An investigation of proportionally fair ramp metering

This paper concerns ramp metering which is one important approach to dealing with congestion on motorways. Congestion occurs when demand exceeds available resources and can significantly reduce the capacity of the motorway network at peak times. Reduced capacity results in additional delays, increased environmental pollution and hinders passenger safety. Congestion is observed to cause low but highly volatile speeds resulting in more uncertain journey times (referred to as flow breakdown or stop-and-go behaviour). Ramp metering is intended to control the entry of new flow in such a way as to maintain steady flow on the motorway and to avoid the loss of capacity associated with congestion. The rate of entry of flow is set according to the particular ramp metering strategy. Such strategies have been the subject of much attention in the transport literature. One of the key issues is the trade-off between efficiency and fair use of resources. This is a trade-off that has been considered extensively in the modelling and control of communication networks. This paper adds to recent work on a ramp metering strategy, proportionally fair metering, inspired by rate control mechanisms developed for the Internet. Specifically, we use simulation results to compare proportionally fair metering with a greedy strategy for a linear network with a series of entry points leading towards a single common destination for all the traffic, such as a radial route towards a city centre. Under our modelling assumptions, the greedy strategy is provably optimal for exogenously determined arrival streams of traffic, but it is unfair, in a certain precise sense, between different entry points and may well have perverse and suboptimal consequences if it influences traffic demand. We further consider a network with parallel roads where flows of traffic may have route choice according to the levels of queueing at the individual entry points.