Calculating conditional passenger travel time distributions in mixed schedule- and frequency-based public transport networks using Markov chains

Document Type

Journal Article

Publication Date


Subject Area

place - europe, planning - service level, planning - methods, operations - scheduling, operations - performance, operations - frequency


Markov chains, Phase-type distributions, Public transport, Travel time distribution


Calculation of passenger travel time distributions in public transport networks is important for the evaluation of the level of service provided to passengers. Passenger travel times are deterministic for punctual and uncongested networks, but in reality usually have random fluctuations caused by vehicle delays and other incidents. Advanced methods are therefore needed to calculate the passenger travel time distribution between a given origin and destination. This paper presents a novel approach for calculating the travel time distribution from origin to destination based on vehicle delays and possible missed connections in a mixed schedule- and frequency-based public transport network. Markov chains are used to model the network, making the travel time from the origin to the destination phase-type distributed. The approach is flexible with regard to the specification of vehicle travel times and provides the distribution of passenger travel times without any need for simulation. Additionally, it facilitates detailed analyses of passenger travel times conditional on the usage of specific line segments or stops. The merits of this approach are demonstrated using a case study from Copenhagen.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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