Transit Vehicles' Headway Distribution and Service Irregularity (original) (raw)
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Transportation research procedia, 2017
Traffic along a transit line involves two kinds of mobile entities: passengers versus vehicles. The paper develops a stochastic model to deal with: headways between successive runs serving stations, wait times at boarding stations, passenger flows per vehicle and by leg (i.e. pair of entry-exit stations), in-vehicle comfort differentiating between seated and standing places. While previous static models of transit assignment consider vehicle passenger flows that are averaged over the vehicle runs, we model distributed headways, thus taking into account the issues of regularity and reliability. The "Rank conservation" postulate of Leurent et al. (2012a,b) is used to establish analytical formulae for the expectation and variance of every traffic variable of interest: leg flows, link flows, wait times, leg physical times, generalized times at waiting and in-vehicle. The linkage between waiting prior to boarding and in-vehicle crowding is modeled: each user is concerned individually, conditionally to the headway during which he waits for the vehicle. A computation scheme is provided to deliver the statistical summaries of the array of traffic variables.
A Stochastic Model of Passenger Generalized Time Along a Transit Line
Procedia - Social and Behavioral Sciences, 2012
Along a transit line, vehicle traffic and passenger traffic are jointly subject to variability in travel time and vehicle load hence crowding. The paper provides a stochastic model of passenger physical time and generalized time, including waiting on platform and in-vehicle run time from access to egress station. Five sources of variability are addressed: (i) vehicle headway which can vary between the stations provided that each service run maintains its rank throughout the local distributions of headways; (ii) vehicle order in the schedule of operations; (iii) vehicle capacity; (iv) passenger arrival time; (v) passenger sensitivity to quality of service. The perspective of the operator, which pertains to vehicle runs, is distinguished from the user's one at the disaggregate level of the individual trip, as in survival theory. Analytical properties are established that link the distributions of vehicle headways, vehicle run times, passenger wait times, passenger travel times, and their counterparts in generalized time, in terms of distribution functions, mean, variance and covariance. Many of them stem from Gaussian and log-normal approximations.
Transit assignment model incorporating the bus bunching effect
This paper proposes a transit assignment model considering the correlation between vehicles' arrival at stops. The correlation of arrival is represented with a correlation coefficient matrix, and the expected waiting time and the arc split probabilities at stops are calculated with a Monte Carlo simulation-based method where the correlated random variates follow a given distribution function. This function is generated using dependent random variates which follow a normal distribution and a correlation coefficient matrix. Since the correlation coefficients are defined as a function of the number of boarding and alighting passengers, it is possible to consider two sources of correlation in the proposed model; i) increasing boarding and alighting time due to passengers' concentration to a certain vehicle, ii) concentrating vehicles on a certain road segment. The proposed model is formulated as a fixed point problem and the solution approach is illustrated with a toy network.
Unreliable public transport systems cause excessive waiting times, late or early arrivals at destinations and missed connections for passengers. Also, unreliability results in economic losses to transit operators through under utilization of vehicles, equipment and work force. The reliability analysis of bus transit, covered in this paper, is based on numerical estimation of headway variations at different bus stops along the route. A number of simulations are conducted to determine the variation of performance of bus operation due to the variability of departure headways. The average waiting time of passengers is used as an indicator of operational performance. Simulation results show that the spread of passenger waiting times widens as the headway variation increases. Impact of size of vehicle on waiting time distributions is also investigated. Irregular headways lead to uneven passenger loads on buses. Such variation in passenger counts result in some buses becoming full and being unable to serve certain stops. Thus, average waiting time increases with smaller bus size. Simulation also reveals that the average waiting time increases for passengers waiting further along the route.
A stochastic model for bus injection in an unscheduled public transport service
Transportation Research Part C: Emerging Technologies, 2019
Randomness affecting the operation of public transport systems generates significant increments in waiting times. A strategy to deal with this randomness is bus injection, in which buses are kept in specific points along the route ready to be dispatched when an event such as an extremely long headway occurs. In this work, a stochastic model based on the second moment of the headways distribution is developed to determine if one or more buses are worth reserving for injection in a public transport service. A single stop approach is initially used to determine an expression for the optimal headway threshold triggering the injection. Then, a model for the complete service is developed and used to determine when the empty bus should be injected within the headway once the decision to inject it has been taken. We show that the bus should be injected approximately when 57% of the headway has passed. Simulations with real data are used to test the proposed model, proving its accuracy in terms of measuring the impact on waiting times. The results show that reserving a bus to be injected can be better than operating the entire fleet continuously.
Passenger arrival rates at public transport stations
2006
The amount of time spent waiting at a public transport station is a key element in a passenger's assessment of service quality and in mode choice decisions. Many transport models estimate the average wait time is half the headway for small headways and use a maximum waiting time for headways over a given value. The assumption is that at small headways passengers do not bother to consult schedules since vehicles arrive frequently; therefore these passengers arrive regularly at the station. In contrast, at longer headways passengers do consult schedules to reduce their waiting time; these passengers arrive clustered around the departure time. This research evaluated the influence of headway and other factors on passenger arrival rates at public transport stations based on data collected at 28 stations in Zurich's public transport network. It found that even at 5-minute headways, some passengers consulted schedules and did not arrive randomly at the station. This finding is interesting since 5-minutes is much lower than many models assume, therefore these models may be overstating passenger wait time. The research also found time-of-day and reliability had an important influence on passenger arrival rates. The research proposes a model for passenger arrival rates at stations that combines a uniform distribution with a shifted Johnson S B distribution.
A stochastic model for bus injection in a public transport service
Transportation Research Procedia, 2019
Randomness affecting the operation of public transport systems generates significant increments in waiting times. A strategy to deal with this randomness is bus injection, which holds buses in specific points along the route ready to be dispatched when an event such as an extremely long headway occurs. In this work, stochastic models based on the second moment of the headways distribution are developed to determine if bus injection is worth using at a given public transport service, how to operate it optimally and its impact on each stop. A single stop approach is initially used to determine a closed expression for the optimal time threshold for dispatch, then a complete service approach determines the optimal stop to locate the injeciton fleet and the instant to dispatch it. Simulations with real data are used to test models, proving their accuracy in terms of measuring impact on waiting times. Results show that injection is worth operating in some cases, reducing total waiting times compared to constant circulation.
Simulated Relationships between Highway Capacity, Transit Ridership, and Service Frequency
Journal of Public Transportation
This article analyzes the relationships between highway capacity additions and transit patronage, both in the short and long run. A methodology using a model of schedule disutility is shown to provide a technique to account for transit service frequency. This technique, combined with a supply-side model of a highway corridor is used to evaluate the impact of transit headway changes and highway capacity, increases on total transit ridership, using a synthetic sample of commuters. Simulation results are used to evaluate the impact on travel times and utility of the two modes and the longrun degradation of transit service predicted by the Downs-Thomson paradox. While the results do not show congestion as necessarily being worse than before capacity expansion, they do show that transit service frequency could be reduced significantly over time.