Congestion Aboard the Vehicles Congestion Outside the Vehicles Some Large Scale Applications Conclusions

Considering Crowding and Capacity in Public Transport

Michael Florian [email protected]

Moscow, 2013 Contents of presentation

Motivation Congestion aboard the vehicles Congestion outside the vehicles Some large scale applications Conclusions

Moscow 2013 Some Vehicles are Truly Congested !

Moscow 2013 London bus

Moscow 2013 Hong Kong MTR

Moscow 2013 Mexico City metrobus

Moscow 2013 Sao Paulo station

Moscow 2013 Perth

Moscow 2013 Sydney

“Sydney bus and train commuters say overcrowding is still their main public transport concern.” http://www.abc.net.au/news/stories/2010/12/31/3104 302.htm?site=sydney “Buses in Sydney on the busiest routes are often overcrowded and do not stop for passengers, with an extraordinary 22% of people missing their service.” http://www.2ue.com.au/blogs/2ue-blog/crowded- buses-just-not-stopping/20111130-1o6f1.html

Moscow 2013 Congested/Capacitated Transit Applications

London (1989-) Hong Kong (2002-) Sao Paulo (2005-) Santiago (2010-) Mexico City (2011-) Rio de Janeiro (2013-) Brisbane (2013-) Others…

Moscow 2013 Tight Trains, Busy Buses

Passengers incur perceived and real costs in congested transit systems Models may ignore crowding and vehicle capacity  ridership is overestimated on busy services  demand for other services and modes underestimated  wrong impedances Two methods to model transit congestion with Emme  better representation of transit ridership  feedback improves mode choice and trip distribution

Moscow 2013 Contents of presentation

Motivation Congestion aboard the vehicles Congestion outside the vehicles Some large scale applications

Moscow 2013 Congestion aboard vehicles

– Models ‘discomfort’ function as vehicles become congested – Increased perceived impedance through in-vehicle time – Optimization model - unique solution

Moscow 2013 Modeling Congestion

The modeling of congestion aboard the vehicles may be done by associating congestion functions with the segments of transit lines to reflect the crowding effects,

The resulting model is nonlinear and leads to a user optimal transit equilibrium model similar to the highway equilibrium assignment.

“ For all origin-destination pairs the paths (strategies) that carry flow are of minimal generalized cost and the strategies that do not carry flow are of a cost which is larger or equal to the minimal cost.”

This leads to a convex cost optimization problem.

Moscow 2013 Modeling Congestion with Segment Crowding Functions

cf() vs

c() caps

v Seated Capacity Capacity s

Moscow 2013 Crowding Function with Incremental increases (from Sydney, Australia)

2.6 cf() vs 2.4

100% 2.2 CityRail car capacity = 187 persons

2 Metro

CityRail 1.8

100% Metro car 1.6 capacity = 213 persons Crowding Crowding Factor

80% CityRail car 1.4 seated capacity = 84 persons

1.2 100% Metro seated capacity = 50 persons

1 100% CityRail car seated capacity = 105 persons

0.8 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 Passengers in car vs Source: PB

Moscow 2013 Americas London Underground Crowding Functions

Crowding Curves by vehicle Type (LU) cf() vs 4.5 BK_curr BK_futu_v1 4 CN_curr 3.5 VT_curr VT_futu_v1 3 WC_curr 2.5 MP_curr

2 MP_futu_v1 Cst_curr

CrowdingFactor 1.5 SubS_futv1 1 Dst_curr EL_curr 0.5 JB_curr 0 North_curr -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 PC_curr Load Factor vs/ c s Railplan Source: TfL

Moscow 2013 Convergence Measures

The difference between the total travel time + total waiting time less the total travel time on shortest strategies is referred to as the GAP of the solution. A perfect equilibrium solution has a GAP=0. A well accepted stopping criterion is the Relative GAP RGAP= GAP/ total travel time + total waiting time Another stopping criterion is the Normalized GAP NGAP = GAP/Total demand

Moscow 2013 Convergence report

Moscow 2013 An Application for London

An example of a large congested transit application is the RAILPLAN model used by TfL.

The Network size is: 13 modes 269 transit vehicle types 4004 zones 2069 transit lines 89651 regular nodes 202020 transit line segments 267058 directional links

Moscow 2013 The RAILPLAN Network

Moscow 2013 London Underground Crowding Functions

Crowding Curves by vehicle Type (LU)

4.5 BK_curr BK_futu_v1 4 CN_curr 3.5 VT_curr VT_futu_v1 3 WC_curr 2.5 MP_curr

2 MP_futu_v1 Cst_curr

CrowdingFactor 1.5 SubS_futv1 1 Dst_curr EL_curr 0.5 JB_curr 0 North_curr -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 PC_curr Load Factor Railplan

Source: TfL Moscow 2013 National Rail Crowding Functions

2c150 4c158e Crowding Curves by vehicle Type (NR) 2c165 3c165 6c313 4 3c313 4c315 8c315 4c317 3.5 8c317-6WNn 8c317-1WNn 4c319 3 8c319 12c321 4c321 8c321 2.5 8c332 8c357 8c365 2 4c455-SOn 8c455-SOn 2c456 8c460 Crowding Factor Crowding 1.5 8c465-CXn 2c466 6cNET 1 3c508 4c4552c456 8cHST 8cHST 0.5 9c225 11c-MK2-AR 9c390 0 8c-MK2-VT 3c165+10% -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 6c375n 4c375n Load Factor 4c376n 8c377n 12c377n 8c442n Source: TfL 8c444n 2c450n Moscow 2013 4c450n 6c450n 4c450d_n 4c455n 8c455n 8c455_n 4c456n 6c456n 8c465n 12c465n 6c159n 8c375e 6c171e 3c171e 4c165e 4c377e Railplan Central London Underground Lines

Moscow 2013 Count Locations

Moscow 2013 Execution times

The RAILPLAN model requires about 3-5 minutes per iteration and a relative gap of 10^-3 is reached in 15-20 iterations; A multi-threaded version of the transit assignment reduces the computational time considerably; The model is being applied and validated against counts; and then the O-D matrix was adjusted to fit the counts.

Moscow 2013 Current performance

Moscow 2013 Multithreaded performance

Railplan congested transit assignment For relative gap of ~10-3 ~17 iterations Emme Emme 4.1 4.0.8 1 thread 2 threads 4 threads 12 threads 45 min 53 min 32 min 23 min 18 min

 Jolokia  Intel Core i7-3930K 3.20GHz  6 Core (12 threads)  4x4GB = 16GB RAM  Seagate HDD 7200 RPM

Moscow 2013 Multithreaded speedup

Moscow 2013 Assignment of Initial Matrix

Moscow 2013 Assignment of Adjusted Matrix

Moscow 2013 Contents of presentation

. Motivation . Congestion aboard the vehicles . Congestion outside the vehicles . Some large scale applications . Conclusions

Moscow 2013 Adding Congestion Outside the Vehicle

– Models ‘discomfort’ function as vehicles become congested – Also adjusts waiting time at stops when passengers cannot board – Affects impedances • In-vehicle time • Waiting times at stops – Convergent iterative procedures

Moscow 2013 Effective Frequency

There is a need to model the limited capacity of the transit lines and the increased waiting times as the flows reach the capacity of the vehicle.

As the transit segments become congested, the comfort level decreases and the waiting times increase.

The mechanism used to model the increased waiting times is that of “effective frequency”.

Moscow 2013 Effective Headway Calculation (Line & Stop Specific) Board

Net Capacity= Stop Volume Stop Total capacity- Volume + Alight

Alight Eff.Hdwy Factor

0 1 Board/Net Cap

Moscow 2013 Effective Frequency of a Transit Line Segment

The “effective frequency” of a line is defined as the frequency which is perceived by the transit traveler and may be less than the nominal line frequency;

The waiting time at a stop may be modeled by using steady state queuing formulae, which take into account the residual vehicle capacity, the alightings and the boardings at stops.

Moscow 2013 A Continuous Headway Factor Function

Moscow 2013 Transit Activity - Overcrowded Transit Activity - Capacitated Convergence: Relative Gap

CAPTRAS Convergence Curve (relative gap)

50 45 40 35 30 25 20 relative gap 15 10 5 0 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 iteration

Moscow 2013 Convergence::Maximum v/c Ratio

CAPTRAS Convergence max. segment v/c

1.8

1.6

1.4

1.2

0.8

max. v/c ratio 0.6

0.4

0.2

0 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 iteration

Moscow 2013 Overcrowded Transit

Moscow 2013 Capacity-constrained Transit

Moscow 2013 Transit Travel Times

Capacitated

Overcrowded

Moscow 2013 Transit Travel Times

Trips Overcrowded

Capacitated

Moscow 2013 Line 27 ae – Initial Flows

Moscow 2013 Line 27 ae – Equilibrated Flows

Moscow 2013 Mexico City

Sistema de Transporte Colectivo (STC) 4.1M passengers/day 2nd largest in N America 8th in world fare increased in 2010 to MXN 3.00 (USD 0.25) Emme Capacitated transit assignment Ana Fernández Olivares Héctor Juárez Valencia Elsa P. Omaña Pulido

Moscow 2013 Mexico City

Sistema de Transporte Colectivo (STC) 4.1M passengers/day 2nd largest in N America 8th in world fare increased in 2010 to MXN 3.00 (USD 0.25)

Line A, La Paz to Pantitlán