d.u.e. hyperpaths in congested bus networks...d.u.e. hyperpaths in congested bus networks v. trozzi...

D.U.E. HYPERPATHS IN CONGESTED BUS

NETWORKS

V. Trozzi 1, G. Gentile2, I. Kaparias3 , M. G. H. Bell4

1 CTS Imperial College London 2 DICEA Università La Sapienza Roma 3 City University of London 4 University of Sydney

Imperial College London

Università La Sapienza – Roma

City University of London

Sidney University

Travel strategies in Transit Networks

2

d

o

BUS STOP 2

BUS STOP 3

BUS STOP 1

2 1

2

1

1 3

3 4

1

3

3

4

3

Travel strategies in Transit Networks

d

o

BUS STOP 2

BUS STOP 3

BUS STOP 1

2 1

2

1

1 3

3 4

1

3

3

4

4

Travel strategies in Transit Networks with FIFO queues

d

o

BUS STOP 2

BUS STOP 3

BUS STOP 1

2 1

2

1

1 3

3 4

1

3

3

4

Queuing Arc Performance Function

κ Bottleneck Queue

model

O/D Demand

Flows

Network flow

propagation

Arc conditional

probabilities

Route Choice Model

Generalized travel times

Stop model

Non flow-dependent Arc Performance Functions

Arc flows

Transit Supply

1. Stop model

BUS STOP 1

2 1 23

2

1

Board the first “attractive line” that becomes available at the stop.

2

1

Sto

p n

ode

Lin

e n

odes

h

2

23 h’

a

a

23

3. Network flow propagation model

9

The flow propagates forward across the network, starting from the origin

node(s). When the intermediate node i is reached, the flow proceeds along

its forward star:

i

4. Arc Performance Functions

Bottleneck queue model



12

Phase 1:

Queuing

Phase 2:

Waiting

Phase 1:

Waiting

Phase 2:

Queuing



13

Dynamic Bottleneck Queue Model

a

QAa

tQAa(ta(τ))

ta(τ)

τ

tQAa(ta(τ)) ?

Effect of congestion in a small network

1

2 3

d


tt1 = 7’

φ1 = 1/6’

K1 = 50 pax

tt1 = 6’

φ1 = 1/6’

K 1= 50 pax

tt3 = 4’

φ3 = 1/15’

K3 = 50 pax

tt4 = 10’

φ4 = 1/3’

K4 = 25 pax

tt3 = 4’

φ3 = 1/15’

K3 = 50 pax

5

pax/

min

7

pax/

min

7

pax/

min

tt2 = 25’

φ2 = 1/6’

K2 = 50 pax

1

2 3

d


1

20

2 3

Effect of congestion (Stop3)

1

2 3

d


Upstream flow reaches stop 3,

no capacity is available on Line 3

κ increases

p changes accordingly

1

2 3

d

07:30




κ increases


1

2 3

d

07:30 → 07:55


1

2 3

d


Upstream flow reaches stop ,

available capacity decreases for Line 1

κ increases


1

2 3

d

07:30 → 07:50


By the time they reach stop 3, they

would encounter congestion

Line 1 is cut out of the choice set

1

2 3

d

08:10 ← 08:20


1

2 3

d




κ increases


1

2 3

d

08:00 ← 08:20

Stop 1

Stop 2

Stop 3

Stop 1

Stop 2

Stop 3

Conclusions (1): the model

The model clearly demonstrates the effects on route choice when congestion

arises (also in a small network)

From a passenger perspective, choosing a shortest hyperpath in case of

congestion may significantly decrease the total travel time (also in a small

network)

Simplified approach that allows for calculating congestion in a closed form (κ)

Congestion is considered in the form of passengers FIFO queues

Conclusions (2): the network

Applications on this network clearly demonstrates the effects on route choice

when congestion arises

Changes in the strategies (in terms for choice set and transfer point are

detected.

It could also allow comparison regular vs irregular services

Open questions:

1. Change of the origin stop – more detailed representation of the network

including centroid/zones

2. «Strategic alighting decisions» cannot be onsidered here – more complex

transfer point are needed

D.U.E. HYPERPATHS IN CONGESTED BUS NETWORKS

Thank you for your attention

[email protected]

30


1 20

2 3


κ > 1

20

1

2 3

Hypergraph vs Graph

Line 001

Line 001

Line 003

Line 004

Line 003

Line 002

1

17

18 19

20

16

2 3

4

22

21

23

24 25

26

6 7 9

10

11

12

13

14

15

5

8

d.u.e. hyperpaths in congested bus networks...d.u.e. hyperpaths in congested bus networks v. trozzi...

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