Optimal Design of Motorway Toll Stations
A Pratelli, Università di Pisa; F Schoen, Università di Firenze, IT
Keywords: toll station design; toll-plaza layout; safety design approach; automatic vehicle identification; toll gate types assignment; quadratic assignment.
In a modern toll station there are various types of toll gates, such as manual gate with operator, unattended gate with automatic teller machine (automatic vehicle identification, or AVI, technologies), semiautomatic short-stop gate. Determination both of the plaza size and of the proper gate type sequence, i.e. toll station layout, in the actual planning process is quite important for an optimal design of the toll station, moreover, it is essential to its future operational efficiency. The planning process is basically a two-stage process: initial planning and then fine-tuning, usually with a microscopic simulation model that can simulate the random nature of vehicle arrivals and the stochastic service performance of the different gates (Polus, 1998). The whole process should generally include the field data collection and analysis, finally resulting in three steps: 1) data collection and analysis; 2) preliminary planning; 3) fine-tuning and adjustments.
Since now the preliminary planning (step 2) has been viewed (Polus, 1998) as a sequence of sub-steps including determination of the number of AVI gates and of the number of gates of other type (semiautomatic or manual) according to the policy of the motorway agency, based on a traffic growth model that provides the estimated traffic composition and flow for a fixed design year. Then, in step 3, it is determined the final number of gates, under selected hypothesis to account for the randomness of traffic and the stochastic performance of the toll system, by using a toll station simulation model (Gulewicz and Danko, 1994; Polus, 1996). This way to proceed can be implemented by a unified step that assign a prefixed number and type of gates (i.e., according to operating policy) in view of a design criterion, i.e. circulation safety. We searched for to develop such a planning approach, as better described in the following.
Vehicles approaching the tollbooths are frequently involved in accidents, mostly due to sudden lane changes of vehicle drivers who try to join the shortest queue, or to the interactions between different classes of vehicles directed to distinct types of available tollgates. Then reciprocal position of each type of gate is crucial for safety goals. Trajectories of higher speed vehicles directed to AVI gates need to be managed in respect to lower speeds of vehicles approaching any other type of stop gate, i.e. manual gate.
In order to cope with such a problem, the knowledge of the relationships between traffic flow, driver's habits, number and type of open toll gates and vehicle arrival and departure patterns is essential from any network-wide design point of view. This paper presents our research progresses in developing a toll station layout optimisation methodology based on toll plaza circulation safety analysis. We propose a mathematical programming approach in order to assess the expected level of traffic safety associated with the toll station layout ? actual or planned ? due to a given configuration for gate types and positions. Our model has been conceived in order to let the planner be able to decide the proper sequence of gate types which minimises the risk of accidents. The optimal solutions in terms of circulation safety, i.e. minimum accident probability, associated with varying traffic flows and patterns and toll station layout, are now explored.
The decision variables are mainly related to the assignment of a gate type ? manual gate with operator, AVI gate, semiautomatic or short stop gate ? to each gate position in the station. The model takes into account the probability of interaction between pairs of traffic streams originated from the different lanes of the highway and directed to specific gate types; different severity and risk indices are associated both with vehicle types and with destination gate types. These risk indices are combined in a criterion objective function, which takes also into account traffic composition, i.e. percentages of heavy and light vehicles, and incidence of AVI equipped vehicles. Finally, the resulting problem is a quadratic assignment problem in which binary decision variables are introduced to characterise the association between physical gate and gate type.
Constraints are added in order to be sure that each gate has a specified type and that the composition of the whole station, in terms of number of gates of each type, is fixed. Although from a theoretical perspective, the problems of this kind are in general extremely burdensome, we are able to obtain optimal solutions for medium sized toll stations (note that 15 gates is generally considered an actual upper bound) in a few minutes on a Pentium PC. The first group of computational experiments performed tend to support the evidence that gates associated to higher risk traffic flows, e.g. traffic directed to AVI gates which approaches the toll station at speeds significantly above the average, should be locate in a central position with respect to other gate types. Our first results, however mostly drawn on a theoretical ground, are in considerable opposition to the general design and operations practice of Italian motorway agencies, that frequently locate the AVI gates on the far side of the toll station, apparently without any coded design criterion. These first conclusions are quite supported by results of a second group of computational experiments performed on a set of observed data which have been gathered by camera films in some toll-plazas of Italian motorway network.
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Association for European Transport