*Article* **Framework for Onboard Bus Comfort Level Predictions Using the Markov Chain Concept**

### **Paweł Wi ˛ecek, Daniel Kubek \*, Jan Hipolit Aleksandrowicz and Aleksandra Strózek ˙**

Department of Transportation Systems, Faculty of Civil Engineering, Cracow University of Technology, 31-155 Kraków, Poland; pwiecek@pk.edu.pl (P.W.); jaleksandrowicz@pk.edu.pl (J.H.A.); aleksandra.strozek@pk.edu.pl (A.S.)

**\*** Correspondence: dkubek@pk.edu.pl; Tel.: +48-12-628-37-21

Received: 15 May 2019; Accepted: 31 May 2019; Published: 4 June 2019

**Abstract:** Efficiently functioning public transport has a significant positive impact on the entire transportation system performance through numerous aspects, such as the reduction of congestion, energy consumption, and emissions. In most cases, the basic elements of public transport are the bus transport subsystem. Currently, in addition to criteria such as punctuality, the frequency of departures, and the number of transfers, a travelling comfort level is an important element for passengers. An overcrowded bus may discourage travelers from choosing this mode of transport and induce them to use a private car despite the existence of many other facilities offered by a given public transport system. Therefore, the forecasting of bus passenger demand, as well as bus occupancy at individual bus stops, is currently an important research direction. The main goal of the article is to present the conceptual framework for the Advanced Travel Information System with the prediction module. The proposed approach assumes that the prediction module is based on the use of the Markov Chain concept. The efficiency and accuracy of the obtained prediction were presented based on a real-life example, where the measurements of passengers boarding and alighting at bus stops were made in a selected Cracow bus line. The methodology presented in the paper and the obtained results can significantly contribute to the development of solutions and systems for a better managemen<sup>t</sup> as well as a cost and energy consumption optimisation in the public transport system. Current and forecasted information related to bus occupancy, when properly used in the travel information system, may have a positive impact on the development of urban mobility patterns by encouraging the use of public transport. This article addresses the current and practical research problem using an adequate theoretical mathematical tool to describe it, reflecting the characteristics and nature of the phenomenon being studied. To the best of the authors' knowledge, the article deals for the first time with the problem of prediction of onboard bus comfort levels based on in-vehicle occupancy.

**Keywords:** onboard comfort level; Markow chain; bus passenger occupancy prediction
