The Supermarket Model with Bounded Queue Lengths in Equilibrium

Journal of Statistical Physics - In the supermarket model, there are n queues, each with a single server. Customers arrive in a Poisson process with arrival rate $$\lambda n$$ , where $$\lambda =...     

Description and Shortcomings of Some Urban Road Traffic Models

In the sense of this paper "traffic models" are formulae for predicting the number of journeys made between one place and another, usually between one part of a town and another. Some models are described and are applied to hypothetical examples. The models are divided into two main classes, "gravity models" and "opportunity models". Gravity models are based on the assumption that the amount of traffic between two areas varies with the size or importance of the areas and with the distance between them in a manner analogous to the inverse square law of gravitation. The idea of opportunity models arises from the supposition that travellers consider possible destinations or opportunities in order of distance from their origin, accepting or rejecting them in a certain proportion. It is inferred that the basic form of gravity model tends to overestimate traffic in high-density areas, whereas the opportunity model has the opposite tendency. However, either type of formula can be adapted so that these defects are overcome. Much of the section on gravity models relates to the work of J. C. Tanner of the Road Research Laboratory.