A Game Theoretic Approach for Managing Multi-Modal Urban Mobility Systems Christos Nikolaou Marina...
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A Game Theoretic Approach for Managing Multi-Modal Urban Mobility Systems Christos Nikolaou Marina Bitsaki Alina Psycharaki George Koutras Transformation
A Game Theoretic Approach for Managing Multi-Modal Urban
Mobility Systems Christos Nikolaou Marina Bitsaki Alina Psycharaki
George Koutras Transformation Services Lab Computer Science
Department University of Crete 13/01/2015nikolau @ tsl.gr1
Slide 2
Table of Contents Collective Adaptive Systems The ALLOW
ENSEMBLES project The Strategic Ensemble Concept The FlexiBus
Scenario Game Theory: Non-cooperative and cooperative games Future
Work - Publications 13/01/2015nikolau @ tsl.gr2
Slide 3
Collective Adaptive Systems (CAS) Collective adaptive systems
consist of many autonomous units that interact in a variety of ways
over multiple scales,
https://www.elec.york.ac.uk/research/intSys/cas.html
https://www.elec.york.ac.uk/research/intSys/cas.html Concept
similar to: complex adaptive systems, cyber-physical systems,
service systems. Autonomous units could be (cyber and/or physical)
systems and/or humans. The Internet of Things (IoT) helps their
proliferation. Collections of autonomous units (networks,
hierarchies) are formed, often with competing interests (for
example for use of resources, of services, etc.). Various concerns
(for example smarter energy use, empowering the patient to improve
quality of life, environmentally friendly easy-to-use urban
mobility) could be addressed if: autonomous units (systems and/or
humans) of CAS learn to cooperate and/or compete, negotiate,
develop strategies to achieve goals. 13/01/2015nikolau @
tsl.gr3
Slide 4
Examples of Collective Adaptive Systems 13/01/2015nikolau @
tsl.gr4 Smart Grid Smart Urban Mobility Smart Health Services
Table of Contents Collective Adaptive Systems The ALLOW
ENSEMBLES project The Strategic Ensemble Concept The FlexiBus
Scenario Game Theory: Non-cooperative and cooperative games Future
Work - Publications 13/01/2015nikolau @ tsl.gr6
Slide 7
The ALLOW ENSEMBLES project (Funded by FET Proactive, 7FP, EC)
http://www.allow-ensembles.eu/ 13/01/2015nikolau @ tsl.gr7 Allow
Ensembles develops new models, theories and algorithms that can:
Autonomously form large-scale collective adaptive units (ensembles)
that can flexibly satisfy arbitrary goals in the real world
environments. Improve the utility of ensembles by adapting the
individual cells within an ensemble such that the overall system
learns to get better at accomplishing goals. Make ensembles robust
Evolve ensembles in order to promote beneficial emergent properties
and suppress detrimental emergent properties. Make ensembles secure
and protect sensitive data by evolving security policies in unison
with ensemble evolution.
Slide 8
Basic Concepts - Cells Cell : a unique identifiable building
block representing a concrete functionality in a larger,
multicellular system. Implementing the functionality may involve
interacting with other cells through predefined protocols. Each
cell is therefore defined in terms of its protocol (exposed process
fragments) and behavior (flow). Cells can be created either by
instantiating cell archetypes 1, or by other cells through the
process of differentiation. (from Terminology, Internal Document,
ALLOW ENSEMBLES consortium). 13/01/2015nikolau @ tsl.gr8
Basic Concepts - Entities Entity: a physical or virtual
organizational unit aggregating a set of cells. Cells can either be
unique in an entity, or they can be replicated by the entity by
instantiating the cell archetype as many times as necessary.
However, each cell belongs to exactly one entity. Each entity has a
context in which it operates, which is accessible by its cells.
Furthermore, an entity has a set of goals that it attempts to
fulfill by initiating or participating in one or more ensembles.
Entity Examples: Bus Driver, Passenger, Route Manager and FlexiBus
Manager. (from Terminology, Internal Document, ALLOW ENSEMBLES
consortium). 13/01/2015nikolau @ tsl.gr10
Slide 11
Basic Concepts - Ensembles Ensemble: a set of cells from
different entities collaborating with each other to fulfill some of
the goals of the entities. Each ensemble is initiated and
terminated by an entity, but more than one entities are expected
and allowed to join and leave through the ensembles lifetime.
Ensemble Example: The Bus Driver, Route Manager and the various
Passenger entities are participating in one Route ensemble (from
Terminology, Internal Document, ALLOW ENSEMBLES consortium).
13/01/2015nikolau @ tsl.gr11
Slide 12
12 Conceptual Integration of the Project
Slide 13
Entities Interactions Entities interact in order to achieve
Individual objectives Group objectives Interactions may: Help
entities make decisions to achieve goals (gather info, learn,
negotiate, optimize, participate in games, form coaltions, etc.)
Implement decisions made by entities (make payments, step in a bus,
schedule a bus, etc.) Interactions result in the creation of
(execution) ensembles in order to fulfill specific goals initiated
by the entities Strategic ensembles in order to handle decision
making and increase entities satisfaction expressed in utility
terms 13/01/2015nikolau @ tsl.gr13
Slide 14
Table of Contents Collective Adaptive Systems The ALLOW
ENSEMBLES project The Strategic Ensemble Concept The FlexiBus
Scenario Game Theory: Non-cooperative and cooperative games Future
Work - Publications 13/01/2015nikolau @ tsl.gr14
Slide 15
The Strategic Ensembles Model A strategic ensemble model uses
the entities utility-cells It is created before the execution
ensemble It runs in parallel to the execution ensemble It affects
the operations of the execution ensemble The objectives of a
strategic ensemble include the following Impose constraints
according to entity goals and preferences in order to reduce the
various choices of entities Assign utility to each entity when
participating in an ensemble in order to make the optimal choice
Manage the negotiation among entities 13/01/2015nikolau @
tsl.gr15
Slide 16
Utility-cells Represent utility and game theoretic
characteristics of entities The utility-cell of an entity has the
following functionalities calculates the utility of an entity when
participating in a given ensemble communicates with other cells and
makes decisions/computes strategies of the entity collects data
from measurements (resource consumption, satisfaction, costs,
delays, prices, ) and passes them to the Evo(lutionary) Knowledge
Data Base Consults EvoKnowledge (learns) about utility function
parameters, external conditions (for example changes in traffic
patterns, special events in city, etc.). runs optimization
algorithms to maximize entities utility or improve the performance
of ensembles 13/01/2015nikolau @ tsl.gr16
Prior Art An efficient transportation system utilizes mass
transit alternatives to the automobile in order to reduce
congestion and support ecological solutions. Travelers make
decisions based on timing, cost, comfort, safety and mode of trips,
while planners face policy questions such as frequency of routes,
itineraries, size, cost, environmental impact, etc. (Lam, Small,
2001): a method to value travel time and its reliability. People
had to choose between two parallel routes, one free but congested
and the other with time-varying tolls by maximizing a utility
function (a function of travel time, variability in travel time,
cost, characteristics such as time-of-day and car occupancy, and a
random component). (Johansson et al., 2003): the labor market
commuter behavior is analyzed taking into account the observation
that the willingness of an individual to commute is different for
short, medium and long time distances. 13/01/2015nikolau @
tsl.gr20
Slide 21
Prior Art (cont.) (Li, Huang, 2005): reliability of morning
commuting in congested and uncertain transport networks Other
studies analyze the interactions between commuters and planners or
transport managers and examine how commuters choose their optimal
routes and trip modes using non-cooperative games. (Sun, Gao,
2007): a non-cooperative, perfect information, static game to
describe how travelers adjust their route choices and trip modes.
(Anas, Berliant, 2010): the authors consider a commuting network
consisting of a finite set of nodes at which the commuters live or
to which they commute or through which they commute and a finite
set of transport links between the nodes (there exists only one
mode of transportation). A non-cooperative game is formulated
consisting of a set of commuters who compete for routes. In our
work, we investigate a dual problem facing both the commuters and
the transportation authority; the commuters choose their trip mode,
while at the same time the transportation company that provides a
bus for example, makes decisions on accepting or not travel
requests dynamically. 13/01/2015nikolau @ tsl.gr21
Slide 22
Table of Contents Collective Adaptive Systems The ALLOW
ENSEMBLES project The Strategic Ensemble Concept The FlexiBus
Scenario Game Theory: Non-cooperative and cooperative games Future
Work - Publications 13/01/2015nikolau @ tsl.gr22
Slide 23
The FlexiBus Scenario: Assumptions A route is a set of
predefined pick-up points We consider two phases in the lifecycle
of a route: The pre-booking phase: a route is going to be executed
if a certain number of requests is reached until a certain deadline
The execution phase: the route is bound to start or it has already
started The pick-up points of a route are bound to change at the
execution phase Add a pick-up point due to a new request Remove a
pick-up point after a cancellation
Slide 24
Time-line End of Route Pre-booking phase Preparation phase
Initialization Running phase Execution Ensemble Strategy Ensemble
Booking phase
Slide 25
Entitys Utility Entitys utility Utility accrued when
participating in a specific ensemble Calculated by the entity
according to Her preferences (that are publicly known) Private
information According to the entitys utility the winning route may
be different from the one resulted by the evaluation of the other
members of the ensemble (e.g. the route manager).
Slide 26
Entity Utility (Example) Consider Peter sending the request
(Destination: Piazza Duomo, arrival time: 21.30) to Urban Mobility
System with preferences Pay with credit card (desired) Non-smoking
bus (demanded) Window seat (desired) Consider the following
candidate routes Route A (at a cost of 10 Euros): non-smoking bus,
pay with credit card, window seat Route B (at a cost of 12 Euros):
non-smoking bus, pay with credit card, aisle seat Route C (at a
cost of 7 Euros): non-smoking bus, pay with credit card, aisle seat
Route A has higher value to Peter than Route B but not clear for
Route C (it depends on how Peter values money)
Slide 27
Table of Contents Collective Adaptive Systems The ALLOW
ENSEMBLES project The Strategic Ensemble Concept The FlexiBus
Scenario Game Theory: Non-cooperative and cooperative games Future
Work - Publications 13/01/2015nikolau @ tsl.gr27
Slide 28
Game theoretic models Analyze models that: show the strategic
interactions among various components my decisions affect others
decisions derive equilibria so that utility/profit is maximized
Nash equilibrium
Slide 29
Nash Equilibrium Nash equilibrium is an outcome of a game in
which each player is assumed to know the equilibrium strategies of
the other players, and no player has anything to gain by changing
only his own strategy unilaterally In a game of two players A and
B, the pair of strategies (s, g) is a Nash equilibrium if s is
optimal for A given g and g is optimal for B given s
Slide 30
Nash Equilibrium (Example) Consider two players A and B
Strategies for player A {Top, Left} Strategies for player B {Left,
Right} Nash equilibria: (Top, Left), (Bottom, Right) B A LeftRight
Top2,10,0 Bottom0,01,2
Slide 31
Non-cooperative Games Static games all players' decisions are
made simultaneously players receive payoffs that depend on the
actions just chosen Dynamic games each player can consider his plan
of action not only at the beginning of the game but also whenever
he has to make a decision perfect/imperfect information At each
move the player with the move knows the full history of the play
thus far Games of complete/incomplete information Each players
payoff function is common knowledge among all players
Slide 32
A Non-cooperative Game of Complete Information Objective: model
the interactions of entities when a new request arrives in a route
that is being executed and compute their optimal choices
(strategies) based on utilities Problem description We consider a
route to be a set of fixed pick-up points and the respective
estimated travel times between pick-up points When a new request
arrives, the various entities make decisions: route planner: accept
or reject the request (in case of accept send conditions (travel
time, cost) new passenger: accept or reject offer We formulate
these interactions as a game Are there equilibrium strategies?
Slide 33
Assumptions All passengers have the same destination Current
passengers do not negotiate for the new conditions (resulted by the
new passenger) of the route The route planner has to take into
account that any violation of his past commitments will affect
negatively his utility We consider a game of complete information
The route planner provides private information of current
passengers to the new passenger The utility functions of all actors
are common knowledge
Slide 34
Assumptions We consider a dynamic game Decision points: request
arrivals new strategies have to de derived each time a new request
arrives (thus a new game is formulated) All these games across the
route have to be synchronized in order to derive optimal profits
for the FlexiBus company and the passengers Each game is sequential
The new passenger makes a request The route planner calculates his
strategy (accept or reject) based on request The new passenger
calculates his strategy based on planners strategy
Slide 35
Game Formulation Set of players: current passengers (1,,n) new
passenger (np) route planner (rp) Strategy profile: (t i : travel
time) t i, i=1,n are fixed and known
Slide 36
Game Formulation Profits: Current passengers: New passenger: G:
the profit gained by alternative solution f: function that
incorporates the risk of adding future passengers Route Planner: g:
function that incorporates the risk of losing future
passengers
Slide 37
37 Set of Processes Subsystem architecture Process/Flow Engine
Utility Module Set of Processes services.tsl.gr Set of Processes
Fragments (Parts of Meta-cells) Set of Processes Fragments (Parts
of Meta-cells) Set of Processes Set of Services Design Time Run
Time
Slide 38
Entity Hierarchies Entities can form hierarchies (of entities):
For example: people and systems participate in a department entity,
which in turn may participate in a division entity, which in turn
may participate in a corporation entity. Utility of higher-level
entity could be defined as the sum of the utilities of the entities
one level below (and so on recursively), But, optimal utility of a
higher-level entity is NOT necessarily the sum of the optimal
values of the utilities of the immediate lower-level entities. a
number of interesting research questions 13/01/2015nikolau @
tsl.gr38
Slide 39
Role of utility in Evolution Utility function with incorrect
(or partially correct) parameters may result in wrong selection of
ensembles e.g., use of incorrect travel duration etc.
ExecutionExecution Context EvoKnowledge Monitor Utility Evolve
Utility function selects the proposed solution with highest utility
taking into account goal, context and user preferences (measured
utility) 1 Ensemble with high utility is executed 2 Parameters of
utility function are adjusted according to past executions and the
calculated utility and monitored utility in a given context 3
Utility Functions
Slide 40
Specialization tree Goal ... specialization Ensemble N Utility
Functions ... specialization
Slide 41
Example Goal: Reach a destination Car sharing Non-Public
Transportation Public Transportation Rent car U 1 (t,c) U 2
(t,c,r,d) t: travel time c: cost r: reliability d: walking
distance
Slide 42
Example (in Collaboration with IPVS) t: travel time c: cost r:
reliability d: walking distance Goal: Reach a destination
Non-Public Transportation Public Transportation TrainFlexibus U 1
(t,c) U 2 (t,c, r,d)
Slide 43
Cooperative Games In cooperative game theory, interest is on
outcomes of coalitions of players rather than actions of individual
players focus in cooperation games is on coalitions that will be
formed and on the sharing of value or cost incurred among members
of the coalition. Cost allocation problem in which players perform
a joint task and allocate its cost among them Why use cooperative
games Helpful tool if performance of an intelligent system and its
entities can be improved when several players cooperate Dynamic
cooperative game (??) Implementation issues: get information on
game parameters and data from EvoKnowledge (?), test game and
obtain results in ALLOW Ensembles platform, . 13/01/2015nikolau @
tsl.gr43
Slide 44
The General Idea of an Algorithm for Cooperative Games
13/01/2015nikolau @ tsl.gr44
Slide 45
Algorithm (cont.) 13/01/2015nikolau @ tsl.gr45
Slide 46
Table of Contents Collective Adaptive Systems The ALLOW
ENSEMBLES project The Strategic Ensemble Concept The FlexiBus
Scenario Game Theory: Non-cooperative and cooperative games Future
Work - Publications 13/01/2015nikolau @ tsl.gr46
Slide 47
Future Work In the case of one route Permit actions such as
adding pick-up points in order to serve new passenger requests or
removing pick-up points in case of cancelations Perform
negotiations with current passengers when a new request arrives
Consider multiple routes for one request as part of the decision
mechanism Design routes according to a decision making mechanism
that takes into account traffic demand
Slide 48
Some recent related publications A Game Theoretic Approach for
Managing Multi-Modal Urban Mobility Systems, Vasilios
Andrikopoulos, Marina Bitsaki, Antonio Bucchiarone, Santiago Gmez
Sez, Dimka Karastoyanova, Frank Leymann, Christos Nikolaou, Marco
Pistore, 2th International Conference on the Human Side of Service
Engineering Human Factors and Ergonomics, 2014/7/19, Krakw, Poland:
CRC Press/Taylor & Francis "Utility-based Decision Making in
Collective Adaptive Systems., Proceedings of the 4th International
Conference on Cloud Computing and Services Science (CLOSER14),
Andrikopoulos Vasilios, Marina Bitsaki, Santiago Gmez Sez, Dimka
Karastoyanova, Christos Nikolaou, and Alina Psycharaki. (2014).
Towards Modelling and Execution of Collective Adaptive Systems. A.
V. Andrikopoulos, A. Bucchiarone, S. Gomez Saez, D. Karastoyanova,
and C. Antares Mezzina. 9th International Workshop on Engineering
Service- Oriented Applications (WESOA 2013), In conjunction with
ICSOC 2013, December 2nd 2013, Berlin, Germany. 13/01/2015nikolau @
tsl.gr48