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 [email protected]
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