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 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 the same. For example, for a detector placed near the end of a 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.

Average Entry Headway Average Entry Headway (Detector Measure)

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

where

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

Time-mean (Spot) Speed (Detector Measure)

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

where

Space-Mean Speed (Link Measure)

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

where

Density

Density Calculation (Link Measure)

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

where

Density Calculation (Detector Measure)

Detector occupancy can be used to approximate density as follows.

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

where,

Relationship between Occupancy and Density

$$k=\frac{Percent Occupancy}{100} \times \frac{5280}{L_e} $$

where,

Percent Followers Percent Followers (Detector Measure) Percent Followers is the percent of vehicles designated as followers within simulation

$$PF=\frac{Followers}{Total Vehicles} \times 100$$ where, PF = percent followers in the analysis direction, Followers = the number of vehicles with headway $$\le$$ 2.5 seconds in SwashSim, NCHRP 17-65 Total Vehicles = total number of vehicles within the simulation duration

Follower Density Follower Density (Detector Measure) Follower Density is the density times the proportion of followers $$FD=\frac{PF}{100} \times \frac{v}{S}$$

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)

Acceleration Noise Acceleration Noise measures the standard deviation associated with successive deceleration and acceleration in an 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)".

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.

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

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 from traffic control devices such as stop signs, signals, etc. In order to determine the running time of a given network, the travel time of vehicles that were not included in a traffic-controlled queue anywhere along the length of the roadway are used.

Delay

Individual Vehicle Delay (Link Measure) $$Delay_{ij} = Link Travel Time_{ij} – \frac{LinkLength_{j}}{Desired Speed_{i}}$$

where, where, $$Link Entrance Time =$$ time when vehicle i entered link j (s) $$Link Exit Time =$$ time when vehicle i exited link j (s)

Total Vehicle Delay (Link Measure)

$$TotalDelay_{j}=\sum_{i=1}^\N\ Delay_{ij}$$

where,

Average Vehicle Delay (Link Measure)

$$AverageDelay_{j}=\frac{TotalDelay_{j}}{TotalVehicles_{j}}$$ where,

Note about Control Delay: Control delay is the portion of the total delay attributed to the influence of a traffic control (signal, stop/yield sign). Care must be taken when selecting the links from which to extract delay to use for control delay purposes, as control delay consists of deceleration delay and acceleration delay, in addition to stop delay.

Queue Length Queue Length (Link Measure)

$$Avg. Queue Length_{j} = \frac{Total Delay_{j}}{Simulation Duration}$$

where,

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,

Stop Rate Stop Rate is the average number of stops per hour. (Link Measure)

$$Stop Rate $$(stops/h) = $$Total Stops/Simulation Duration$$(h) where,

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’. 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