two slow vehicles is full of fast vehicles and subsequently fragment again. Fast vehicles do not necessarily all have the same speed. An expression is derived for the mean speed attainable by fast vehicles and a relation found between flow and concentration of fast vehicles. The basic model can be developed in a variety of ways, which give additional information about the fundamental diagram of traffic. Two special cases are treated.