CEE518 ITS Guest Lecture ITS and Traffic Flow Fundamentals

Transcription

1 EE518 ITS Guest Lecture ITS and Traic Flow Fundamentals Daiheng Ni Department o ivil and Environmental Engineering University o Massachusetts mherst The main objective o these two lectures is to establish the connection between Intelligent Transportation Systems (ITS) and traic low undamentals. Introduction o traic low undamentals has appeared on virtually every ITS boo and the reader is very curious about why should an ITS boo tal about traic low undamentals. Unortunately, a connection between these two subjects is typically missing, or at least vague, in these ITS boos. This motivates these two lectures. In Lecture 1, a qualitative introduction is presented to wal the reader step by step rom ITS to traic low undamentals without involving any math. In Lecture 2, a quantitative introduction is given by using a concrete example to show how traic low undamentals help solve real-world ITS problems. Questions and comments should be directed to Dr. Daiheng Ni. Lecture 1: Qualitative Introduction Why ITS? ongestion, better use o roads, wise trip maing, peace in mind, etc. What does ITS do? TIS - travel times, queues, delays TMS throughput, bottlenecs, control strategies, etc. Underlying methodology? Watch Sensor technologies Mobile sensors Point sensors Space sensors ontrol Traic low analysis Where are bottlenecs? How long will a queue build up? How long does it tae or the queue to dissipate? How much delay will be encountered? In case o an accident, what s the best cleanup strategy, ull closure or partial closures? Traic low undamentals How does traic loo lie low, speed, density, and their relationships Traic stream characteristics 3 basic char q,, u Other char throughput, queue, delay, travel time built on q,, u Equilibrium traic low models See q--u observations and itting.doc How will traic evolution traic low models and simulation Dynamic traic low models Simple models omplex models Manual calculation Traic simulation Flow-speed-density: Time-space domain: sensor technologies and traic low characteristics Fundamental relationship

2 Equilibrium traic low model pair-wise relationship between speed and density Field observations u Greenshields: u u Northwestern: = u u e j j Greenberg: u = u ln Generalized: u = u 1 m m Underwood: u u e / = Fundamental diagrams: Speed-density: mainly used in research Flow-density: highway traic control Speed-low: highway capacity analysis and LOS o = Dynamic traic low models Equilibrium traic low models are just a summary o observations over time and space, so these models alone won t answer questions regarding traic evolution, i.e. traic conditions at any time-space point (x, t). onsidering that low, speed, and density all vary over time and space, these traic stream characteristics are unctions o time and space. Thereore, the independent variables here are time t and space x and the dependent variables here are q(x, t), u(x, t), and (x, t). ny ormulation that describes the relationship between these time- and space-dependent variables is called a dynamic traic low model. Derivation o conservation law equation o continuity LWR model a system o two equations The equation o continuity has one equation but contains two unnown variables. Need to supply an additional equation in order to solve or the unnown variables. Equilibrium traic low model comes into play. Thereore, ( x, t) q( x, t) + = 0 t x q = ( ) I we can solve the LWR model with certain boundary and initial conditions, then we now q(x,t), (x,t), and u(x,t) or everywhere in the time-space domain, and various MOEs can be calculated such as queues, delays, travel times, etc. How to solve LWR model? Shoc waves Starting rom boundary and initial conditions in time-space domain, draw shoc waves which will divide the time-space domain into regions and each region contains the same traic conditions. Questions: what are shoc waves and how to draw them? Shoc waves Shoc waves are lines in time-space domain delineating regions o dierent traic conditions. Example: shoc wave at a highway bottlenec. shoc wave at an intersection j n

3 Lecture 2: Quantitative Introduction Shoc waves How to determine shoc wave speeds? How does this relate to the undamental diagram? How can this relation help solve LWR model? How to apply LWR model? n example ITS problem n example ITS problem: On Wednesday 9:00 M, there is an accident on northbound Interstate-91. The traic operation center (TO) has to decide how to cleanup the accident. ter collecting inormation and communicate with highway patrol and emergency operator, the TO determines that there are two alternative: 1. ompletely shut the interstate o or 10 minutes, do cleanup, and then reopen the Interstate or normal operation, or 2. Partially open the Interstate at reduced capacity, but the cleanup requires longer time about 30 minutes beore normal operation can be resumed. One o the concerns at the TO is how long the queue will grow because the queue on the Interstate will overlow via ramps and urther bloc upstream surace streets. s a transportation engineering student in UMass mherst, you are ased to oer you nowledge to help the TO mae the decision. More details: rrival low (condition ): q = 2000 veh/hr, = 40 veh/mi, u = 50 mi/hr Queued low (condition D): q = 0 veh/hr, = 200 veh/mi, u = 0 mi/hr apacity low (condition ): q = 2200 veh/hr, = 60 veh/mi, u = 36.7 mi/hr Reduced capacity low (condition E): q = 1100 veh/hr, = 50 veh/mi, u = 22 mi/hr Find: which alternative creates longer queue?

4 Flow O B D Density Space, x a 10 min b c D U D U D x U D = (0-2000) / (200-40) = / 160 = mph = x / ac ac = x / 12.5 U D = (0-2200) / (200-60) = / 140 = mph = x / bc bc = x / min = 1/6 hour = ac bc = x / 12.5 (x / 15.7) = x x = 1 / (6 * 0.016) = 10.2 mi Time, t

5 Flow O E B D Density Space, x a 30 min b c B U B U B x Time, t U B = ( ) / (145-40) = / 105 = mph = x / ac ac = x / 8.57 U B = ( ) / (145-60) = / 140 = mph = x / bc bc = x / min = 1/2 hour = ac bc = x / 8.57 (x / 12.94) = x x = 1 / (2 * 0.039) = 12.7 mi

6 Flow Density This graph shows how the example in the ITS text boo is ill-posed. The main reason is that the q- relationship is not convex or the congested regime.