The out-of-kilter algorithm applied to traffic congestion
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#2002 Operational Research Society Ltd. All rights reserved. 0160-5682/02 $15.00 www.palgrave-journals.com/jors
The out-of-kilter algorithm applied to traffic congestion P Wackrill1* 1
Middlesex University, London, UK
The out-of-kilter algorithm finds a minimum cost assignment of flows to a network defined in terms of one-way arcs, each with upper and lower bounds on flow, and a cost. It is a mathematical programming algorithm which exploits the network structure of the data. The objective function, being the sum taken over all the arcs of the products, cost flow, is linear. The algorithm is applied in a new way to minimise a series of linear functions in a heuristic method to reduce the value of a non-convex quadratic function which is a measure of traffic congestion. The coefficients in these linear functions are chosen in a way which avoids one of the pitfalls occurring when Beale’s method is applied to such a quadratic function. The method does not guarantee optimality but has produced optimal results with networks small enough for an integer linear programming method to be feasible. Journal of the Operational Research Society (2002) 53, 1133–1141. doi:10.1057=palgrave.jors.2601339 Keywords: optimisation; heuristics; traffic; mathematical programming; networks and graphs
Introduction One aim of traffic management is to facilitate circulation while paying due attention to safety and environmental considerations. When traffic management is being considered, a network of streets will be studied together with the likely demand for traffic to be accommodated within and through it. The application described in this paper takes the whole network and the demand for routes through it as its starting point, and finds a coherent routeing pattern to facilitate circulation. Finding routes that minimise the amount of conflict is, however, more than an academic exercise. A driver can be encouraged to use the desired route in various ways. Firstly, in many urban areas signposts to car parks and for through traffic are needed when the number of suitable alternative routes has been restricted by pedestrianisation and traffic calming measures. Such redevelopment effectively involves choosing and signing routes which traffic planners desire. Secondly, encouragement can be given by allowing longer green time to desired movements at traffic lights; one uses the desired volumes of turning traffic as the input to signal optimising programs such as TRANSYT.1 One would thus reward drivers following the desired route with greater priority at traffic lights. It is the volume of traffic queuing up to pass through bottlenecks in the network which prompts traffic managers
*Correspondence: P Wackrill, Middlesex University Business School, The Burroughs, London NW4 4BT, UK.
to react with some management measure to relieve the situation. They use a combination of experience and modelling to guide them. However, they can also be proactive and try to encourage choices which make the most efficient use of the network in terms of journey times
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