Busy Hour Traffic & Erlang Converter

1. The Physics of Teletraffic Measurement: Defining the Erlang

Telecommunications networks transmit information in discrete temporal sessions—voice calls, video conferences, or packetized RTP streams. Unlike mechanical transportation networks where capacity is measured in physical vehicles per hour, telephony capacity is defined by the product of call arrival frequency and temporal session duration.

In 1946, the International Telephone and Telegraph Consultative Committee (CCIF, the predecessor of the ITU-T) formally adopted the Erlang (E) as the international standard unit of telephone traffic intensity, named in honor of Danish mathematician and teletraffic pioneer Agner Krarup Erlang.

The Erlang is a pure, dimensionless unit representing the continuous occupancy of one telecommunications circuit, channel, or service facility over a specified observation interval T. Formally:

where:

• A is the traffic intensity in Erlangs.
• N is the number of call arrivals during observation window T (e.g., Busy Hour Call Attempts / BHCA when T = 3,600 seconds).
• h is the average holding time (AHT) per call, expressed in the same temporal unit as T.
• λ is the mean arrival rate of calls per unit time (λ = N / T).

Physical Interpretation: Exactly 1.0 Erlang represents one circuit held busy for 100% of the observation period. In dimensional terms, 1.0 Erlang equates to 1 call-hour per hour, 60 call-minutes per hour, or 3,600 call-seconds per hour. A primary rate interface (PRI) E1 span with 30 B-channels carrying 22.5 Erlangs operates at an instantaneous physical trunk occupancy of ρ = 22.5 / 30 = 75%.

2. North American Legacy Units: Centum Call Seconds (CCS)

Before the global standardization of the Erlang, the North American telecommunications industry (AT&T, Bell Operating Companies, and Bell Laboratories) quantified traffic volume in Centum Call Seconds (CCS), frequently termed "Hundred Call Seconds" (from the Latin centum meaning one hundred).

The 100-Second Scanning Cycle: The technical origin of CCS traces back to early electromechanical step-by-step (Strowger) and crossbar central office switches. Automatic traffic registers utilized rotary mechanical scanners that stepped across trunk groups once every 100 seconds, recording a peg count for every circuit found busy. One registered hit represented one circuit occupied for 100 seconds—defined as 1 CCS.

The Mathematical Equivalence to Erlangs:

• One standard hour contains exactly 3,600 seconds.
• A single circuit occupied continuously for one hour generates 3,600 call seconds of traffic volume.
• Dividing by the 100-second scanning interval: 3,600 ÷ 100 = 36 CCS.

When sizing circuits on private enterprise networks or legacy PBX equipment in North America, trunk loads are often still reported in CCS/hour. Modern softswitches and session border controllers (SBCs) native to IP telephony report traffic in Erlangs or BHCA, requiring engineers to execute instantaneous dimensional conversions.

3. The Busy Hour Concept: ITU-T Recommendations E.490 & E.500

Telephone traffic varies dramatically across the 24 hours of a day. Dimensioning a telecommunications exchange using 24-hour average traffic will severely underestimate peak voice demand, leading to catastrophic daytime blocking. Conversely, sizing for an absolute isolated annual spike (such as Mother's Day or Midnight on New Year's Eve) creates economically unviable over-capacity.

Telecommunications networks are dimensioned around the Busy Hour (BH)—the continuous 60-minute window within a 24-hour cycle during which network traffic volume reaches its sustained maximum.

The International Telecommunication Union (ITU-T) establishes formal statistical methodologies for identifying and measuring the busy hour in Recommendations E.490 and E.500:

1. Time-Consistent Busy Hour (TCBH): The continuous 60-minute interval that begins at the exact same clock time each day (e.g., 10:00 AM to 11:00 AM) and yields the highest average traffic load over a 20-day or 30-day reporting window. TCBH is the carrier-grade gold standard for trunk group dimensioning because it eliminates transient, isolated anomalies.
2. Fixed Daily Measurement Hour (FDMH): A predetermined administrative 60-minute window (e.g., 2:00 PM to 3:00 PM) selected for recurring operational surveillance and billing verification.
3. Bounce / Floating Busy Hour (BBH): A dynamic measurement where switch telemetry is divided into 15-minute intervals, and the continuous 60-minute span exhibiting the absolute maximum volume on any given day is captured, regardless of what time it commences.
4. Extreme Value Weekday (EVW): The highest single busy hour observed across an entire week or month, utilized by mission-critical emergency dispatch centers (E911) to assess network resilience under stress.

4. Call Completion Ratio (CCR / ASR) and Unsuccessful Call Attempts

In practical telecommunications engineering, not every Busy Hour Call Attempt (BHCA) results in a completed, two-way conversation. Raw BHCA metrics capture all dialed attempts, including network busy signals, unanswered calls, abandoned calls, and wrong numbers.

The proportion of call attempts that successfully transition to an answered state is defined as the Call Completion Ratio (CCR) or Answer-Seizure Ratio (ASR):

In modern commercial telephony, typical CCR values hover between 65% and 75%. Sizing voice media channels using raw BHCA without accounting for CCR creates significant error:

• Completed Conversations (CCR × BHCA): Occupy bearer channels and media paths (RTP/G.711) for the full Average Holding Time (h), typically 120 to 240 seconds.
• Unsuccessful / Abandoned Attempts ((1 - CCR) × BHCA): Hold signaling equipment, PSTN circuits, and media gateways for only 10 to 20 seconds during ringing, ring-no-answer, or busy tone generation before channel teardown.

Rigorous capacity planning partitions offered traffic into productive conversation Erlangs and transient signaling Erlangs. This ensures media gateways and SIP trunk licenses are not over-purchased, while signaling processors (SIP Proxies, SBCs, Call Managers) are properly engineered for peak session setup rates.