1 QHM The Quantitative Hierarchical Model A Systems Engineer's Contribution to Network...

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QHM The Quantitative Hierarchical

Model

A Systems Engineer's Contribution to

Network Management

with application to

Coordinated Ramp MeteringJos Vrancken, Min Zhi

Fac. TPM, Systems Engineering SectionDelft University of Technologyj.l.m.vrancken@tudelft.nl

Transport Thursday, 16 October 2014

Acknowledgements• QHM: Developed in the European FP7 Con4Coord project

• Cooperation with Jan van Schuppen and Yubin Wang• Cooperation with the Trinité Automation B.V. company in

Uithoorn, The Netherlands• partially implemented in SCM (Scenario Coordination

Module) in the Amsterdam area, operational since September 2010

• basis for the development of the DVM-Exchange interface standard for traffic control systems

• Application to Coordinated Ramp Metering: Min Zhi’s graduation project, with assistance of Amir Meshkat.

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Overview

• Systems Engineering Concepts• QHM:• Hierarchical Network Partitioning• Hierarchical Control Synthesis

• Examples: • Coordinated Ramp Metering• The Coentunnel area• ...

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What is the problem of Network Management?

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Scaling up! While keeping complexity manageable

We need scalable notions to express traffic management

Systems EngineeringBuilding and managing big systems,put together from components

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Systems Engineering (SE) Concepts

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environment

• Environment

• Boundary (=

interface between

inside and outside

of system)

• Recursion

Complexity shielding by the boundary in both directions

How to reduce complexity?

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State space is, in principle, the product of the two child state spaces,=> exponentially growing complexity

1. Abstraction to boundary behavior2. Boundary agreement (with parent) for a larger time scale than the time scale of internal management => decoupling of internal management=> Linear complexity!

A system T ("parent")with two subsystems A and B ("children")

A B

T

This fits very well with road networks

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• Systems are networks (= subnetworks of the total network)• A network boundary is a finite set of points (entries and exits)• Internal traffic behavior can be abstracted to boundary

behavior

Still too big? Split it up further...

Splitting up networks

One level =>too many subnetworks or subnetworks still too big=> not scalable

=>A recursive splitup is scalable

Recursive Split Up of a Network• Tree-structured, recursive

decomposition of a network

into non-overlapping areas

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and nodes

A network is a network of networks

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NL D

L

F

BUK

Each edge represents a set of boundary points

Requirements for Network Splitups

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1. Boundary points at quiet places2. Networks shall be closed under "shortest route"3. Adjacent networks shall differ in child priority (see

below)4. Number of boundary points must be kept limited5. ...

Finding effective splitups in an automated way is the hardest problem of Network Management

Behavior of traffic in points

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Boundary agreements apply to traffic in boundary points:

• Speed, flow, density• Partial flows for different

destinations• Travel times for entry-exit

pairs

• Per vehicle:• Type of vehicle: person car, truck,

bus, motorcycle,...• Type of traffic: private, public

transport, ...• Destination, intended route• Type of cargo (f.i. hazardous)

Groups of Boundary Points

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Bigger network => more boundary points =>

loss of scalability

Solution: grouping of boundary points

For a group of points:• group flow is the sum of point flows• same for destination specific flows• route via group means route via one of

its points• travel time to group becomes a

minimum travel time and maximum travel time

• speed in group: minimum speed and maximum speed

Recursive buildup of Network Management

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Recursive definition in general: • property P holds at lowest

level • P(A) & P(B) => P(A+B)

For instance: guaranteed travel time

Assumption on Sensors and Actuators

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All Sensors and Actuators we need are assumed present

Why?

In this way, one can answer the question which sensors and actuators are really needed.

Needed sensors and actuators can often be installed

Cooperative systems make this assumption more and more realistic.

The general network

Types of traffic

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For a general network:

• Outside – outside (oo)• Outside – inside (oi)• Inside – outside (io)• Inside – inside (ii)

For the time being, we focus on OO-traffic (transit traffic)

The lowest level 1: The Segment

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baTraffic control objectives: (depending on policy)

- process demand as much as posssible but avoid overloading

- find a balance between high throughput and short travel time - make travel time predictable (or predictable upper bound)

- smoothing traffic flow

Measures:- Gating: allow in at a as much as goes out at b (on

average)- Set maximum speed- Supply information about expected travel time

Boundary agreements: the guaranteed travel time

The lowest level 2: The Choice Point

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ba

c

Traffic control objectives: (depending on policy)- those for the segment + - facilitate rerouting

Measures:- those for the segment + - Gating: set maximum partial flow at a, per exit- Supply information about expected travel times a-b and

a-c

Boundary agreements: the guaranteed travel times a-b and a-c

The lowest level 3: The Merge Point

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b

ac

Traffic control objectives: (depending on policy)- those for the segment

Measures:- those for the segment + - Gating: set maximum flow at a and at b- Supply information about expected travel times

Boundary agreements: flow priorities x,y at a and b, with x+y = 1

Flow Priorities for a general network

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Flow Priority matrix: a

b

c

d

pac pad

pbc pbd

• pij are percentages of maximal flows allowed

• pij x sj is the maximal flow at entry i to exit j (sj is the outflow at j)

• Rows correspond to entry points• Columns correspond to exit points

1

0

i

ij

ij

p

p

Travel Times for a general network

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Travel Time Matrix: a

b

c

d

tac tad

tbc tbd

• Applies to realized, expected, guaranteed travel times

From A and B to A+B

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Key problem: recursive

consistency at multi-border points

Boundary agreements expressed in:• speed• flow priorities• guaranteed travel times

• type of traffic (Public Transport, trucks, hazardous goods)

• any other point property of traffic

Recursive consistency of flow priorities

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T

AB

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3

Recursive consistency ofGuaranteed Travel Times

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= +

p q

How to do Network Management?

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Three components in traffic:- regular, expected traffic demand

pattern ("scenario")- unpredictable deviations from this

pattern- exceptional events (accidents, ...)

How to do Network Management?

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Expected demand => Network configuration(half-hour to hours, but function of

time)

Unpredictable variations => Multi-agent control

(seconds to minutes)

Exceptional events => Network reconfiguration

(half-hour to hours, function of time)

Network configuration

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Traffic policy + expected demand

=>

Network configuration=

1. Recursive Network Partitioning2. Consistent Boundary agreements

- flow priorities- guaranteed travel times- child priorities (see

below...)- possibly other agreements

(speed, trucks, ...)

configuration buildup is iterative process up and down the tree

Multi-Agent Control, 1

Deviations => Multi-Agent Control

At time scale of seconds to minutes: max flows, max speeds settings on

boundaries

Peer-to-peer requests, governed by network config

Multi-Agent Control, 2

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baU D

S

If supply at b drops, S sends request to U to lower inflow at a

U sends corresponding requests to its upstream neighbors

Local traffic problem results in a chain reaction of requests

Multi-Agent Control, 3

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At multiborder point:- two stacks of nested areas- one lowest common parent P- one highest child of P on both sides: A

and B

Requests go from segment s to segment t, while parents are informed and they update their max flow settings as well with max flow requests

P

A Bst

Multi-agent Control, 4

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Danger of cyclic request storms:=> acyclic priority graph for the children of P

Restrictive requests are mandatory from high to low child priority areas

=> traffic is pushed back to low priority areas (residential areas, parking lots, ...)

Various mechanisms to keep number of requests limited

P

A B

Example: Coordinated Ramp Metering

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A B C

D E F

TS U

34Application of the Quantitative Hierarchical Model to Coordinated Ramp Metering

Research question• Main question:

• Will the Quantitative Hierarchical Model be feasible for Coordinated Ramp Metering?

• Sub-questions:• 1. What are useful traffic performance measures for the target

control area?

• 2. What are effective algorithms for traffic control for the motorway and

on-ramps, given the chosen performance measures?

• 3. Can the gating principle can be implemented with the proposed

algorithm?

• 4. Can the fairness principle can be implemented and how well is this

maintained?

Introduction Model Design Experiments Discussion Conclusion & Recommendation

35Application of the Quantitative Hierarchical Model to Coordinated Ramp Metering

Research method

• VISSIM• VISSIM COM• VISSIM and Matlab

VISSIM Matlab 

VISSIM COM

Data collection

Control algorithm

Introduction Model Design Experiments Discussion Conclusion & Recommendation

Interfacing of VISSIM and Matalb

36Application of the Quantitative Hierarchical Model to Coordinated Ramp Metering

Conceptual model• Assumptions

• traffic signals• input

• System goal• Achieve allowed outflow• Priority distribution• Internal performance

Part of a motorway with three on-ramps

Introduction Model Design Experiments Discussion Conclusion & Recommendation

37Application of the Quantitative Hierarchical Model to Coordinated Ramp Metering

Experiments design

• KPIs• Actual outflow• Priority conformance• Merge area speed

• Scenarios

Introduction Model Design Experiments Discussion Conclusion & Recommendation

Scenario Priority matrix /T I_out (veh/h)0 NA NA

1 [0.35,0.35,0.1,0.1,0.1] [1500,2000,2500,3000,4000,2500]

2 [0.25,0.25,0.1,0.15,0.25] [1500,2000,2500,3000,4000,2500]

3 [0.25,0.25,0.15,0.1,0.25] [1500,3000,2500,4000,1500,4000]

Table 1: Different scenarios configuration

38Application of the Quantitative Hierarchical Model to Coordinated Ramp Metering

Simulation results

Outflow of the motorway and three onramps

• Boundary performance• Actual outflow vs. allowed outflow

• Warmup period

• Capacity restriction

• Priority conformance

Introduction Model Design Experiments Discussion Conclusion & Recommendation

500 1000 15000

500

1000

1500

2000

2500

3000

time (s)

flo

w (

veh

/h/lan

e)

Scenario 1-flow

desired outflow

real outflow

on-ramp 1

on-ramp 2

on-ramp 3

500 1000 15000

500

1000

1500

2000

2500

3000

time (s)

flo

w (

veh

/h/lan

e)

Scenario 2-flow

desired outflow

real outflow

on-ramp 1

on-ramp 2

on-ramp 3

500 1000 15000

500

1000

1500

2000

2500

3000

time (s)

flo

w (

veh

/h/lan

e)

Scenario 3-flow

desired outflow

real outflow

on-ramp 1

on-ramp 2

on-ramp 3

39Application of the Quantitative Hierarchical Model to Coordinated Ramp Metering

Simulation results

Speed at the three merge areas

• Internal performance• Above 40 km/h

• The difference between the three onramps

Introduction Model Design Experiments Discussion Conclusion & Recommendation

0 1000 20000

20

40

60

80

100

120

time (s)

sp

ee

d (

km

/h)

Scenario 1-speed

merge area 1

merge area 2

merge area 3

0 1000 20000

20

40

60

80

100

120

time (s)

sp

ee

d (

km

/h)

Scenario 2-speed

merge area 1

merge area 2

merge area 3

0 1000 20000

20

40

60

80

100

120

time (s)

sp

ee

d (

km

/h)

Scenario 3-speed

merge area 1

merge area 2

merge area 3

Coentunnel Area

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Main roads (motorway + urban) are all kept fluid,by also limiting theflow on the motorway

Summary and Conclusions

• QHM is an approach to Network Management, very similar to the governance of a country: Hierarchical Control

• Key SE notions: scalability, recursion, boundary agreements• A recursive splitup of networks is scalable• Scalable Network Management can be built up recursively• Scenarios result in network configurations• Network configuration: recursive splitup, flow priorities, child

priorities, guaranteed travel times, ...• Deviations from the scenario can be handled by Multi-Agent

Control• Accidents can be handled by network reconfiguration• CRM with priorities becomes a relatively easy problem

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Future Research

• Automate Network Partitioning• Automate the computation of Network Configurations• Testing QHM in gradually increasing sample networks• Scalable traffic simulation in a network of networks• Testing the emergent effects of the Multi-Agent Control• Priorities for Public Transport• Organizing Evacuations• Transitions after network reconfigurations• Mathematical framework for Network Management• Route Choice, Traffic Spreading, Rerouting in a network with

guaranteed travel times• ...

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Request: Mathematical Description of NM

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Every aspect of NM can (we hope) be expressed in this picture.

Does it allow a mathematical description of NM?

Help is welcome with this problem!

Thanks for listening and for your comments and questions!

Route Choice and Traffic Spreading

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• Operator: collective optimum (throughput + travel times)

• Driver: individual optimum within current traffic state

• Problem: route choice depends on traffic state and traffic state depends on all the route

choices• QHM: 1. guaranteed travel times

2. speed measures to improve traffic spreading