Corridor-Level Queuing Prediction Model

Transcription

1 Corridor-Level Queuing Prediction Model August 8, 2012 Jeffrey Taylor & Dr. Xuesong Zhou University of Utah 1

2 Overview Key Modeling Concepts Methodology Queue model Stochastic inputs Corridor Analysis Spreadsheet 2

3 Key Modeling Concepts Simplified corridor representation 0 1 R1 R2 Modeled as self-contained system 2 3 M-1 M Stochastic capacity, demand (inflow, outflow) Vertical queue model for internal dynamics User-specified conditions (weather, incidents, special events, etc.) 3

4 Key Modeling Concepts Sampling-based approach Generate many random instances, representing a day or scenario Use sampled travel time to construct distribution Vehicle trajectory-based approach Simulate individual vehicle trajectories based on stochastic bottleneck capacity 4

5 Model Assumptions 1. First-In-First-Out (FIFO) conditions along corridor 2. Vertical/point queue model can be used to describe the queues along the corridor 3. Ramps (merge and diverge links) are located before vertical queue 4. Queue discharge rates and net ramp flow rates are constant over prediction horizon Implicit Assumptions: 1. Travel time variability attributed primarily to variation in supply and demand, queues 2. FIFO, vertical queue is reasonable approximation to internal traffic flow dynamics 5

6 Methodology Corridor is a series of potential bottlenecks 0 1 R1 R2 2 3 M-1 M Given stochastic bottleneck capacity, net ramp flow rates, and number of vehicles on each link Simulate the end-to-end travel time for a sample of probe vehicles passing through corridor under varying supply/demand conditions 6

7 Methodology Step 1: Calculate arrival time at bottleneck Step 2: Calculate number of vehicles behind queue Step 3: Calculate delay Step 4: Update end-to-end travel time Probe Vehicle Number of Vehicles Before Probe Vehicle Vertical Queue Stochastic Capacity Stochastic Net Ramp Flow Rate 7

8 Notation FFTA = Free-flow time of arrival to queue n = Number of vehicles on link when probe vehicle entered corridor V = Vehicles preceding probe vehicle L = Queue length (# of vehicles) W = Waiting time in queue (min) Fnet = Net flow at ramps (veh/hr) m = Index for bottlenecks 8

9 Methodology Step 1: Calculate arrival time (FFTA) at bottleneck FFTA = FFTA + W + FFTT Probe Vehicle m m 1 m 1 m Number of Vehicles Before Probe Vehicle Vertical Queue Stochastic Capacity Stochastic Net Ramp Flow Rate 9

10 Methodology Step 2: Calculate number of vehicles behind queue V m = Number of Vehicles Before Probe Vehicle V m-1 = Vehicles before probe from previous link Vm = max(0, nm + Fnetm FFTAm + Vm 1) n = Density LinkLength m m m n m = Vehicles already on link at start time Fnet Vertical Queue Stochastic Capacity 10

11 Step 3: Calculate delay Methodology L = max(0, V Cap FFTA ) m m m m W = L Cap m m m Probe Vehicle V m = # Vehicles in Vertical Queue Cap m = Stochastic Capacity 11

12 Methodology Step 4: Update end-to-end travel time FFTA = FFTA + W + FFTT Probe Vehicle m m 1 m 1 m Number of Vehicles Before Probe Vehicle Vertical Queue Stochastic Capacity Stochastic Net Ramp Flow Rate 12

13 Queue Prediction Spreadsheet 13

14 Component Worksheets Inputs Random Number Generation Calculations Histograms Outputs Vehicle Trajectory Data MOEs & Visualization 14

15 Inputs Density, capacity, and ramp flow rates Different conditions Link attributes Length, FFTT, Ramp flags, condition flags/probabilities 15

16 Random Number Generation Secondary input for simulation Three variables per link * # of probe vehicles Normal distribution N(0,1) Used to randomly generate input density, capacity, and ramp flows for each link Translated to Log-Normal distribution 16

17 Calculations For each probe vehicle, entering each link Calculate FFTA, Preceding vehicle count, Queue length, Waiting time, and Link travel time Update variables at next link/bottleneck 17

18 Histograms Analyze inputs and outputs Inputs: Density, capacity, ramp flow Outputs: Delay, travel time Future revisions Dynamic histogram bins 18

19 Outputs Mean & variance for density, capacity, ramp flow rate, and travel time Corridor modeling checks 19

20 Outputs 20

21 Outputs/Visualization 21

22 Thank You! Questions? 22