Modelling Public Transport Congestion

Modelling Public Transport Overcrowding and Delay

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We have developed a new modelling technique to investigate the effect of public transport overcrowding and delay caused by passenger congestion which we have implemented as part of Visual-tm. This can work in conjunction with time-of-day modelling which splits the day into time periods (eg 8.00 to 9.00 am). It can also be used in conjunction with highway junction delay modelling so that buses are delayed at junctions as well as the cars. It can be turned-off so that you can do conventional frequency-based assignments if you do not want the new features. The new features are as follows:
Timetable Assignment where paths are found according to the timetabled services on the basis of least generalised cost as opposed to one based on the service frequency (you can do conventional frequency based assignment too). This gives the number of passengers on each individual service.

Overcrowding. You specify the type of vehicle, capacity etc of each individual service and Visual-tm’s Interchange Microsimulation limits the passengers boarding at each stop to the vehicle’s capacity and calculates the alighting and boarding time. Any extra and it delays the vehicle downstream.

Interchange Microsimulation models the individual ‘packets’ of passengers who alight at one platform/ bus stop and board another or enter/ leave the interchange on foot. Individual platforms, bus stops, entry/ exit walkways, interconnecting walk links, capacities and crowd equations are coded into an interchange network to which each passenger ‘packet’ is assigned. Speeds are given by user-defined crowd/ speed equations. At the boarding platform/ bus stop the packet queues for the next train/bus and if it can’t get on, it waits for the next one. Delays are passed back to assignment.

To activate the new features you need to do a timetable path build which finds a reference path according to the timetabled services. For example the path of a trip could leave the origin at 8.00 am, walk to Stevenage station, take the 8.02 from Leeds to Kings Cross alighting at 8.32, walk to the Northern line southbound platform, board a Northern line southbound train at 8.42 to Bank alighting at 8.50 and walk to the destination arriving at 8.57. In our timetable assignment travellers chose their least generalised cost route on the basis of whichever service arrives at their railway station first (rather than splitting it by for example service frequency). The reference path build process records the clock time at which the path arrives at each node along the path. In the case of a bus stop or train station, the time of arrival and departure at each stop is recorded.
The assignment process splits the modelled time period (eg 8.00 to 9.00 am) into timeslices of the order of 1 minute each. It takes the reference path and loads them onto the network walking until it boards a public transport service at a public transport interchange. After completing the public transport part of the trip, it walks to its destination. Walking is loaded onto the network in the usual way. At each public transport interchange, the assignment process keeps track of the number of passengers interchanging between every pair of services which it passes to the public transport interchange micro-simulation as an interchange flow trip matrix.
Interchanges, be they bus stops, railway or tube stations, airports or any other type of interchange, can be coded in detail with their own sub-network of walk links, nodes, individual platforms, station entrances or exits. Use-defined equations relate crowd density to the walk speed; relate alighting time as a function of the vehicle, number of passengers on the train, number alighting and the welcoming crowd size; relate boarding time to the free space on the vehicle and the number of passengers boarding. Interchange paths are found on a least generalised cost basis and passengers are assigned to the sub-network in the usual way. The micro-simulation outputs passenger volumes and interchange delays.
The interchange micro-simulation software uses time dependent queuing to estimate the interchange delays for each interchange flow. The assignment process provides details of each interchange flow where an interchange flow is the number of passengers who alight each train (or bus or public transport vehicle) and board each other train (or bus or public transport vehicle). Interchange flows can also comprise passengers who enter the station at a station entrance in order to board a train (or bus or public transport vehicle) and passengers who alight and leave the station at a station exit, in which case these flows are accumulated on a ten-minute (or other user defined time interval) basis. In the interchange flow matrix, the rows and columns represent each public transport vehicle arrival, departure, station entrance or station exit and a matrix is given for each 10-minute time interval.
The software takes these interchange flows and calculates the best estimate of delay which they would incur by considering the sequence of events which happen at a station. The software identifies the next event and processes what can happen to each interchange flow. The following event processes are run, so if the next event is:
A train or bus arriving at a platform or bus stop, then the passengers:
alight from the train incurring an alighting time, which is dependent upon the how full the train is, the number of people alighting and the door configuration of the train vehicle itself.
Incur a delay getting through the welcoming crowd (the crowd of passengers waiting to board the train), depending upon the crowd density and the number of passengers alighting.
Incur a time to exit the platform, walk to the boarding platform and join the back of the queue of passengers waiting to board. As they walk through the passageways from one platform (bus stop etc) to another, their speed depends upon the crowd density of those using the passageway (using user-defined speed/ crowd density curves). They themselves contribute to the crowd.
These passengers then join the boarding queue and contribute to the welcoming crowd when the train (they want to board) arrives.
If they are leaving the interchange or station (instead of boarding another train) they do not incur delays due to c) or d).

A train or bus about to depart from a platform or bus stop, then the boarding passengers:
Incur a wait while those getting off the train, alight
Incur a time to board depending upon the number already on the train, the number of passengers boarding and the door configuration. Only the number of passengers up to the capacity of the train, can get on to the train. The rest of the passengers wait for the next train (so this queue gets passed onto the queue for the next train).

A set of passengers enter a station (comprising all passengers in the next time interval), who are going to board a train (bus etc). In this case the processing sequence is that described in event 1 (above) but omitting the alighting delays (ie a and b).

The interchange simulation process has divided the matrix into ‘packets’ of passengers. Where passengers alight one train and manage to board another (ie there was enough available capacity on the boarding train for them to get on), then these are accumulated into larger ‘packets’. Those passengers who did not get on the train they wanted, and who got on the next train, would comprise another ‘packet’ (and so on for other ‘packets’ comprising those who had to wait for several trains before there was enough space for them to board).

The final output from the interchange simulation, is the delay incurred by each flow which alights one train and wants to board another (some of which may have to wait for the next or subsequent trains because there was not enough space for them to get on the train they wanted to get on). This interchange delay is then input into the assignment process so that passengers who incur delay can find alternative routes. The assignment and interchange delay simulations can be iterated until convergence.
An additional step in the process could be undertaken to relate to the effect of the interchange delay on the train (bus or public transport vehicle) schedule. Train schedules can be redefined so that the dwell time at the stop can be increased in-line with the alighting + crowding + boarding delay time calculated during the simulation phase and the assignment process rerun to see the effect of interchange congestion on the timetable. This could then be compared with the slack time available for the train path, to assess the effect of congestion on the operation of the other trains using the same line; on trains using other lines, on connecting trains and on the public transport system generally.
We have implemented a similar junction simulation for highway junctions using the Arcady/ Picady/ Oscady/ Linsig capacity and time dependent queuing equations to provide estimates of highway junction delay to the highway assignment process. This highway delay can be passed through to the bus timetable times so as to assess the combined effect of traffic congestion and bus interchange delay. This bus delay could also be fed through to rail interchanges and its delay so as to assess the inter-dependencies of highway congestion, bus congestion and rail congestion.

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