Performance Measures

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Performance measure statistics are only calculated for the simulation duration time, not during the warm-up time. Therefore, the warm-up time should be sufficient to fill the network with vehicles so that performance measure calculations do not include simulation time when parts of the network are empty. Performance measures are calculated on either a point (detector) basis or a link basis. Whereas all vehicles that cross a detector within the simulation duration time are are factored into the performance measure(s) calculation, for link-based measures, only vehicles that both enter and exit a link within the simulation duration time are considered. Thus, in addition to any difference due to point- versus space-based measures, the sets of vehicles included in the respective calculations will typically not be exactly the same. For example, for a detector placed near the end of long link, some vehicles may enter the link during the warm-up time and cross the detector during the simulation duration time. These vehicles would not be factored into the link performance calculation because they only exited, not both entered and exited, the link during the simulation duration time.

Flow Rate

Point (detector) measurement

$$q=\frac{n}{t}$$

where

Link measurement

$$q=\frac{n\times 3600/t}{NL}$$

where

Also equivalent to Link Density (veh/h/ln) $$\times$$ Link Average Speed (mi/h).

Average Speed

Space-Mean Speed (Link Measure)

$$S=\frac{VMT}{VHT}$$

where

Time-mean (Spot) Speed (Detector Measure)

$$S=\frac{1}{N} \sum_{i=1}^\N\ u_{i}$$

where

Average Headway Average Entry Headway (Detector Measure)

$$\bar{h}=\frac{1}{N} \sum_{i=1}^\N\ h_{i}$$

where

Percent Followers Percent Follower (Detector Measure)

$$PF=\frac{number of vehicles with headway \le 2.5 s}{total vehicles} \times 100$$

Follower Density Follower Density (Detector Measure)

$$FD=\frac{PF}{100} \times \frac{V}{S}$$

where, FD = follower density in the analysis direction (followers/mi/h), PF = Percent Followers in the analysis direction,  V = flow rate in analysis direction (veh/h/ln), S = average spot speed in analysis direction (mi/h)

Lane Occupancy

Density Calculation

$$D=\frac{v}{S}$$

where,

Detector Occupancy

$$Percent Occupancy =\frac{To}{T} \times \ 100 $$

where,

Relationship between Occupancy and Density

$$k=\frac{Percent occupancy}{100} \times \frac{5280}{Le} $$

where,

Acceleration Noise Acceleration Noise measures the standard deviation associated with successive deceleration and acceleration in a uninterrupted flow environment. It provides an indication of the smoothness of traffic flow.

Where:

See LinkResults.csv output file, with columns labeled "Accel Noise-Mean Zero (ft/s2)" and "Accel Noise-Mean NonZero (ft/s2)".

Saturation Flow Rate

Saturation Flow Rate (Detector Measure)

$$h_{sat}=\frac{T_{i}-T_{4}}{i-4}$$

$$SLT=T_{4} - 4h_{sat}$$

$$s=\frac{3600}{h_{sat}}$$

where,

Queue Length Queue Length

$$Avg. Queue Length = \frac{Total Delay}{Simulation Duration}$$

where,

Signal Delay $$Avg. Control Delay (s/veh) = \frac{Total Delay (veh-s)}{Total Vehicles}$$ $$Total Delay (veh-s) = ∑Individual Vehicle Delay (s)$$ $$Individual Vehicle Delay (s) = Link Travel Time (s) – LinkLength (ft) / Vehicle Desired Speed (ft/s)$$ $$Link Travel Time (s) = Link Exit Time (s) - Link Entrance Time (s) $$ $$Vehicle Desired Speed (ft/s) = LinkFreeFlowSpeed (ft/s) × Vehicle Driver Type Desired Speed Multiplier$$

Stop Rate $$Stop Rate (stops/h) = Total Stops/Simulation Duration (h)$$ Notes about Total Stops measure: If a vehicle stops one or more times on the link, it only gets counted as one stop. In the case of cycle failures, this number will likely not reflect the actual number of stops. To be counted as a stop, SwashSim only considers the ‘StoppedInQueue’ status, not ‘SlowingInQueue’ or ‘QueueDischarge’.

Travel Time

Detector or link measurement

The travel time of a vehicle is the total time of movement between two points, including any time of delay that may have occurred from traffic lights, stop signs, etc. to reach a destination.

$$\bar{TT}=\sum_{i=1}^\N\ TT_{t}$$

where

Also,

$$\bar{TT}=\frac{LinkLength}{AvgSpeed}$$

where

Running Time

The running time of a vehicle is the time spent in motion as it travels between specific stations on a given traffic network. Running time will not include any delays that vehicle may encounter. In order to determine the running time of a given network, the travel time of vehicles that were not included in a queue anywhere along the length of the roadway are used. Vehicle-Hours-Traveled (VHT) $$VHT=V\times AnalysisPeriodDuration\times TravTime_{Avg}$$ The above are specific to HCM Freeway Facility methodology, where the variables are as defined below. where Alternate Calculations $$VHT=\sum_{i=1}^\N\ TT_{i}$$ where See LinkResults.csv output file, columns V & W Vehicle-Hours-Delayed (VHD) $$Delay=TravTime_{Avg}-TravTime_{FF}$$ $$VHD=(TravTime_{Avg}-TravTime_{FF})\times V\times AnalysisPeriodDuration$$ where

Vehicle-Miles-Traveled (VMT) $$VMT=V\times AnalysisPeriodDuration\times Length$$ The above are specific to HCM Freeway Facility methodology, where the variables are as defined below. where Alternate Calculations $$VMT=N\times Linklength$$ where See LinkResults.csv output file, columns V & W

Emissions and Fuel Consumption VSP-based emissions/fuel use calculations OBD-based emissions/fuel use calculations