Development of a model of the service system of batch arrivals in the passengers flow of public transport - Raskin, Lev; Sira, Oksana; Palant, Oleksii; Vodovozov, Yevgeniy (Eastern-European Journal of Enterprise Technologies, 2019)
A mathematical model of the queuing system for the passenger flow of urban public transport is proposed. The resulting model differs from canonical models of queuing theory by taking into account the fundamental features of real systems. Firstly, the service process is divided into different successive service sessions. Secondly, arrival and departures are batch. Thirdly, the arrival rates vary in different service sessions. Fourthly, the laws of distribution of the number of jobs in batch arrivals for different sessions are different. Fifth, the laws of distribution of the number of batch arrivals and departures are also different. A criterion of efficiency of the service system is developed. The criterion is based on the calculation of the probability distribution of the service system states at the input and similar distribution at the output. These distributions are determined independently for each service session, into which the entire service cycle is divided. The numerical value of the criterion is set by the ratio of the average number of service rejections to the average number of jobs in the batch arrival for the entire service cycle. It can be used to assess the efficiency of the service system at any selected time interval during the day, because the value of the proposed criterion depends on the length of the interval between sessions, determined by the number of vehicles on the route. The resulting models adequately reflect the functioning of the system, which makes it possible to predict many different situations and evaluate the consequences of proposed solutions. Thus, it becomes possible to predict the provision of the population with public transport and determine quantitative values of efficiency of the urban public transport system