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Improving the public transit system for routes with scheduled headways

This research contributes to the improvement of the optimal headway solution for the transit performance functions derived from the traffic model proposed by Hendrickson. The purpose of this paper is threefold. First, we prove that that model has a unique solution for headway. Second, we offer a formulated approximation for headway. Third, numerical examples illustrate that our formulated approximation performs more accurately than the Hendrickson’s. | Yugoslav Journal of Operations Research 24 (2014) Number 2, 237 - 248 DOI: 10.2298/YJOR130207011C IMPROVING THE PUBLIC TRANSIT SYSTEM FOR ROUTES WITH SCHEDULED HEADWAYS Jones Pi-Chang CHUANG Department of Traffic Science, Central Police University, Taiwan, R. O. C. una050@mail.cpu.edu.tw Peter CHU Department of Traffic Science, Central Police University, Taiwan, R. O. C. una211@mail.cpu.edu.tw Received: February 2013 / Accepted: April 2013 Abstract: This research contributes to the improvement of the optimal headway solution for the transit performance functions (e. g., minimize total cost; maximize social welfare) derived from the traffic model proposed by Hendrickson. The purpose of this paper is threefold. First, we prove that that model has a unique solution for headway. Second, we offer a formulated approximation for headway. Third, numerical examples illustrate that our formulated approximation performs more accurately than the Hendrickson’s. Keywords: Analytical approach, headway of bus, stop-spacing, public transportation. MSC: 90B20. 1. INTRODUCTION Researchers developed analytical traffic models to provide a simplified version for the real but too complicated real world situations. The formulated solution for analytical modes is a useful indicator to reveal relations among parameters and decision variables. From the explicit expression, researchers noticed which parameter has significant impact on the optimal solution; so, they could operate a comprehensive examination of the important parameters to obtain more representative mean and variance of the parameters. For examples, Golob et al. [6] examined an analysis of consumer preferences for a public transportation system to improve the quality of information about potential public transportation users, their needs and preferences. 238 J.P.C. Chuang, P. Chu/ Improving The Public Transit System For Routes Renault et al. [16] studied discounted and finitely repeated minority games with public signals