15.1 Travel Time, Delay, & Intersection Queue Studies

15.1 Travel Time, Delay, & Intersection Queue Studies

PTOE Exam Focus: Travel time, delay, and queue studies form the empirical foundation of traffic operations analysis in Domain 5. Candidates must master test vehicle data collection methods (particularly the floating car and moving observer techniques), understand GPS probe telemetry metrics (Travel Time Index, Buffer Index, Planning Time Index), distinguish between control delay and stopped delay, analyze Queue Accumulation Polygons (QAPs), and size turn bay storage lengths using 95th-percentile queue formulations.

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1. Objectives & Scope of Travel Time & Delay Studies

Travel time and delay studies evaluate the quality of traffic movement along an arterial corridor or network by determining the time required to traverse specific segments, the locations and durations of operational delays, and overall running versus travel speeds.

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|                    FUNDAMENTAL SPEED & TIME DEFINITIONS                           |
|                                                                                   |
|  • Travel Time (T): Total elapsed time from origin to destination, including all  |
|    stopped and operational delays:  T = Running Time + Total Delay                |
|  • Running Time (T_r): Time the vehicle is in physical motion: T_r = T - Delay    |
|  • Travel Speed (S_t): Segment length divided by total travel time: S_t = L / T   |
|  • Running Speed (S_r): Segment length divided by running time: S_r = L / T_r     |
|  • Control Delay: Total delay attributable to a traffic control device            |
|    (deceleration, stopped delay, queue move-up time, and acceleration).           |
+-----------------------------------------------------------------------------------+

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2. Test Vehicle Data Collection Techniques

Direct field measurement of travel times along corridors traditionally relies on instrumented test vehicles driven through the study segment using one of four standardized driving protocols:

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|                   TEST VEHICLE DRIVING PROTOCOLS                            |
|                                                                             |
|   1. Floating Car Technique: Driver attempts to pass as many vehicles as    |
|      pass the test vehicle (net overtakes = 0). Represents stream median.   |
|   2. Average Speed Technique: Driver travels at the estimated average speed |
|      of the surrounding traffic stream without tracking overtakes.          |
|   3. Maximum Speed Technique: Driver operates at the posted speed limit or  |
|      maximum safe speed unless impeded by congestion or traffic controls.   |
|   4. Moving Observer Method (Wardrop): Test vehicle makes round trips to     |
|      count oncoming, overtaking, and overtaken vehicles to derive q and t.  |
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The Moving Observer Method (Wardrop's Method)

The moving observer method (developed by Wardrop and Charlesworth) allows a single test vehicle to determine both the average traffic flow rate ($q$) and the average travel time ($\bar{t}$) for a stream of traffic by making round trips along a section of length $L$:

1. Trip Against the Stream (Opposing Direction): The test car travels against the stream being surveyed (travel time $t_a$) and counts all oncoming vehicles ($x$).
2. Trip With the Stream (Survey Direction): The test car travels in the direction of the stream (travel time $t_w$), counting the number of vehicles that overtake the test car ($m_p$) and the number of vehicles the test car overtakes ($m_o$). The net overtakes are $y = m_p - m_o$.

$\text{Traffic Flow Rate: } q = \frac{x + y}{t_a + t_w}$ $\text{Average Travel Time: } \bar{t} = t_w - \frac{y}{q}$

Where:

• $q$ = Traffic volume/flow rate on the surveyed stream (veh/min or veh/h)
• $x$ = Number of vehicles met while traveling against the stream
• $y = m_p - m_o$ = Net vehicles passing the test car while traveling with the stream
• $t_a$ = Travel time of test car traveling against the stream (min or hr)
• $t_w$ = Travel time of test car traveling with the stream (min or hr)
• $\bar{t}$ = Mean travel time of the traffic stream (min or hr)

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3. Automated Methods & GPS Probe Telemetry

Modern traffic operations increasingly utilize automated sensing and passive telemetry in place of or in combination with test vehicle runs:

A. License Plate Matching / ALPR

Automatic License Plate Recognition (ALPR) cameras or manual observers record vehicle license plates and timestamps at entry and exit stations. Travel time is calculated as $T = t_{\text{exit}} - t_{\text{entry}}$. Spurious matches (e.g., intermediate stops or deliveries) are filtered using statistical outlier algorithms.

B. Crowdsourced GPS Probe Data & Reliability Indices

Commercial data providers (e.g., INRIX, HERE, TomTom) aggregate high-frequency GPS probe telemetry from connected vehicles and mobile navigation devices. Transportation engineers use this data to calculate system reliability metrics:

1. Travel Time Index (TTI): Ratio of peak-period travel time ($T_{\text{peak}}$) to free-flow travel time ($T_{\text{ff}}$): $\text{TTI} = \frac{T_{\text{peak}}}{T_{\text{ff}}}$
2. Planning Time Index (PTI): Ratio of the 95th-percentile travel time ($T_{95}$) to free-flow travel time ($T_{\text{ff}}$), representing total travel time a commuter must budget to arrive on time $95%$ of the time: $\text{PTI} = \frac{T_{95}}{T_{\text{ff}}}$
3. Buffer Index (BI): Percentage of extra buffer time needed above the average travel time ($T_{\text{avg}}$) to ensure on-time arrival $95%$ of the time: $\text{BI} = \frac{T_{95} - T_{\text{avg}}}{T_{\text{avg}}} \times 100\%$

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4. Delay Typologies at Interrupted Flow Facilities

In Highway Capacity Manual (HCM) and PTOE terminology, delay is classified into distinct functional categories:

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|                        DELAY TYPOLOGY CLASSIFICATION                        |
|                                                                             |
|  1. Control Delay (d): Delay caused by the traffic control mechanism        |
|     • Initial Deceleration Delay (d_dec)                                    |
|     • Stopped Delay (d_stop): Vehicle completely stationary (v = 0)         |
|     • Queue Move-Up Time (d_mu): Creeping forward in queue                  |
|     • Final Acceleration Delay (d_acc): Accelerating back to cruising speed |
|                                                                             |
|     d = d_dec + d_stop + d_mu + d_acc                                       |
|     Empirical rule: d_stop ≈ 0.65 to 0.85 × d                               |
|                                                                             |
|  2. Geometric Delay: Delay induced by roadway alignment or turning radii    |
|     (e.g., sharp curves, roundabout geometry) independent of traffic.       |
|  3. Incident / Operational Delay: Delay caused by temporary disruptions,    |
|     stalls, crashes, or downstream spillback.                               |
+-----------------------------------------------------------------------------+

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5. Intersection Queue Dynamics & Queue Accumulation Polygons

Queue analysis evaluates the accumulation and dissipation of stopped vehicles on an intersection approach during signal cycles:

A. Key Queue Parameters

• Back of Queue ($Q_b$ / Maximum Queue): The furthest point upstream reached by the rear of the last vehicle joining the queue during a cycle. Sizing turn pockets based on $Q_b$ prevents turn lane overflow into through lanes.
• Residual Queue ($Q_1$ / Initial Queue): Unserved queued vehicles remaining at the end of the green interval, indicating cycle failure and oversaturated conditions ($v/c > 1.0$).

B. Queue Accumulation Polygon (QAP)

A Queue Accumulation Polygon (QAP) plots the cumulative arrival profile $A(t)$ and departure profile $D(t)$ over a signal cycle of duration $C$ (seconds):

• Arrival slope = Uniform arrival rate ($v$ in veh/s).
• Departure slope during red = $0$.
• Departure slope during green = Saturation flow rate ($s$ in veh/s).
• The vertical distance between $A(t)$ and $D(t)$ represents the instantaneous queue size $Q(t)$.
• The area enclosed between the arrival and departure curves equals the total aggregate delay (vehicle-seconds or vehicle-hours) experienced by all vehicles during the cycle.

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6. Sizing Storage Pocket Lengths (95th-Percentile Queue)

Turn lane storage bays (left-turn or right-turn pockets) must accommodate the 95th-percentile queue ($Q_{95}$) plus a safety factor to prevent blockage:

$L_{\text{storage}} = Q_{95} \times S_L$

Where:

• $S_L$ = Average vehicle queue spacing ($25\text{ ft/veh}$ standard; $30\text{ to }40\text{ ft/veh}$ if heavy truck percentage is high).
• $Q_{95}$ = 95th-percentile number of queued vehicles.
• Under Poisson arrival assumptions with uniform signal cycling, an empirical approximation widely accepted in AASHTO and DOT design standards is: $Q_{95} \approx 1.5 \text{ to } 2.0 \times N_{\text{avg}}$ where $N_{\text{avg}} = \frac{V_{\text{turn}} \times C}{3600}$ is the average number of arriving vehicles per cycle.

Travel Time, Delay, & Queue Measurement Methodologies Comparison