METROPOLIS2 Course

Session 5: Simulation Output

Lucas Javaudin

Spring 2024

Questions regarding last Session?

Output Files

  • log.txt: METROPOLIS2 log messages during the simulation
  • running_times.json: simulation running time, by category
  • report.html: webpage summarizing the results
  • iteration_results.{parquet,csv}: aggregate results for each iteration
  • 3 CSV / Parquet output files for the population results
  • 4 CSV / Parquet output files for the road-network results

Plan of this Session

  1. Aggregate Results
  2. Population Results
  3. Road-Network Results
  4. Task for Next Session

Aggregate Results

Running times (1/3)

File running_times.json


						{
							"total": "49181.060006808",
							"total_skims_computation": "37804.951886765",
							"total_demand_model": "2943.497363545",
							"total_supply_model": "8150.961492634",
							"total_learning_model": "9.425217904",
							"total_aggregate_results_computation": "148.839589353",
							"total_stopping_rules_check": "0.000029886",
							"per_iteration": "245.905300034",
							"per_iteration_skims_computation": "189.024759433",
							"per_iteration_demand_model": "14.717486817",
							"per_iteration_supply_model": "40.754807463",
							"per_iteration_learning_model": "0.047126089",
							"per_iteration_aggregate_results_computation": "0.744197946",
							"per_iteration_stopping_rules_check": "0.000000149"
						}

skims_computation: computation of OD-level travel-time functions given the expected road-network conditions

Running times (2/3)

Impact of simulation size on running times:
Skims comp. Demand model Supply model
# agents · Large¹ Large¹
# nodes / edges Large · Medium
# unique origin / dest. Very large · ·
# unique OD pairs Large · ·
# breakpoints Small Very small Very small
¹: A priori, the number of agents increases linearly the running time of the demand and supply models but, if congestion is larger, the global running time gets larger.

Running times (3/3)

Comparing two Paris simulations
Old scenario New scenario Variation
# agents 477 192 629 314 ×1.32
# road trips 477 192 548 480 ×1.15
# virtual trips 0 1 442 883 ×∞
# nodes 20 648 116 971 ×5.67
# edges 43 857 196 980 ×4.49
# unique origins 1326 50 774 ×38.29
# unique destinations 1326 49 607 ×37.41
# unique OD pairs 161 871 466 079 ×2.88
# breakpoints 27 93 ×3.44
Old scenario New scenario Variation
Total 01:49:42 09:00:28 ×4.93
Skims computation 00:20:04 06:57:25 ×20.80
Demand model 00:44:43 00:39:28 ×0.88
Supply model 00:42:35 01:19:11 ×1.86

HTML Report

  • Table of aggregate results by iterations
  • Graphs of convergence through iterations
  • Graphs of departure-time / arrival-time distribution for last iteration

Iteration Results

  • Parquet or CSV file
  • 1 row for each iteration; 145 columns
  • Aggregate results at the agent-level, road-trip level, virtual-trip level and road-network level
  • Same variables as in the HTML report (with standard-deviation, minimum and maximum)

Route vs Global Free-Flow Travel Time

  • Route free-flow travel time: no-congestion travel time on the route that was taken
  • Global free-flow travel time: no-congestion travel time on the fastest possible route
  • Route / Global congestion: share of travel-time spent in congestion, relative to route / global free-flow travel time

Population Results

Output Files

All the results are specific to the last iteration

  • agent_results.{parquet,csv}: results at the agent-level
  • trip_results.{parquet,csv}: results at the trip-level
  • route_results.{parquet,csv}: detailed itineraries for the road trips

Agent Results

  • Parquet or CSV file
  • 1 row for each agent; 12 columns
  • Results specific to the agents and their selected alternative

Utility Indicators (1/4)

  • utility: Simulated utility, based on the selected alternative $j$ and departure time $\tau$: $V^{\text{sim}}_{j}(\tau)$
  • alt_expected_utility: Expected utility of the departure-time choice of the selected alternative $j$: $\mathbb{E}_{\varepsilon}[\max_{\tau} U_j(\tau)]$
  • expected_utility: Expected utility of the alternative choice: $\mathbb{E}_{\varepsilon}[\max_{j} U_j]$

Utility Indicators (2/4)

Example with a deterministic alternative-choice model and a constant departure time

  • utility: Simulated utility, based on the selected alternative $j$, departure time $\tau$ and simulated travel times: $V^{\text{sim}}_{j}(\tau)$
  • alt_expected_utility: Expected utility, based on the selected alternative $j$, departure time $\tau$ and expected travel times: $V^{\text{exp}}_{j}(\tau)$
  • expected_utility: Expected utility, based on the selected alternative $j$, departure time $\tau$ and expected travel times: $V^{\text{exp}}_{j}(\tau)$

When the simulation has converged: $V^{\text{sim}}_j(\tau) \approx V^{\text{exp}}_j(\tau)$

Utility Indicators (3/4)

Example with a Logit alternative-choice model and a Continuous Logit departure-time choice model

  • utility: Simulated utility, based on the selected alternative $j$, departure time $\tau$ and simulated travel times: $V^{\text{sim}}_{j}(\tau)$
  • alt_expected_utility: Logsum of departure-time choice for the selected alternative $j$ \[ \bar{U}_j \equiv \mathbb{E}_{\varepsilon}[\max_\tau U_j(\tau)] = \mu \ln \int_{t^0}^{t^1} e^{V_j^{\text{exp}}(\tau) / \mu} \text{d} \tau + \mu \cdot 0.577 \]
  • expected_utility: Logsum of alternative choice ("logsum of logsum") \[ \mathbb{E}_{\varepsilon}[\max_j U_j] = \mu \ln \sum_j e^{\bar{U}_j / \mu} + \mu \cdot 0.577 \]

Utility Indicators (4/4)

Which one to use (e.g., for cost-benefit analysis)?

  • utility: not really adapted when using random-utility models (the random perturbations $\varepsilon$ are omitted); recommended when using deterministic models (including models with drawn epsilons)
  • alt_expected_utility: intermediate indicator, useful in some special cases only
  • expected_utility: recommended when using random-utility models (it depends on the range of alternatives available, not just the realized choice: two identical agents always have the same expected_utility but they can have different utility if their uniform draws differ)

Trip Results

  • Parquet or CSV file
  • 1 row for each selected trip (road or virtual); 19 columns
  • 11 columns are specific to road trips

Route Results

  • Parquet or CSV file
  • 1 row for each edge taken during road trips; 6 columns
  • Detailed itinerary followed by the agents, as a list of edges with entry and exit time

Route Results

The route_results.{csv,parquet} output file allows to show the detailed itinerary of an agent.

Route Results

The route_results.{csv,parquet} output file allows to show a video of the vehicle movements.

Road-Network Results

Output Files

Three files for the road-network conditions (edge-level travel-time functions):

  • net_cond_sim_edge_ttfs.{parquet,csv}: last iteration, simulated
  • net_cond_exp_edge_ttfs.{parquet,csv}: last iteration, expected
  • net_cond_next_exp_edge_ttfs.{parquet,csv}: next iteration, expected

One extra file:

  • skim_results.json.zst: OD-level (expected) travel-time functions

METROPOLIS2 Fundamental Flow Diagram

Network Conditions

  • The network conditions consist in a travel-time function for each link and for each vehicle type
  • The travel-time functions are represented as piecewise-linear functions with a fixed interval $\delta$ between two breakpoints
  • Simulated network conditions: Network conditions observed, given some travel decisions (from the supply model).
  • Expected network conditions: Network conditions anticipated by the agents when taking travel decisions (in the demand model). They are used to compute road trips' travel times.

Network Conditions File Format

  • Parquet or CSV file
  • Number of rows: # edges × # breakpoints × # vehicle types
  • Departure-time and travel-time breakpoints for each edge and vehicle type
  • Departure-time breakpoints with simulated period [6 a.m., 10 a.m.] and recording interval 20 min.: [06:00, 06:20, 06:40, 07:00, 07:20, ..., 09:20, 09:40, 10:00]

Network Conditions Map

When merged with the edges' geometries, the network conditions can be plotted on a map.

Starting Simulation from Network Conditions

  • Default: use free-flow conditions as expected network conditions for the first iteration
  • Initial network conditions can be given as input
  • Input file format is the same as network conditions output file format

						{
								"input_files": {
										"agents": "agents.csv",
										"alternatives": "alts.csv",
										"trips": "trips.csv",
										"edges": "edges.csv",
										"vehicle_types": "vehicles.csv",
										"road_network_conditions": "net_cond_next_exp_edge_ttfs.csv"
								},
								"output_directory": "output",
								"period": [
										25200.0,
										28800.0
								],
								"road_network": {
										"recording_interval": 60.0,
										"spillback": false,
										"max_pending_duration": 0.0
								},
								"max_iterations": 100,
								"init_iteration_counter": 100,
								"saving_format": "CSV",
								"learning_model": {
										"type": "Exponential",
										"value": 0.4
								}
						}
parameters.json

Skim Results

  • Travel-time function for each origin-destination pair in the population input (road trips)
  • The travel-time functions are the one used in the demand model for the last iteration
  • File format: compressed JSON for now; Parquet or CSV in a future update

Task for Next Session

Session 5 Task

From the results of your simulation (Task of Session 4), create some relevant graphs (e.g., travel-time distribution, travel utility vs schedule utility as a function of departure times) or maps (e.g., congestion on links as a function of time, link flows).