On the task of allocating investment to facilities preventing unauthorized movement of road vehicles across level crossings for various statistical criteria

Aim. Railway transportation is affected by a whole range of transportation incidents, both related to rolling stock, i. e. vehicle-to-vehicle collisions, derailments, broken cast parts of bogies, etc. , and infrastructure, i. e. broken rail, fires at railway stations and terminals, broken catenary, etc. Among the above incidents, collisions at level crossings are the most likely to cause a public response, as collisions between trains and road vehicles often cause multiple deaths that are reported in national media, which entails significant reputational damage for JSC RZD. Additionally, collisions often cause derailment of vehicles, which may cause deaths and major environmental disasters, if dangerous chemical products are transported. Beside the reputational damage, collisions at level crossings cause significant expenditure related to the repair of damaged infrastructure and rolling stock, as well as damage caused by trains idling due to maintenance machines operation at the location of incident. That brings up the issue of optimal allocation of investment to facilities preventing unauthorized movement of road vehicles across level crossings (hereinafter referred to as protection systems). This problem is of relevance, as replacing level crossings with tunnels and viaducts is not going fast and does not imply the eventual elimination of all level crossing. Hence is the requirement for rational allocation of funds to the installation of protection systems over the extensive railway network. Given the above, the aim of this paper is to develop decision-making guidelines for the reduction of the number of transportation incidents in terms of statistical criteria, i. e. quantile and probabilistic.

 Methods. The paper uses methods of deterministic equivalent, of equivalent transformations, of the probability theory, of optimization.

 Results. The problem of maximizing the probability of no incidents is reduced to integer linear programming. For the problem of minimizing the maximum number of incidents guaranteed at the given level of dependability, a suboptimal solution of the initial problem of quantile optimization is suggested that is obtained by solving the integer linear programming problem through the replacement of binomially distributed random values with Poisson values. 

Conclusions. The examined models not only allow developing an optimal strategy with guaranteed characteristics, but also demonstrate the sufficiency or insufficiency of the investment funds allocated to the improvement of level crossing safety. Decision-making must be ruled by the quantile criterion, as the probability of not a single incident occurring may seem to be high, yet the probability of one, two, three or more incidents occurring may be unacceptable. The quantile criterion does not have this disadvantage and allows evaluating the number of transportation incidents guaranteed at the specified level of dependability.

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