Clocktime Assignment: a New Mesoscopic Junction Delay Highway Assignment Approach to Continuously Assign Traffic over the Whole Day
P Davidson, P Clarke, A Thomas, Peter Davidson Consultancy, UK; M Shahin, University of Alexandria, EG
This paper puts forward clock time assignment, an innovative approach to highway assignment modelling which provides significant benefits over traditional methods especially for activity and tour based models.
Traffic queues and delay are the most difficult things to model, yet they are the most crucial for forecasting traffic levels, for defining the routes people take and for moderating travel demand. The biggest determinant of traffic queues and delay is the flow history of the junction. For many assignment models this goes back well before the start of the time period being assigned and continues well after the assignment model time period finishes - especially when forecasting the much higher level of congestion in the future. Yet we persist in modelling the peak hour.
During the modelled time period, levels of queuing and delay are not spread evenly and nor are the traffic levels - they usually grow near the beginning and decline towards the end. But this pattern is not homogeneous throughout the study area - some roads peak much earlier, some much later and some don't peak at all - motorways in particular exhibit different characteristics to main roads and both are often different to minor roads. The study area of many large models is so large that it can take considerably more than an hour to traverse it. Traffic which starts at the edge of the study area (maybe commuting to the centre) may not even get to the centre within the modelled hour and if they do, some would have started earlier and be in-transit when the modelled hour starts. Our models normally assume that traffic follows a homogeneous temporal-spatial pattern - yet it is its very heterogeneity which has the biggest effect on queuing and delay.
We would argue that to model traffic queuing and delay successfully, our assignment models need to model the whole day as a continuum. We have developed a methodology to do just that:
In this, traffic is divided into half hourly (or a shorter user defined period) origin-destination trip matrices which are sliced into time slices of demand for assignment (eg slices of 1 minute or so using a spatial-temporal template to mirror the heterogeneity). Paths are built at 10 minute intervals (eg 7.00, 7.10, 7.20 etc) keeping track of the clock time (see note 1) at each junction the path passes through. The delay at each junction turning movement is stored for every 10 minute period throughout the day on the basis of the clock time. As the path passes through each junction, the delay experienced by traffic passing through the junction at that clock time, is added-on to the path. Similarly link times are held in 10 minute clock-time bins and accumulated by the path. For one minute time slices and 10 minute paths, the ten time slices are assigned to those paths, keeping track of the actual clock time when the time slice goes through the junction. This is so that the traffic in that time slice can be added to the turning volume at that junction at the clock time it passes through the junction. All traffic is therefore assigned to the network experiencing the junction delay and link speed which it would experience at the time of day when it passed through the junction or along the link. At the end of the assignment, the ten minute bins of traffic are put through ARCADY/ PICADY/ OSCADY to calculate the queues and delays. The traffic on the network at the end of the assignment 'day' is held in a 'Too Late' matrix from which to start the next day.
This approach leads to questions about convergence. Do Wardrop's principals still relate to this type of model? Is convergence to an equilibrium point achievable? The paper examines these issues.
The precise methodology is more fully described in the paper which also describes its implementation and the results from a case study. Incorporating outputs from this type of assignment model into a demand model is also explored. The methodology leads to providing a different skim or cost for each individual traveller which fits will into the discrete choice modelling framework and particularly lends itself towards activity based models using household microsimulation. It may also have application for improving our representation of journey time reliability.
Note 1: Clock time is the time on the clock eg 7.10, 18.30
Association for European Transport