P Systems for Passenger Flow Simulation

P Systems for Passenger Flow Simulation

Zbynek Janoska

Department of Geoinformatics, Palacky University in Olomouc

October 30, 2012

P Systems for Passenger Flow Simulation

Introduction

P systems – Introduction

◮ Computational model from the family of natural computing

◮ Inspired by the living cell

◮ its structure

◮ its functionality

◮ Gheorghe Paun (1998) - Computing with membranes

◮ Research concerned with computational power, not biological

modelling

◮ No application to spatial phenomena (so far)

P Systems for Passenger Flow Simulation

Introduction

P systems – Introduction

Main components of P systems◮ membrane structure

◮ objects

◮ rules

Basic features

◮ maximal paralelism

◮ non-determinism

P Systems for Passenger Flow Simulation

Introduction

P systems – Introduction

Step 1◮ environment – #

◮ membrane 1 – #

◮ membrane 2 – #

◮ membrane 3 – ac

◮ a → ab

◮ a → bδ

◮ c → cc

ac → abcc

P Systems for Passenger Flow Simulation

Introduction

P systems – Introduction

Step 2◮ environment – #

◮ membrane 1 – #

◮ membrane 2 – #

◮ membrane 3 – abcc

◮ a → ab

◮ a → bδ

◮ c → cc

abcc → bbccccδ

P Systems for Passenger Flow Simulation

Introduction

P systems – Introduction

Step 3◮ environment – #

◮ membrane 1 – #

◮ membrane 2 – bbcccc

◮ b → d

◮ d → de

◮ (cc → c) > (c → δ)

bbcccc → ddcc

◮ membrane 3 – dissolved

P Systems for Passenger Flow Simulation

Introduction

P systems – Introduction

Step 4◮ environment – #

◮ membrane 1 – #

◮ membrane 2 – ddcc

◮ b → d

◮ d → de

◮ (cc → c) > (c → δ)

ddcc → ddcee

◮ membrane 3 – dissolved

P Systems for Passenger Flow Simulation

Introduction

P systems – Introduction

Step 5◮ environment – #

◮ membrane 1 – #

◮ membrane 2 – ddcee

◮ b → d

◮ d → de

◮ (cc → c)4 > (c → δ)

ddcee → ddeeeeδ

◮ membrane 3 – dissolved

P Systems for Passenger Flow Simulation

Introduction

P systems – Introduction

Step 6◮ environment – #

◮ membrane 1 – ddeeee

◮ e → eOUT

[ddeeee]1 → [dd]1 [eeee]ENV

◮ membrane 2 – dissolved

◮ membrane 3 – dissolved

P Systems for Passenger Flow Simulation

Introduction

P systems – Introduction

Final configuration

[dd]1 [eeee]ENV

Calculation succesfull – no other rule

can be applied

P Systems for Passenger Flow Simulation

Transportation modelling

Transportation modelling

Three levels of traffic flow models (Hoogendoorn & Bovy, 2001)

◮ microsimulation

◮ mesosimulation

◮ macrosimulation

Public transportation models – meso-models – detailed passenger

flow simulation, vehicle modelling omitted (Peeta &

Ziliaskopoulos, 2001)

P Systems for Passenger Flow Simulation

Proposed model

Informal description

◮ tram stops – membranes

◮ road network – graph

topology

◮ trams – membranes

◮ passengers – objects

◮ behaviour – rules

◮ passengers getting on

and off the tram

◮ tram moving between

stops

◮ passenger decisions

P Systems for Passenger Flow Simulation

Proposed model

Formal description

Rules describing passengers getting on and off the tram

◮ [tram empty ]−tram people → [tram people ]−tram

◮ [tram people ]−tramp1≤1−−−→ [tram empty ]−tram peopleOUT

◮ [tram people ]−tramp2≤1−−−→ [tram people ]−tram

P Systems for Passenger Flow Simulation

Proposed model

Formal description

Rules describing movement of the trams

◮ [i [tram ]+tram@j ]it≥1−−→ [j [tram ]−tram ]j

◮ [i [tram ]−tram ]i → [i [tram ]+tram ]i

P Systems for Passenger Flow Simulation

Proposed model

Formal description

Rules describing passenger arrival and departure from tram stops

◮ [i ]i → [i people ∗ N ]i

◮ [i peopleOUT ]i → [i ]i

P Systems for Passenger Flow Simulation

Proposed model

Parameters of the model

◮ topology of the network

◮ number of vehicles, their schedule

◮ capacity of vehicles

◮ number of passengers using the system

◮ probabilities of passengers getting off the tram

P Systems for Passenger Flow Simulation

Experimental results

Model 1

Experimental results - model 1

◮ topology of the network – circular

◮ number of vehicles, their schedule – 3

trams, 5 mins between stops

◮ capacity of vehicles - 55 passengers

◮ number of passengers using the

system – Poisson dist. with λ = 3

◮ probabilities of passengers getting off

the tram – 0.50, 0.55, 0.60

P Systems for Passenger Flow Simulation

Experimental results

Model 1

Experimental results – probability 0.50

0 200 400 600 800 1000

050

100

150

200

250

passengers waiting at the stop

time units

pass

enge

rs

P Systems for Passenger Flow Simulation

Experimental results

Model 1

Experimental results – probability 0.50

0 200 400 600 800 1000

010

2030

4050

empty spaces in tram

time units

empt

y sp

aces

P Systems for Passenger Flow Simulation

Experimental results

Model 1

Experimental results – probability 0.55

0 200 400 600 800 1000

020

4060

80

passengers waiting at the stop

time units

pass

enge

rs

P Systems for Passenger Flow Simulation

Experimental results

Model 1

Experimental results – probability 0.55

0 200 400 600 800 1000

010

2030

4050

empty spaces in tram

time units

empt

y sp

aces

P Systems for Passenger Flow Simulation

Experimental results

Model 1

Experimental results – probability 0.60

0 200 400 600 800 1000

010

2030

4050

passengers waiting at the stop

time units

pass

enge

rs

P Systems for Passenger Flow Simulation

Experimental results

Model 1

Experimental results – probability 0.60

0 200 400 600 800 1000

010

2030

4050

empty spaces in tram

time units

empt

y sp

aces

P Systems for Passenger Flow Simulation

Experimental results

Model 2

Experimental results - model 2

◮ topology of the network – line

◮ number of vehicles, their schedule – 2

trams, 5 mins between stops

◮ capacity of vehicles - 55 passengers

◮ number of passengers using the

system – Poisson dist. with λ = 3

◮ probability of passengers getting off

the tram – 0.95

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P Systems for Passenger Flow Simulation

Experimental results

Model 2

Experimental results – stop 1

0 200 400 600 800 1000

020

040

060

080

010

0012

00

passengers waiting at the stop

time units

pass

enge

rs

P Systems for Passenger Flow Simulation

Experimental results

Model 2

Experimental results – stop 2

0 200 400 600 800 1000

020

4060

80

passengers waiting at the stop

time units

pass

enge

rs

P Systems for Passenger Flow Simulation

Experimental results

Model 2

Experimental results – stop 3

0 200 400 600 800 1000

010

2030

4050

6070

passengers waiting at the stop

time units

pass

enge

rs

P Systems for Passenger Flow Simulation

Experimental results

Model 2

Experimental results – empty spaces

0 200 400 600 800 1000

010

2030

4050

empty spaces in tram

time units

empt

y sp

aces

P Systems for Passenger Flow Simulation

Future work

Future and related work

Future work◮ P systems for vehicular

flow simulation

◮ Dvorsky et al, 2012 –

first ideas, XML

specification, software

◮ real data aquisition -

Breclav city

(population 25 000, 5

traffic lights)

◮ Background model for

traffic optimisation

Related work

◮ Population dynamics

modelling using P systems

◮ superior for small

populations

◮ previous research

available

◮ experimental results

proven usefull

P Systems for Passenger Flow Simulation

Conclusion

Conclusion

◮ P systems are computational models inspired by the living cell

◮ Enable hierarchical representation of modelled system,

behavior is ruled by ’chemical equations’

◮ Expressive and efficient

◮ Simple to extend existing models

P Systems for Passenger Flow Simulation

Conclusion

Conclusion

Advantages of proposed model

◮ discrete representation of

vehicles, passengers

◮ expressive

◮ easy to extend

Drawbacks of proposed model

◮ objects are not inteligent

◮ can not incorporate

representation of world by

the means of physical laws

◮ detail of the model is

limited

P Systems for Passenger Flow Simulation

Bibliography

[Dvorsky et al, 2012] J. Dvorsky, Z. Janoska & L. Vojacek.

P systems for traffic flow simulation,

Lecture Notes in Computer Science Volume 7564,, 2012.

[Hoogendoorn & Bovy, 2001] S.P. Hoogendoorn & P.H.L.

Bovy.

State-of-the-art of vehicular traffic flow modelling,

Delft University of Technology, Delft,, 2001.

[Paun, 1998] Gh. Paun.

Computing with membranes,

TUCS Report 208, Turku Center for Computer Science, 2000.

[Paun, 2004] Gh. Paun.

Introduction to membrane computing,

P Systems for Passenger Flow Simulation

Bibliography

First brainstorming Workshop on Uncertainty in Membrane

Computing, 2004.

[Peeta & Ziliaskopoulos, 2001] S. Peeta & A. Ziliaskopoulos

Foundations of dynamic traffic assignment: The past, the

present and the future,

Networks and Spatial Economics, 2001.

[P systems web page]

http://ppage.psystems.eu/