An Application of Queuing Theory to Rotary Intersection Traffic Model and Control Using Safe Petri-net for Deadlock Avoidance
|
|
- Cornelius Williamson
- 6 years ago
- Views:
Transcription
1 International Journal of Manufacturing Science and Technology 5(2) December 2011; pp Serials Publications An Application of Queuing Theory to Rotary Intersection Traffic Model and Control Using Safe Petri-net for Deadlock Avoidance Makoto KATOH * Abstract: This paper focuses on the effect of Poisson arrival at a low-capacity entrance in a rotary intersection model. The model is constructed using Mark Flow Graph which is a kind of safe Petri-net. The purpose is deadlock avoidance. The arrival interval of car was found to change the deadlock time. This paper propose an Entrance passing and Exit passing control system using a waiting agent counter at each entrance. Keywords: Petri-net, Multi-agent, Poisson Arrival, Traffic and Logistic, Deadlock, Percolation. 1. INTRODUCTION There have been many studies on traffic models such as the percolation model [1] [2], cellular automata model [3], neural net work model [4], and Petri-net model [5] [6] [7]. In particular, there have been interesting attempts to obtain new information by comparing the cellular automata and multi-agent models, or to use a hybrid Petri-net model which allows continuous values for speed of agents, and discrete values for their existence. Recently, there has been a fusion of traffic studies and logistic ones in Japan. The present authors previously developed a simple, hybrid simulator using CAD (Simulink, Mathworks Co. Ltd.), and applied it to the analysis of an abnormal diagnosis warning display system and the causes of failure diagnosis and obtained excellent results. The purpose of the present study was to enhance this simple colored logic-mfg (Mark Flow Graph [8]: Safe Petri-Net) hybrid simulator by combining multi-valued logic specifying an agent s destination type with a conventional binary logic approach to the existence of an agent. A multi-agent flow model that was allowed to join and bifurcate was then applied to a rotary intersection model. It is well known that an economic loss and an environmental destruction due to congestion is very large in all of the world and the avoidance of congestion will be useful for both problems [8]. Though he presents the following various causes of congestion of reality, the modeling of them is very difficult and the useful results will not be obtained even if it could be done. (1) Obstacles caused by road works, accidents, break down cars or illegal parker etc.. (2) Natural congestion caused by speed down before slopes, tunnels, toll gates or railroad crossings etc.. (3) Forced congestion caused by suspension of traffic for a fixed time Then, we have simulated on the congestion rate characteristics based on cellular automata like ASEP and a percolation type complex system in a scientific manner. [1] * Department of Mechanical Engineering, Osaka Institute of Technology, , Ohmiya, Asahi-ku, Osaka, Osaka-fu , Japan
2 102 / International Journal of Manufacturing Science and Technology Moreover, K. Nishinari has been studied precisely on congestion [9]. He presents some causes of congestion as follows: (1) Queuing Theory: When the average service rate of the toll gate becomes below the average arrival rate of the car, the queue is generated. The queue length is the average arrival rate of cars * average waiting time (2) Asymmetric Simple Execution Process (ASEP) Rule: All agents can advance if the cell forward is empty. (There is the same rule in MFG) (3) Matrix Products Ansatz (MPA) method in ASEP A strictly solution of ASEP. (4) ASEP with pheromone of ants As for the action that ants move in the state of the group generated naturally, similar happens to cars. (5) Stochastic Optimal Velocity Model (SOV) Assumption: Speed of a car in Optimal Velocity Model (OV) is advanced probability in ASEP. A study on the kinds, properties and judgment methods of deadlocks (stopping of mark flow) in a discrete production system described by MFG has been discussed [11] [12]. Deadlocks are caused by circular waiting due to an imbalance between the input and output. Two approaches for deadlock avoidance were proposed, which are the Input suppression method and States suppression method, and some compensation methods have also been presented [11]. The present paper focuses mainly on the effects of Poisson arrival at the entrance of the rotary intersection model proposed in the literature [1] on the occurrence of deadlock, which we define a criteria for judgment of it by becoming percolation rate as molecule of water in the rotary section to a constant. We assume the reason that cars move in the state of the group generated naturally as percolation of molecular of water not but pheromone of ants. The percolation system [13] is well known as a kind of complex systems. Then, we can introduce the critical probability which is the phenomena of the percolation system as one in general complex systems. In the next section, we will describe the specifications of the model used Basic Specifications 2. ROTARY INTERSECTION MODEL (1) In rotary boxes, the initial existence probability of a multi-agent can be set by initial marking (initially set of marks in rotary boxes). (2) In source boxes, the entry probability of multi-agents, can be set (entry probability of marks in source boxes). The color distribution of multi-agents in the entrance is uniform. The arrival distribution of multi-agents in the entrance hall is Poisson, and we refer to this situation as Poisson arrival [14]. The number of multi-agents in the entrance hall is computed from the arrival and departure rates.
3 An Application of Queuing Theory to Rotary Intersection Traffic Model and / 103 (3) In sink boxes, the exit probability of multi-agents can be set. The color distribution of multi-agents in the exit is uniform. (4) For all transitions, 3 input terminals are available, i.e., the mark input terminal, the permission/inhibition terminal and the activate/ inactivate terminal, which are connected to a common pulse signal with a fixed cycle time and a fixed split rate. This terminal is an extension of the original MFG [10] [11] [12]. Only a single output terminal exists Configuration and Assumptions A low-capacity (Transition = Box = 12) rotary intersection multi-agent flow model using a colored MFG format is configured as shown in Figure 1. Logic sets for functions such as color decoding are omitted to avoid confusion. A high-capacity (Transition = Box = 16) model was not used here because deadlock hardly occurred with such a model. The assumptions of this model are as follows. (1) There is only one lane and overtaking is prohibited. (2) Assuming a mark in box describe an agent, that is, a car. The color number (of colored mark in the colored Petri-net) of each agent mark is decoded in logic sets. The number ijk of each digit i,j,k shows 3 terms set (i,j,k) = (bifurcation position, bifurcation direction, speed). Then, a total of 999 kinds of colored multi-agent are classified by logic sets. Then, 50% of the multi-agents are initially set to travel fast on a straight lane and 50% are set to make a slow exit turn? (3) Movement from the entrance to the rotary section is executed using two competition transition on the entrance and rotary intersection for the same output box connected from the transitions, that is, if the one is fired, the other can not be fired.. All entrance signals are assumed to synchronous. (4) Bifurcation from the rotary section to the exit is executed using two competition transition on the rotary section and the exit for the same input box connected to the transition. Coordination of exit and advance competition is executed at the discretion of each agent, which is setting statistically in the simulation. No change is assumed to occur along the lane. Figure 1: Configuration of Low-capacity (Transition = Box = 12) Rotary Intersection Multi-agent Flow Model [1]
4 104 / International Journal of Manufacturing Science and Technology 3.1. Poisson Arrival and Entry Rate 3. SIMULATION AND RESULTS It is well known that many phenomena related to physics, biology and production systems are governed by Poisson distributions. Here, we assume that the number of arriving agents at the entrance hall of the rotary intersection per unit time is determined by such a Poisson distribution. Moreover, we create an algorithm to calculate the number X (t, τ) of Poisson arrivals in unit time t using a 2-D table with a probability variable x and a mean value µ as in (1). x µ µ p() x = e. (1) x! If you assign an entry pulse with color number to y(t), subtracting the number of entries Y(t) from the number of arrivals, the number waiting in the entrance hall is obtained using a digital integrator as in (2). KT Z( t,) τ = min[ {( s X,)()},max t τ Y t ] capacity z 1 d 1() when 1 y t < where Y() t = dt 0 otherwise. (2) where max-capacity in the entrance hall is assumed to 10. Non-linear feedback of Z is carried out to control the entries at a given probability based on a production rule Deadlock Generation Deadlock is defined as stopping marks or agents, then makes percolation rate to a constant. Moreover, we define a parameter referred to as the Deadlock Time (DLT) as shown in (3). d DLT = max[ ti {() t PR t 0}]. > eps > i dt This is the most significant monitoring parameter as it is changed by the Exit Control Probability (ECP) based on random arrival. The entry control probability and the initial existence probability in the rotary box are set to be the same as the independent variable ECP. This method is used to change the triple probability (Initial existence probability, Entry probability, Exit probability) similarly and concurrently. If the entry control probability is changed based on Poisson arrival, the DLT becomes 1181 s and the critical probability of ECP and the Congestion Rate (CR) become 65% as shown in Figure 2, because the entry control probability is matched to ECP only when there are more than one agents in the entrance. Here, the activation signal has a cycle time of 40 s and a split rate of 50%. Assuming Poisson arrival at all entrances of the rotary intersection, the number of arriving agents is calculated based on the mean and the variation. Subtracting the entry number from (3)
5 An Application of Queuing Theory to Rotary Intersection Traffic Model and / 105 the arrival number and integrating, we can obtain the number waiting in each entrance hall. Assuming that the Poisson arrival may not change if it attains once the maximum number in entrance hall (assumed to be 10 here), we obtain the results shown in Figure 2 for arrival intervals are 2 s and 3 s. The solid line indicates the number of agents through entrance No. 1, the broken line through entrance No. 2, the solid line through entrance No. 3, and the broken line through entrance No. 4. (a) At arrival interval 2 s (b) At arrival interval 3 s Figure 2: Number of Waiting Agents in Entrance Hall by Changing Interval of Poisson Arrival 3.3. Deadlock Avoidance There are many approaches to deadlock avoidance [11] [12]. It is well known that input flow into the system must be suppressed for deadlock avoidance [1] [12]. Here, we show that it is sensitive to the interval of Poisson arrival at the entrance hall of the rotary intersection, as seen in Figure 3. That is, a longer leads to more effective deadlock avoidance by suppression of the entry rate. Figure 3: Deadlock Avoidance Due to Entry Rate Suppression by Interval of Poisson Arrival
6 106 / International Journal of Manufacturing Science and Technology Three different areas are seen in the figure. The upper left area is a region of deadlock, the center area is deadlock-free, and the lower area is without cars Mean Waiting Time The entrance passing control system is constructed by feedback of the waiting agent number computed as the difference between the Poisson arrival agent number and the passing agent number using a non-linear entrance passing rate controller with a probability distribution to an entrance passing gate with a passing rate for colored agents only when there is at least one waiting agent, as shown in Figure 4. Figure 4: Configuration of Entrance Passing Control System There were 3 critical probability 30%(~1/3), 40%(~1/2.5), 66%(~/1/1.5), (theoretical critical probability is atom numbers/total bifurcation numbers [13]). That is, in these probabilities, there are the largest effect on the mean waiting time in entrance hall computed as shown in Figure 5. Figure 5: Computation of Mean Waiting Time for Each Agent in Entrance Hall after Simulation for 1200 s with Arrival Interval of 3 s by Changing 3 Terms Similarly
7 An Application of Queuing Theory to Rotary Intersection Traffic Model and / 107 However, adequate standard probability value of the 3 terms (Initial existence probability, Entry probability, Exit probability) may not be 40% in all entrance. Here, the mean waiting time in the entrance hall after a simulation time T, MWT(T), is computed using the mean entry time, MET(T), and the mean waiting length in entrance hall, MWL(T), as follows, where MWL(T) = Z(T, τ) where d t i = t when y() t < 1 dt where MWT ()() T *{() = MEPT 1} T MWL T + (4) KTs MEPT () T = {() /()} t t Y t z 1 T 0 i i 1 i The theoretical MWL for one gate is obtained from queuing theory, as follows. λ = mean_arrival_rate µ = mean_service_rate M/M/1 λ2 MWL = ( x 1)() p x = µ ( µ ) λ x= 0 Figure 6 shows an example of the dependence of MWL described as vertical axis for the mean service rate described as the horizontal axis when an arrival rate is and a maximum MWL is 10. (5) (6) Figure 6: MWL Dependence for Service Rate
8 108 / International Journal of Manufacturing Science and Technology We can determine from this figure that a new critical probability occurred in the left-hand side of Figure 5(b) may be caused the service rate (entry control probability) and the arrival rate in the approach. It is not due to deadlock in the rotary section which is the cause of the critical probability on the right-hand side of the figure. When deadlock occur, the actual service rate is decreases to zero. Then, the MWL in Figure 5 will exhibit a valley shape as shown in Figure 5(b). 4. CONCLUSIONS We determined that setting a long interval of Poisson arrival of multi-agents in the entrance hall of a rotary intersection is very effective for deadlock avoidance by entry rate suppression. However, the arrival interval has made not to change almost critical probability by concurrently changing the triple probabilities (Initial existence probability, Entry probability, Exit probability) in a similar manner. The longer arrival interval is also effective to keep the deadlock time larger in the periods. Moreover, it can be increasing the time that it takes to fill the entrance and reducing the time that the entrance is full. This study on Poisson arrival at a low-capacity rotary intersection provided new insights into methods of avoiding deadlock, and long waiting times, even though the results are intuitively clear. That is, control of interval of multi-agent arrival is important based on control of the entry rate. In particular, queuing theory may provide reasons of generating the critical probability in entrance systems with deadlock, considering that arrival interval of queuing cars gives very influence to the values or timings of the critical probability in which the steepest changing of state happens. We assume the reason that cars move in the state of the group generated naturally as percolation of molecular of water not but pheromone of ants. Then, we can introduce the critical probability which is the phenomena of the percolation system as one in general complex systems. In future work, we hope to improve the queuing theory such that it can treat not only service rate of an entrance gate and arrival rate of the agents to the gates but also conjunction rate after the entrance gate and bifurcation rate before next exit gate. And the relation between atoms of percolation systems and boxes, transitions of MFG is expected to be clear by theoretical critical probability. Moreover, the communication among agents or between each agent and the control center are expected as it has been realized recently or will be done in the actual agent flow systems. Acknowledgments The first author cordially acknowledges the cooperation of his many students including Mr. Y. Araki, Mr. H. Watanabe and Mr. T. Inoue for the initial research, Mr. M. Kawaguchi for the traffic simulation using the multi-agent simulator, and Mr. Xue Li, Mr. Mitsugu Arimura for discussions on queuing theory and congestion. He wish to express his gratitude also to Mr. Masaki Ishitani who encouraged the issue of this paper by an association study.
9 . T o r b a ( ), C o n t i n u o u s Petrinets An Application of Queuing Theory to Rotary Intersection Traffic Model and / 109 References [1] M. Katoh, T. Inoue, H. Watanabe and Y. Araki (2004), A Basic Design of a Rotary Intersection Model with Multi-agent Flows, The 47 th Automatic Control Joint Conference, 407. (in Japanese). [2] I. R. Tsang and I. J. Tsang (1999), Cluster Size Diversity, Percolation and Complex Systems, Phys. Rev. E Stst Nonlinear Soft Matter Phys., 60-3, [3] M. E. Fouladvand, M. R. Shaebani and Z. Sadjadi (2004), Intelligent Controlling Simulation of Traffic Flow in a Small City Network, J. Phys. Soc. Jpn., 73-11, [4] G. Shen, H. DAI, X. Liu, Z. Wang, Y. Sun (2003), Urban Expressway Traffic Flow Modeling and Control Using Artificial Neural Networks, IEEE Intell. Transp. Syst Proc., 1, [5] I. Koh (1999), Design of Traffic Adaptive Signal Controller and Analysis of Traffic Flow in Intersections Using Stochastic Petri-nets, J. Inst. Electron. Eng. Korea S., 36-S-3, [6] C Models for the Analysis of Traffic Urban Networks, Proc. IEEE Int. Conf. Syst. Man Cybern., 2, [7] T. Kato et al. (2005), Model Predictive Control of Traffic Flow Based on Hybrid System Modeling, IEICE Trans. on FECCS, E88-A(2), [8] F. Matsushita (2005), Economics on Road, Kodansha in Japan, (in Japanese) [9] K. Nishinari (2009), Science of Congestion, What is Congestion Study?, Statistical Mathematical Principle Laboratory, Gizyutsu Hyouronsha (in Japanese). [10] K. Hasegawa, K. Takahashi and P. E. Miyagi (1988), Application of the Mark Flow Graph to Represent Discrete Event Systems and System Control, Trans of the Society of Instrument and Control Engineers, 24-1, [11] R. Masuda, M. Okazaki and K. Hasegawa (1978), On Kinds, Property and Methods of Judgements of Deadlock in Mark Flow Graph, The 17 th SICE Annual Conference, (in Japanese). [12] M. Sugisawa (1998), Study on Modeling and Dead Lock Avoidance of Discrete Production System with Common Resources, Doctor Thesis of Toin Yokohama University, Yokohama, Japan, (in Japanese). [13] T. Tsuda (1977), Montecarlo Methods and Simulatio, Stochastic Application of Computer, 11, Baifukan (in Japanese). [14] A. Tarco and N. Rouphail (1994), Distribution-free Model for Estimating Random Queues in Signalized Networks, Transp res rec, 1457,
Traffic Flow Simulation using Cellular automata under Non-equilibrium Environment
Traffic Flow Simulation using Cellular automata under Non-equilibrium Environment Hideki Kozuka, Yohsuke Matsui, Hitoshi Kanoh Institute of Information Sciences and Electronics, University of Tsukuba,
More informationA MODIFIED CELLULAR AUTOMATON MODEL FOR RING ROAD TRAFFIC WITH VELOCITY GUIDANCE
International Journal of Modern Physics C Vol. 20, No. 5 (2009) 711 719 c World Scientific Publishing Company A MODIFIED CELLULAR AUTOMATON MODEL FOR RING ROAD TRAFFIC WITH VELOCITY GUIDANCE C. Q. MEI,,
More informationPerformance Analysis of Delay Estimation Models for Signalized Intersection Networks
Performance Analysis of Delay Estimation Models for Signalized Intersection Networks Hyung Jin Kim 1, Bongsoo Son 2, Soobeom Lee 3 1 Dept. of Urban Planning and Eng. Yonsei Univ,, Seoul, Korea {hyungkim,
More informationCHAPTER 3. CAPACITY OF SIGNALIZED INTERSECTIONS
CHAPTER 3. CAPACITY OF SIGNALIZED INTERSECTIONS 1. Overview In this chapter we explore the models on which the HCM capacity analysis method for signalized intersections are based. While the method has
More informationAnalytical investigation on the minimum traffic delay at a two-phase. intersection considering the dynamical evolution process of queues
Analytical investigation on the minimum traffic delay at a two-phase intersection considering the dynamical evolution process of queues Hong-Ze Zhang 1, Rui Jiang 1,2, Mao-Bin Hu 1, Bin Jia 2 1 School
More informationEfficiency promotion for an on-ramp system based on intelligent transportation system information
Efficiency promotion for an on-ramp system based on intelligent transportation system information Xie Dong-Fan( 谢东繁 ), Gao Zi-You( 高自友 ), and Zhao Xiao-Mei( 赵小梅 ) School of Traffic and Transportation,
More informationFormative Assessment: Uniform Acceleration
Formative Assessment: Uniform Acceleration Name 1) A truck on a straight road starts from rest and accelerates at 3.0 m/s 2 until it reaches a speed of 24 m/s. Then the truck travels for 20 s at constant
More informationCellular Automata Models of Traffic on Ant Trails
Cellular Automata Models of Traffic on Ant Trails Andreas Schadschneider Institut für Theoretische Physik Universität zu Köln www.thp.uni-koeln.de/~as www.thp.uni-koeln.de/ant-traffic Introduction Organized
More informationDYNAMIC MODEL OF URBAN TRAFFIC AND OPTIMUM MANAGEMENT OF ITS FLOW AND CONGESTION
Dynamic Systems and Applications 26 (2017) 575-588 DYNAMIC MODEL OF URBAN TRAFFIC AND OPTIMUM MANAGEMENT OF ITS FLOW AND CONGESTION SHI AN WANG AND N. U. AHMED School of Electrical Engineering and Computer
More information7. Queueing Systems. 8. Petri nets vs. State Automata
Petri Nets 1. Finite State Automata 2. Petri net notation and definition (no dynamics) 3. Introducing State: Petri net marking 4. Petri net dynamics 5. Capacity Constrained Petri nets 6. Petri net models
More informationAvailable online at ScienceDirect. Procedia Computer Science 22 (2013 )
Available online at www.sciencedirect.com ScienceDirect Procedia Computer Science 22 (2013 ) 1121 1125 17 th International Conference in Knowledge Based and Intelligent Information and Engineering Systems
More informationCourse Outline Introduction to Transportation Highway Users and their Performance Geometric Design Pavement Design
Course Outline Introduction to Transportation Highway Users and their Performance Geometric Design Pavement Design Speed Studies - Project Traffic Queuing Intersections Level of Service in Highways and
More informationAnalysis and Optimization of Discrete Event Systems using Petri Nets
Volume 113 No. 11 2017, 1 10 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Analysis and Optimization of Discrete Event Systems using Petri Nets
More informationTransient situations in traffic flow: Modelling the Mexico City Cuernavaca Highway
arxiv:cond-mat/0501561v1 [cond-mat.other] 24 Jan 2005 Transient situations in traffic flow: Modelling the Mexico City Cuernavaca Highway J.A. del Río Centro de Investigación en Energía Universidad Nacional
More informationCELLULAR AUTOMATA SIMULATION OF TRAFFIC LIGHT STRATEGIES IN OPTIMIZING THE TRAFFIC FLOW
CELLULAR AUTOMATA SIMULATION OF TRAFFIC LIGHT STRATEGIES IN OPTIMIZING THE TRAFFIC FLOW ENDAR H. NUGRAHANI, RISWAN RAMDHANI Department of Mathematics, Faculty of Mathematics and Natural Sciences, Bogor
More informationTraffic Progression Models
Traffic Progression Models Lecture Notes in Transportation Systems Engineering Prof. Tom V. Mathew Contents 1 Introduction 1 2 Characterizing Platoon 2 2.1 Variables describing platoon............................
More informationTraffic flow theory involves the development of mathematical relationships among
CHAPTER 6 Fundamental Principles of Traffic Flow Traffic flow theory involves the development of mathematical relationships among the primary elements of a traffic stream: flow, density, and speed. These
More informationTraffic Signal Control with Swarm Intelligence
009 Fifth International Conference on Natural Computation Traffic Signal Control with Swarm Intelligence David Renfrew, Xiao-Hua Yu Department of Electrical Engineering, California Polytechnic State University
More information1.225 Transportation Flow Systems Quiz (December 17, 2001; Duration: 3 hours)
1.225 Transportation Flow Systems Quiz (December 17, 2001; Duration: 3 hours) Student Name: Alias: Instructions: 1. This exam is open-book 2. No cooperation is permitted 3. Please write down your name
More informationIMPLEMENTATION OF PROGRAMMABLE LOGIC DEVICES IN QUANTUM CELLULAR AUTOMATA TECHNOLOGY
IMPLEMENTATION OF PROGRAMMABLE LOGIC DEVICES IN QUANTUM CELLULAR AUTOMATA TECHNOLOGY Dr.E.N.Ganesh Professor ECE Department REC Chennai, INDIA Email : enganesh50@yahoo.co.in Abstract Quantum cellular automata
More informationCHAPTER 5 DELAY ESTIMATION FOR OVERSATURATED SIGNALIZED APPROACHES
CHAPTER 5 DELAY ESTIMATION FOR OVERSATURATED SIGNALIZED APPROACHES Delay is an important measure of effectiveness in traffic studies, as it presents the direct cost of fuel consumption and indirect cost
More informationRecent Researches in Engineering and Automatic Control
Traffic Flow Problem Simulation in Jordan Abdul Hai Alami Mechanical Engineering Higher Colleges of Technology 17155 Al Ain United Arab Emirates abdul.alami@hct.ac.ae http://sites.google.com/site/alamihu
More informationDerivation of the Yellow Change Interval Formula
Derivation of the Yellow Change Interval Formula Brian Ceccarelli, Joseph Shovlin The yellow change interval formula traffic engineers use to set yellow light durations originated from a paper written
More informationNovel Approach for Prediction of Traffic Flow
Novel Approach for Prediction of Traffic Flow Prof. P. R. Patil Assistant Professor at PICT, Pune. prpatil@pict.edu Vishal S. Chaudhar Amol Bhombe Student at PICT, Pune amolbhombe.2@gmail.com Student at
More informationVISUAL EXPLORATION OF SPATIAL-TEMPORAL TRAFFIC CONGESTION PATTERNS USING FLOATING CAR DATA. Candra Kartika 2015
VISUAL EXPLORATION OF SPATIAL-TEMPORAL TRAFFIC CONGESTION PATTERNS USING FLOATING CAR DATA Candra Kartika 2015 OVERVIEW Motivation Background and State of The Art Test data Visualization methods Result
More informationStéphane Lafortune. August 2006
UNIVERSITY OF MICHIGAN DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE LECTURE NOTES FOR EECS 661 CHAPTER 1: INTRODUCTION TO DISCRETE EVENT SYSTEMS Stéphane Lafortune August 2006 References for
More informationMULTIPLE CHOICE QUESTIONS DECISION SCIENCE
MULTIPLE CHOICE QUESTIONS DECISION SCIENCE 1. Decision Science approach is a. Multi-disciplinary b. Scientific c. Intuitive 2. For analyzing a problem, decision-makers should study a. Its qualitative aspects
More informationMinimizing Total Delay in Fixed-Time Controlled Traffic Networks
Minimizing Total Delay in Fixed-Time Controlled Traffic Networks Ekkehard Köhler, Rolf H. Möhring, and Gregor Wünsch Technische Universität Berlin, Institut für Mathematik, MA 6-1, Straße des 17. Juni
More informationElevator Dispatching as Mixed Integer Linear Optimization Problem
Elevator Dispatching as Mixed Integer Linear Optimization Problem Mirko Ruokokoski 1 Harri Ehtamo 1 Janne Sorsa 2 Marja-Liisa Siikonen 2 1 Systems Analysis Laboratory Helsinki University of Techonology,
More informationCumulative Count Curve and Queueing Analysis
Introduction Traffic flow theory (TFT) Zhengbing He, Ph.D., http://zhengbing.weebly.com School of traffic and transportation, Beijing Jiaotong University September 27, 2015 Introduction Outline 1 Introduction
More informationSignalized Intersection Delay Models
Signalized Intersection Delay Models Lecture Notes in Transportation Systems Engineering Prof. Tom V. Mathew Contents 1 Introduction 1 2 Types of delay 2 2.1 Stopped Time Delay................................
More informationManagement of intermodal container terminals using feedback control
Management of intermodal container terminals using feedback control A. Alessandri, S. Sacone $, S.Siri $ Institute of Intelligent Systems for Automation ISSIA-CNR National Research Council of Italy Via
More informationADMISSION CONTROL IN THE PRESENCE OF PRIORITIES: A SAMPLE PATH APPROACH
Chapter 1 ADMISSION CONTROL IN THE PRESENCE OF PRIORITIES: A SAMPLE PATH APPROACH Feng Chen Department of Statistics and Operations Research University of North Carolina at Chapel Hill chenf@email.unc.edu
More informationConservation laws and some applications to traffic flows
Conservation laws and some applications to traffic flows Khai T. Nguyen Department of Mathematics, Penn State University ktn2@psu.edu 46th Annual John H. Barrett Memorial Lectures May 16 18, 2016 Khai
More informationMotivation. Evolution has rediscovered several times multicellularity as a way to build complex living systems
Cellular Systems 1 Motivation Evolution has rediscovered several times multicellularity as a way to build complex living systems Multicellular systems are composed by many copies of a unique fundamental
More informationCharacteristics of vehicular traffic flow at a roundabout
PHYSICAL REVIEW E 70, 046132 (2004) Characteristics of vehicular traffic flow at a roundabout M. Ebrahim Fouladvand, Zeinab Sadjadi, and M. Reza Shaebani Department of Physics, Zanjan University, P.O.
More informationIs the ventilation control for longitudinal system difficult?
Is the ventilation control for longitudinal system difficult? Akisato MIZUNO and Tomoaki OKUBO, Kogakuin University, Tokyo, Japan ABSTRACT By adopting longitudinal ventilation system, construction costs
More informationTIME DEPENDENT CORRELATIONS BETWEEN TRAVEL TIME AND TRAFFIC VOLUME ON EXPRESSWAYS
TIME DEPENDENT CORRELATIONS BETWEEN TRAVEL TIME AND TRAFFIC VOLUME ON EXPRESSWAYS Takamasa IRYO Research Associate Department of Architecture and Civil Engineering Kobe University 1-1, Rokkodai-cho, Nada-ku,
More informationNon-equilibrium statistical mechanics and applications to transport modelling. Rosemary Harris
Non-equilibrium statistical mechanics and applications to transport modelling Rosemary Harris Goldsmiths Company Maths Course, July 24th 2008 Transport processes Outline Framework Stochastic Markovian
More informationPHYS 100 MidTerm Practice
University of the Fraser Valley Physics 100 PHYS 100 MidTerm Practice Name: Directions: Fill in the scantron form with the following information: 1. ID number (student number) 2. Name at top of form 3.
More informationIndustrial Automation (Automação de Processos Industriais)
Industrial Automation (Automação de Processos Industriais) Discrete Event Systems http://users.isr.ist.utl.pt/~jag/courses/api1516/api1516.html Slides 2010/2011 Prof. Paulo Jorge Oliveira Rev. 2011-2015
More informationTraffic Flow Theory & Simulation
Traffic Flow Theory & Simulation S.P. Hoogendoorn Lecture 7 Introduction to Phenomena Introduction to phenomena And some possible explanations... 2/5/2011, Prof. Dr. Serge Hoogendoorn, Delft University
More informationCar-Following Parameters by Means of Cellular Automata in the Case of Evacuation
See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/228528638 Car-Following Parameters by Means of Cellular Automata in the Case of Evacuation
More informationDiscrete Event Systems Exam
Computer Engineering and Networks Laboratory TEC, NSG, DISCO HS 2016 Prof. L. Thiele, Prof. L. Vanbever, Prof. R. Wattenhofer Discrete Event Systems Exam Friday, 3 rd February 2017, 14:00 16:00. Do not
More informationSpontaneous Jam Formation
Highway Traffic Introduction Traffic = macroscopic system of interacting particles (driven or self-driven) Nonequilibrium physics: Driven systems far from equilibrium Collective phenomena physics! Empirical
More informationDES. 4. Petri Nets. Introduction. Different Classes of Petri Net. Petri net properties. Analysis of Petri net models
4. Petri Nets Introduction Different Classes of Petri Net Petri net properties Analysis of Petri net models 1 Petri Nets C.A Petri, TU Darmstadt, 1962 A mathematical and graphical modeling method. Describe
More informationDerivation of the Yellow Change Interval Formula
Derivation of the Yellow Change Interval Formula Brian Ceccarelli, PE; Joseph Shovlin, PhD The yellow change interval formula traffic engineers use to set yellow light durations originated from a paper
More informationModeling Traffic Flow for Two and Three Lanes through Cellular Automata
International Mathematical Forum, Vol. 8, 2013, no. 22, 1091-1101 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2013.3486 Modeling Traffic Flow for Two and Three Lanes through Cellular Automata
More informationOn the Applicability of an Interval Time Structure for Protocol Verification
On the Applicability of an Interval Time Structure for Protocol Verification Jerzy BRZZIŃSKI, Michał SAJKOWSKI Institute of Computing Science, Poznań University of Technology Piotrowo 3a, 60-965 Poznań,
More informationStochastic models in product form: the (E)RCAT methodology
Stochastic models in product form: the (E)RCAT methodology 1 Maria Grazia Vigliotti 2 1 Dipartimento di Informatica Università Ca Foscari di Venezia 2 Department of Computing Imperial College London Second
More informationA Cellular Automaton Model for Heterogeneous and Incosistent Driver Behavior in Urban Traffic
Commun. Theor. Phys. 58 (202) 744 748 Vol. 58, No. 5, November 5, 202 A Cellular Automaton Model for Heterogeneous and Incosistent Driver Behavior in Urban Traffic LIU Ming-Zhe ( ), ZHAO Shi-Bo ( ô ),,
More informationReal Time Traffic Control to Optimize Waiting Time of Vehicles at A Road Intersection
International Journal of Research in Engineering and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Print): 2320-9356 w Volume 6 Issue 4 Ver. II ǁ 2018 ǁ PP. 25-33 Real Time Traffic Control to Optimize
More informationBackground and Hong Kong Statistics. Background. Estimation of Network Reliability under Traffic Incidents for ITS Applications
Estimation of Network Reliability under Traffic Incidents for ITS Applications Ir Prof. William H.K. Lam Chair Professor of Civil & Transportation Engineering and Head Department of Civil & Environmental
More informationAvailable online Journal of Scientific and Engineering Research, 2017, 4(4): Research Article
Available online www.jsaer.com, 2017, 4(4):137-142 Research Article ISSN: 2394-2630 CODEN(USA): JSERBR A Qualitative Examination of the Composition of the Cooperative Vehicles Çağlar Koşun 1, Çağatay Kök
More informationMODELING WITH CURRENT DYNAMICS AND VIBRATION CONTROL OF TWO PHASE HYBRID STEPPING MOTOR IN INTERMITTENT DRIVE
MODELING WITH CURRENT DYNAMICS AND VIBRATION CONTROL OF TWO PHASE HYBRID STEPPING MOTOR IN INTERMITTENT DRIVE Ryota Mori, Yoshiyuki Noda, Takanori Miyoshi, Kazuhiko Terashima Department of Production Systems
More informationDesign Priciples of Traffic Signal
Design Priciples of Traffic Signal Lecture Notes in Transportation Systems Engineering Prof. Tom V. Mathew Contents 1 Overview 1 2 Definitions and notations 2 3 Phase design 3 3.1 Two phase signals.................................
More informationNATHAN HALE HIGH SCHOOL PARKING AND TRAFFIC ANALYSIS. Table of Contents
Parking and Traffic Analysis Seattle, WA Prepared for: URS Corporation 1501 4th Avenue, Suite 1400 Seattle, WA 98101-1616 Prepared by: Mirai Transportation Planning & Engineering 11410 NE 122nd Way, Suite
More informationSINGLE-ELECTRON CIRCUITS PERFORMING DENDRITIC PATTERN FORMATION WITH NATURE-INSPIRED CELLULAR AUTOMATA
International Journal of Bifurcation and Chaos, Vol. 7, No. (7) 365 3655 c World Scientific Publishing Company SINGLE-ELECTRON CIRCUITS PERFORMING DENDRITIC PATTERN FORMATION WITH NATURE-INSPIRED CELLULAR
More informationHOPFIELD neural networks (HNNs) are a class of nonlinear
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II: EXPRESS BRIEFS, VOL. 52, NO. 4, APRIL 2005 213 Stochastic Noise Process Enhancement of Hopfield Neural Networks Vladimir Pavlović, Member, IEEE, Dan Schonfeld,
More informationControl of Hybrid Petri Nets using Max-Plus Algebra
Control of Hybrid Petri Nets using Max-Plus Algebra FABIO BALDUZZI*, ANGELA DI FEBBRARO*, ALESSANDRO GIUA, SIMONA SACONE^ *Dipartimento di Automatica e Informatica Politecnico di Torino Corso Duca degli
More informationFrom Applied Maths to Transport Modelling. Rosemary Harris
From Applied Maths to Transport Modelling (via non-equilibrium statistical mechanics) Rosemary Harris Goldsmiths Company Maths Course, July 22nd 2014 Transport processes Outline Framework Stochastic Markovian
More informationModelling of Railway Network Using Petri Nets
Modelling of Railway Network Using Petri Nets MANDIRA BANIK 1, RANJAN DASGUPTA 2 1 Dept. of Computer Sc. & Engg., National Institute of Technical Teachers' Training & Research, Kolkata, West Bengal, India
More informationLecture 19: Common property resources
Lecture 19: Common property resources Economics 336 Economics 336 (Toronto) Lecture 19: Common property resources 1 / 19 Introduction Common property resource: A resource for which no agent has full property
More informationSIMULATION OF EMERGENCY EVACUATION BEHAVIOR DURING A DISASTER BY USE OF ELLPTIC DISTINCT ELEMENTS
13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 134 SIMULATION OF EMERGENCY EVACUATION BEHAVIOR DURING A DISASTER BY USE OF ELLPTIC DISTINCT ELEMENTS
More informationSignalized Intersection Delay Models
Transportation System Engineering 56. Signalized Intersection Delay Models Chapter 56 Signalized Intersection Delay Models 56.1 Introduction Signalized intersections are the important points or nodes within
More informationTime Reversibility and Burke s Theorem
Queuing Analysis: Time Reversibility and Burke s Theorem Hongwei Zhang http://www.cs.wayne.edu/~hzhang Acknowledgement: this lecture is partially based on the slides of Dr. Yannis A. Korilis. Outline Time-Reversal
More informationA weighted mean velocity feedback strategy in intelligent two-route traffic systems
A weighted mean velocity feedback strategy in intelligent two-route traffic systems Xiang Zheng-Tao( 向郑涛 ) and Xiong Li( 熊励 ) School of Management, Shanghai University, Shanghai 200444, China (Received
More informationWaseda University Do ctoral Disse rtation. Elevato r Group Supervisory Control of. Double-De ck and Multi-Car Elevator Systems
Waseda University Do ctoral Disse rtation Elevato r Group Supervisory Control of Double-De ck and Multi-Car Elevator Systems using Genetic Ne two rk Programming YU, Lu Graduate S chool of Inf ormation,
More informationTraffic Modelling for Moving-Block Train Control System
Commun. Theor. Phys. (Beijing, China) 47 (2007) pp. 601 606 c International Academic Publishers Vol. 47, No. 4, April 15, 2007 Traffic Modelling for Moving-Block Train Control System TANG Tao and LI Ke-Ping
More informationSECTION 7 RAMP TERMINAL SIGNS
SECTION 7 Part 3: Motorways and Expressways CONTENTS Reference Page Page Number Date SECTION 7: 7.1 GENERAL... 7-1 7.2 SIGN COLOUR... 7-1 7.3 MOTORWAY AND EXPRESSWAY NAMING... 7-1 7.4 ADVANCE DIRECTION
More informationHybrid Petri net model of a traffic intersection in a urban network
Hybrid Petri net model of a traffic intersection in a urban network C. Renato Vázquez, Herman Y. Sutarto, René Boel, Manuel Silva Abstract Control in urban traffic networks constitutes an important and
More informationCellular Automata Models of Pedestrian Dynamics
Cellular Automata Models of Pedestrian Dynamics Andreas Schadschneider Institute for Theoretical Physics University of Cologne Germany www.thp.uni-koeln.de/~as www.thp.uni-koeln.de/ant-traffic Overview
More informationIntuitionistic Fuzzy Estimation of the Ant Methodology
BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 9, No 2 Sofia 2009 Intuitionistic Fuzzy Estimation of the Ant Methodology S Fidanova, P Marinov Institute of Parallel Processing,
More informationMODELING AND SIMULATION BY HYBRID PETRI NETS. systems, communication systems, etc). Continuous Petri nets (in which the markings are real
Proceedings of the 2012 Winter Simulation Conference C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose, and A. M. Uhrmacher, eds. MODELING AND SIMULATION BY HYBRID PETRI NETS Hassane Alla Latéfa Ghomri
More informationLecture Notes 7 Random Processes. Markov Processes Markov Chains. Random Processes
Lecture Notes 7 Random Processes Definition IID Processes Bernoulli Process Binomial Counting Process Interarrival Time Process Markov Processes Markov Chains Classification of States Steady State Probabilities
More informationAdvanced information feedback strategy in intelligent two-route traffic flow systems
. RESEARCH PAPERS. SCIENCE CHINA Information Sciences November 2010 Vol. 53 No. 11: 2265 2271 doi: 10.1007/s11432-010-4070-1 Advanced information feedback strategy in intelligent two-route traffic flow
More informationThe effect of probabilities of departure with time in a bank
International Journal of Scientific & Engineering Research, Volume 3, Issue 7, July-2012 The effect of probabilities of departure with time in a bank Kasturi Nirmala, Shahnaz Bathul Abstract This paper
More informationReal-time, Adaptive Prediction of Incident Delay for Advanced Traffic Management Systems
Real-time, Adaptive Prediction of Incident Delay for Advanced Traffic Management Systems Liping Fu and Bruce Hellinga Department of Civil Engineering, University of Waterloo, Waterloo, Canada Phone: 59
More informationUNIVERSITY OF YORK. MSc Examinations 2004 MATHEMATICS Networks. Time Allowed: 3 hours.
UNIVERSITY OF YORK MSc Examinations 2004 MATHEMATICS Networks Time Allowed: 3 hours. Answer 4 questions. Standard calculators will be provided but should be unnecessary. 1 Turn over 2 continued on next
More informationA SIMPLIFIED MODEL OF URBAN RAILWAY SYSTEM FOR DYNAMIC TRAFFIC ASSIGNMENT
1 A SIMPLIFIED MODEL OF URBAN RAILWAY SYSTEM FOR DYNAMIC TRAFFIC ASSIGNMENT T. SEO a, K. WADA b and D. FUKUDA c a Department of Civil and Environmental Engineering, School of Environment and Society, Tokyo
More informationA Brief Introduction to Model Checking
A Brief Introduction to Model Checking Jan. 18, LIX Page 1 Model Checking A technique for verifying finite state concurrent systems; a benefit on this restriction: largely automatic; a problem to fight:
More informationProceedings of the 2015 Winter Simulation Conference L. Yilmaz, W. K. V. Chan, I. Moon, T. M. K. Roeder, C. Macal, and M. D. Rossetti, eds.
Proceedings of the 2015 Winter Simulation Conference L. Yilmaz, W. K. V. Chan, I. Moon, T. M. K. Roeder, C. Macal, and M. D. Rossetti, eds. EVALUATING ADVANTAGE OF SHARING INFORMATION AMONG VEHICLES TOWARD
More informationResource-Oriented Petri Nets in Deadlock Avoidance of AGV Systems
Proceedings of the 2001 IEEE International Conference on Robotics & Automation Seoul, Korea May 21-26, 2001 Resource-Oriented Petri Nets in Deadlock Avoidance of AGV Systems Naiqi Wu Department of Mechatronics
More informationControlo Switched Systems: Mixing Logic with Differential Equations. João P. Hespanha. University of California at Santa Barbara.
Controlo 00 5 th Portuguese Conference on Automatic Control University of Aveiro,, September 5-7, 5 00 Switched Systems: Mixing Logic with Differential Equations João P. Hespanha University of California
More informationCell Transmission Models
Cell Transmission Models Lecture Notes in Transportation Systems Engineering Prof. Tom V. Mathew Contents 1 Introduction 1 2 Single source and sink CTM model 2 2.1 Basic Premise...................................
More informationMechanics. In the Science Program, Mechanics contributes to the following program goals described in the Exit Profile:
Mechanics Objectives: 00UR Discipline: Physics Ponderation: 3-2-3 Course Code: 203-NYA-05 Prerequisite: Sec. V Physics 534, Mathematics 536 (or equivalent) Course Credit: 2 2/3 Corequisite: 00UP (Calculus
More informationMatrices and Systems of Equations
M CHAPTER 3 3 4 3 F 2 2 4 C 4 4 Matrices and Systems of Equations Probably the most important problem in mathematics is that of solving a system of linear equations. Well over 75 percent of all mathematical
More informationApplying a cellular automaton model to describing the anomalous relaxation of the metastable states in the disordered porous media
Journal of Physics: Conference Series PAPER OPEN ACCESS Applying a cellular automaton model to describing the anomalous relaxation of the metastable states in the disordered porous media o cite this article:
More informationCS 347 Parallel and Distributed Data Processing
CS 347 Parallel and Distributed Data Processing Spring 2016 & Clocks, Clocks, and the Ordering of Events in a Distributed System. L. Lamport, Communications of the ACM, 1978 Notes 15: & Clocks CS 347 Notes
More informationProperties of Phase Transition of Traffic Flow on Urban Expressway Systems with Ramps and Accessory Roads
Commun. Theor. Phys. 56 (2011) 945 951 Vol. 56, No. 5, November 15, 2011 Properties of Phase Transition of Traffic Flow on Urban Expressway Systems with Ramps and Accessory Roads MEI Chao-Qun (Ö ) 1, and
More informationreversed chain is ergodic and has the same equilibrium probabilities (check that π j =
Lecture 10 Networks of queues In this lecture we shall finally get around to consider what happens when queues are part of networks (which, after all, is the topic of the course). Firstly we shall need
More informationA lattice traffic model with consideration of preceding mixture traffic information
Chin. Phys. B Vol. 0, No. 8 011) 088901 A lattice traffic model with consideration of preceding mixture traffic information Li Zhi-Peng ) a), Liu Fu-Qiang ) a), Sun Jian ) b) a) School of Electronics and
More informationPhysics: spring-mass system, planet motion, pendulum. Biology: ecology problem, neural conduction, epidemics
Applications of nonlinear ODE systems: Physics: spring-mass system, planet motion, pendulum Chemistry: mixing problems, chemical reactions Biology: ecology problem, neural conduction, epidemics Economy:
More informationsuppressing traffic flow instabilities
suppressing traffic flow instabilities S S VF VC VL D D Berthold K.P. Horn Traffic flow instabilities waste energy: At high densities traffic flow becomes unstable Traffic acts as if it was a dilatant
More informationModelling and Simulation for Train Movement Control Using Car-Following Strategy
Commun. Theor. Phys. 55 (2011) 29 34 Vol. 55, No. 1, January 15, 2011 Modelling and Simulation for Train Movement Control Using Car-Following Strategy LI Ke-Ping (Ó ), GAO Zi-You (Ô Ð), and TANG Tao (»
More informationOptimizing traffic flow on highway with three consecutive on-ramps
2012 Fifth International Joint Conference on Computational Sciences and Optimization Optimizing traffic flow on highway with three consecutive on-ramps Lan Lin, Rui Jiang, Mao-Bin Hu, Qing-Song Wu School
More informationPBW 654 Applied Statistics - I Urban Operations Research
PBW 654 Applied Statistics - I Urban Operations Research Lecture 2.I Queuing Systems An Introduction Operations Research Models Deterministic Models Linear Programming Integer Programming Network Optimization
More informationSwitched Systems: Mixing Logic with Differential Equations
research supported by NSF Switched Systems: Mixing Logic with Differential Equations João P. Hespanha Center for Control Dynamical Systems and Computation Outline Logic-based switched systems framework
More informationTRAVEL TIME RELIABILITY ON EXPRESSWAY NETWORK UNDER UNCERTAIN ENVIRONMENT OF SNOWFALL AND TRAFFIC REGULATION
TRAVEL TIME RELIABILITY ON EXPRESSWAY NETWORK UNDER UNCERTAIN ENVIRONMENT OF SNOWFALL AND TRAFFIC REGULATION Hiroshi Wakabayashi Faculty of Urban Science, Meijo University, 4-3-3, Nijigaoka, Kani-City,
More informationContinuum Modelling of Traffic Flow
Continuum Modelling of Traffic Flow Christopher Lustri June 16, 2010 1 Introduction We wish to consider the problem of modelling flow of vehicles within a traffic network. In the past, stochastic traffic
More information