Improving ramp metering 271

motorway throughput – an answer to flawed criticism THE ALINEA ALGORITHM Consider the sketched motorway/on-ramp merge area dis-played on Figure 1. Local ramp metering corresponds to con-trolling (by use of traffic lights) the traffic flow merging into the mainstream from the on-ramp so as to maximise the mainstream flow downstream of the on-ramp in response to the prevailing traffic conditions. Different proposed methods may use different kinds or locations of measurements and dif-ferent algorithms in order to achieve the stated goal (down-stream flow maximisation), see [9] for an overview. ALINEA was the first algorithm to be based on a feedback concept (to be more elementarily explained later, see also [6-9]). Local ramp metering strategies are activated at each time interval T, whose value typically is selected in the range from 20 to 60 s. More specifically, at the end of each running pe-riod T, time-averaged measurements of traffic volume (flow) or occupancy (depending on the requirements of the em-ployed control strategy) from the ending period are used to calculate (via the corresponding strategy) the ramp flow to be implemented in the next period. The particular ALINEA algo-rithm reads (1) where: • k = 1, 2,... is the discrete time index; • r(k) is the ramp flow (veh/h) to be implemented during the new period k; • is the last measured motorway occupancy (%) (averaged over all lanes) downstream of the ramp; • KR>0 is a regulator parameter; • is the set (desired) value for the downstream occu-pancy. The following issues are quite crucial for a proper ALINEA application as emphasised in [6, 7]: (i) The same value of KR has been used in most simulation or field applications of ALINEA without any need for fine-tuning. The utilised KR-value is not mentioned in [5]. (ii) The ramp flow r(k) resulting from (1) is truncated if it ex-ceeds a range where is the ramp’s flow capacity (eg equal to 1800 veh/h for single-lane ramps) and is a minimum admissible ramp flow (typi-cally 200...400 veh/h). There is no mention of this in [5]. (iii) This truncated ramp flow value is used as r(k – l) in (1) in the next time step to avoid the well-known wind-up ef-fect of I-type (integral) regulators as ALINEA; note tha