Expected distributions in the intervening opportunities model

Two modifications of the intervening opportunities model, accounting for the “long lines effect” are proposed. The first modification deals with the instant reaction of customers at long queues and incorporates statistical dependence of their behaviour. In the second model customer behaviour is determined by the past data, which makes their behaviour statistically independent. The concept of self-consistent distribution is introduced, its existence is investigated and properties of self-consistent distributions are discribed.