5.3 Choosing Police & Medical Units on a Map: Routes, Travel Time & Closest Unit

Public safety telecommunicators are held accountable for every second that elapses between the initial 911 ring and the arrival of emergency units on scene. Resource allocation is not merely a matter of finding an available unit; it requires calculating travel times, assessing vehicle capabilities, evaluating traffic choke points, and selecting the optimal apparatus. A telecommunicator who understands response physics, speed dynamics, detour mathematics, and the critical distinction between straight-line distance and actual road network distance ensures that emergency resources arrive in the shortest possible timeframe.

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The Express Written Dispatcher Test

NTN describes it this way: "Test takers are presented with maps to assist in keeping track of three police units and two medical units. When new calls come in, the test taker decides which police and medical units to send, if any." Three phrases matter:

• Two kinds of units. A crime needs police and an injury or illness needs medical. Some calls need both, and some need neither right now.
• "If any." Sending nothing can be the right answer, for example when no unit shown is suitable for the call. Read the test's instructions for when this applies.
• Maps. Distance comes from the map in front of you, so the closest unit is the one with the shortest drivable route, not the shortest straight line.

Worked practice map (written for this guide, not an NTN item)

A river runs north-south through the map. The only bridge is at 5th Street. Streets are numbered from 1st Street at the south edge, one block apart.

New call: A cyclist has been struck by a car on the east bank at 1st Street. The driver stayed, and the cyclist is bleeding.

• Police. P3 is closest but is busy on a disturbance, so it stays. P1 is directly across the river, but its route runs 4 blocks north to the bridge, across, and 4 blocks back south: about 8 blocks. P2 drives 5 blocks south on the same bank. Send P2.
• Medical. M1 crosses the bridge and drives 4 blocks south: about 4 blocks. M2 is 9 blocks away. Send M1.
• Immediately? Yes. Someone is injured.

The trap in this map is P1, which looks nearest because it sits just across the water. The skill being tested is reading the route, not the gap.

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1. Kinematic Formulas & Mental Math Benchmarks

In dispatch operations, telecommunicators frequently perform rapid travel time estimations to coordinate converging units, establish perimeter containment, or update callers awaiting CPR assistance. The core travel time formula is:

$\text{Travel Time (minutes)} = \frac{\text{Distance (miles)}}{\text{Average Velocity (mph)}} \times 60$

Because dispatchers cannot open a spreadsheet during an active call, they memorize standardized Mental Math Benchmarks:

• 60 mph (Freeway / Rural Arterial): Exactly 1.0 minute per mile ($1\text{ min/mi}$). Traveling 7 miles takes exactly 7 minutes.
• 45 mph (Suburban Major Arterial): Exactly 1.33 minutes per mile ($4\text{ minutes for every }3\text{ miles}$). Traveling 6 miles takes 8 minutes ($6 \times 1.33 = 8\text{ minutes}$).
• 30 mph (Urban Commercial / Collector): Exactly 2.0 minutes per mile ($2\text{ min/mi}$). Traveling 3.5 miles takes 7 minutes ($3.5 \times 2 = 7\text{ minutes}$).
• 20 mph (Congested Core / Residential): Exactly 3.0 minutes per mile ($3\text{ min/mi}$). Traveling 2 miles takes 6 minutes.
• 15 mph (Heavy Snow / Severe Gridlock): Exactly 4.0 minutes per mile ($4\text{ min/mi}$). Traveling 1.5 miles takes 6 minutes.

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2. Deconstructing Total Emergency Response Time

Public safety performance standards measure the complete timeline of an emergency, known as Total Response Time, which has three parts:

+-----------------------------------------------------------------------------------+
|                             TOTAL RESPONSE TIME                                   |
+-----------------------+-------------------------+---------------------------------+
| 1. Processing Time    | 2. Turnout / Chute Time | 3. Travel Time                  |
| (Call Intake to Alert)| (Alert to Wheels Moving)| (Wheels Moving to On Scene)     |
| ~30 - 60 seconds      | ~30 - 90 seconds        | Variable by distance and speed  |
+-----------------------+-------------------------+---------------------------------+

1. Dispatch Processing Time (Call Intake to Dispatch): The interval from the initial 911 phone ring until the telecommunicator enters the incident into CAD and broadcasts the alert tones to field units. Fire and EMS performance standards set processing targets of about a minute for the most urgent calls.
2. Turnout Time (Chute Time): The interval between the dispatcher's broadcast of the alert and the moment the emergency vehicle's wheels begin rolling out of the station or patrol staging area.
   • Law Enforcement: Patrol officers already mobile in their cruisers have a turnout time of 15 to 30 seconds.
   • EMS and Fire Rescue: Personnel stationed in quarters require 60 to 90 seconds (the 2020 edition of NFPA 1710 set 60 seconds for EMS and 80 seconds for fire responses) to don structural firefighting gear, board the apparatus, and open bay doors.
3. Travel Time (Transit Time): The interval from wheels rolling until the unit calls "on scene" at the physical address.
4. Estimated Time of Arrival (ETA): Calculated as Current Time + Remaining Turnout Time + Travel Time.

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3. Response Modes: Code 3 vs. Code 1 Dynamics

The authorized response mode establishes the operational velocity and legal status of responding units:

Code 3 (Emergency / Hot Response)

• Definition: Transit utilizing audible warning sirens and flashing emergency lights (visual warning devices).
• Legal Privileges & Due Regard: Emergency vehicle operators are permitted to exceed posted speed limits, drive on roadway shoulders, and proceed past red traffic signals and stop signs. However, state vehicle codes strictly mandate that responders operate with due regard for the safety of all persons.
• The Intersection Friction Factor: An emergency vehicle cannot blast through a red light at 50 mph. The driver must decelerate to a complete or rolling stop, ensure cross-traffic has seen the emergency lights and yielded in all lanes, and then accelerate through the intersection. Because of frequent intersection stops, pedestrian congestion, and erratic civilian motorist reactions, average Code 3 travel speeds in dense urban areas rarely exceed 30 to 40 mph, even when posted speed limits are 35 mph. On open freeways or rural corridors, Code 3 speeds can reach 55 to 65 mph.

Code 1 (Routine / Cold Response)

• Definition: Non-emergency transit without sirens or flashing warning lights.
• Operational Rules: Units must adhere strictly to all posted speed limits, execute complete stops at all stop signs and red traffic signals, and yield right-of-way normally. Average urban travel speeds range from 18 to 25 mph.

Code 2 (Expedited / Silent Approach)

• Definition: Urgent response used in specific jurisdictions for in-progress property crimes (e.g., silent bank alarms, commercial burglaries). Units travel briskly but deactivate sirens several blocks prior to arrival to prevent alerting armed suspects, enabling officers to establish a silent tactical perimeter.

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4. Closest-Unit Selection: Euclidean vs. Network Routing Distance

A primary cognitive pitfall on emergency communications testing is the Euclidean Distance Fallacy:

• Euclidean (Straight-Line) Distance: The direct radial distance between two points measured across the surface of the earth ("as the crow flies"). Basic CAD Automated Vehicle Location (AVL) displays often sort available units based on simple radial distance.
• Network Routing Distance: The actual physical driving distance a vehicle must traverse following the legal street network, accounting for one-way streets, divided highways, elevation changes, and physical barriers.

The River Barrier Case Study

Consider an active structure fire at an industrial facility located on the East bank of a wide, unbridged river:

• Unit A (Patrol Cruiser): Stationed on the West bank, directly across the water from the fire. Unit A's AVL shows a Euclidean distance of only 1.2 miles. However, the nearest vehicle bridge is located 3.5 miles to the south. To reach the fire, Unit A must drive 3.5 miles south, cross the bridge, and travel 4.0 miles north along the east bank—a total street network distance of 7.5 miles. At an average speed of 30 mph, Unit A will take 15 minutes to arrive.
• Unit B (Engine Company): Stationed on the East bank, 3.5 miles north of the industrial facility along a continuous, direct four-lane arterial. Unit B's Euclidean distance is 3.5 miles (nearly triple Unit A's straight-line distance). However, its street network driving distance is also exactly 3.5 miles with zero bridge crossings. Traveling at 45 mph along the direct arterial, Unit B will arrive in 4.6 minutes ($3.5 \div 45 \times 60 = 4.67\text{ minutes}$).

If the dispatcher blindly assigns Unit A based on the CAD radius list, emergency arrival is delayed by over 10 minutes, potentially resulting in total structural loss and civilian casualties. Telecommunicators must constantly audit CAD recommendations against physical street network geography.

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5. Dynamic Detour Evaluation: Hold vs. Reroute Decisions

When a primary transit corridor is compromised by unexpected events (train crossing delays, water main breaks, construction barricades), dispatchers must evaluate whether units should wait or detour:

The Rail Crossing Decision

A freight train stops across a primary two-lane arterial. Experience indicates a stopped train switching cars takes 8 to 12 minutes to clear. The dispatcher identifies an alternate route utilizing a grade-separated overpass located 1.5 miles out of direction.

• Detour Distance: 1.5 miles out + 1.5 miles back = 3.0 additional miles.
• Detour Speed: 45 mph (Code 3 on secondary arterial).
• Detour Transit Time: $\text{Detour Time} = \frac{3.0\text{ miles}}{45\text{ mph}} \times 60 = 4.0\text{ minutes}$
• Operational Decision: Taking the 4-minute detour saves 4 to 8 minutes compared to waiting at the blocked crossing. The dispatcher immediately orders all responding units to divert to the overpass.

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6. Boundary-Adjacent Incidents & Mutual Aid Protocols

When high-priority emergencies occur along or directly adjacent to jurisdictional boundaries (city limits or county borders), dispatchers follow strict public safety priority rules:

• The Closest Unit Rule: The supreme operational priority is the preservation of life and property. If an armed assault or pediatric respiratory arrest occurs 200 feet outside a city border, and a city police cruiser or fire medic is 1 minute away while the responsible county unit is 12 minutes away, the city dispatcher must dispatch the city unit immediately.
• Automatic Aid vs. Mutual Aid:
  • Automatic Aid: A binding, pre-authorized inter-agency agreement where CAD systems communicate seamlessly across borders, and the closest emergency resource is dispatched automatically regardless of political boundaries.
  • Mutual Aid: A formal request for supplemental equipment or personnel made when an agency's internal resources are exhausted by a major disaster or specialized hazard (e.g., wildland task forces, HAZMAT teams).
• Concurrent Notification: While the closest unit is rolling to the boundary scene, the telecommunicator immediately contacts the neighboring jurisdiction's dispatch center via dedicated CAD-to-CAD data links or telephone tie-lines. The telecommunicator relays all call details, confirms the responding unit's ETA, and coordinates whether command will transfer to the jurisdictional agency upon their arrival.

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7. Practical Reference Tables

Speed, Distance, and Travel Time Lookup Matrix

Emergency Response Modes and Operational Characteristics

Straight-Line (Euclidean) vs. Road Network Distance Case Study