Optimal coordination for an integrated multimodal and multi-operator transit system

Abstract

With rapid urbanisation in most parts of the world, modern transit systems have been made more and more convenient, reliable and integrated. In Singapore, more than 60% of the daily commuting trips in year 2005 are made in public transport and this share will likely continue to increase, due to the policy governing land transport. In the mean time the service level of public transport needs to continue to be enhanced to help achieve this goal. The aim is to make public transport, especially transit, seamless and sustainable. The public transport system in Singapore is currently operated by two multimodal transit operators on an integrated network with each of them providing services in different geographical areas. Currently this multimodal network is integrated mainly in infrastructure. The operation schedule is still in the domain of each individual operator which resulted in unnecessarily long delays for passengers. To provide better service especially during off-peak hours, it is necessary to coordinate the transit system. What the coordination results would be, when multi-operators co-exist in the same multimodal transit system with fully or partially overlapping services, originates this research topic. This research focuses on optimal coordination of public transit operated by multiple operators. The optimal results would be achieved when the system reaches an equilibrium state that the operators and users would not modify their behaviour, i.e. operators would not adjust fare and schedule of transit services, while each groups of users keep on the same shortest paths. The objective function is the total cost which consists of operator cost and user cost. The formulation of the total cost in different coordination scenarios are analysed under three different operation policies, i.e. cooperation, competition and independence, respectively. By categorizing different groups of passengers in detail, the categorized passenger flows are traced on different paths that passengers have choosen. The optimal results in the equilibrium state can be obtained by the feedback optimisation algorithm developed in this study.The objective functions in scenarios of non-coordination and common headway coordination, which are identified as nonlinear programming problems, are solved by considering the first order and second order conditions; whereas the objective function in integer-ratio headway coordination is identified as a mixed integer nonlinear