Erlang (E): Telecommunications Traffic Intensity

Introduction

The erlang (symbol E) is a dimensionless unit representing traffic intensity in telecommunications. One erlang equals one resource (such as a voice channel) being continuously occupied for a specified interval, typically one hour. Fractional erlangs describe average utilisation; for example, 0.3 E indicates a channel occupied 30% of the time. The unit enables planners to size switching systems, trunk groups, and contact centres to meet target service levels under stochastic demand.

Definition and Queueing Foundations

Traffic intensity is defined as A = λ × h, where λ is the average arrival rate (calls per unit time) and h is the average holding time (duration). When λ is expressed in calls per second and h in seconds, the product is dimensionless and equals erlangs. Queueing models, notably Erlang B (loss systems) and Erlang C (waiting systems), use this intensity to estimate blocking probability or waiting time given a finite number of servers. Erlang B assumes no queue: blocked calls are cleared. Erlang C allows waiting and computes average delay and probability of delay.

Modern traffic engineering extends these formulas to multi-service systems, incorporating priority classes, retrials, and time-varying demand. However, the core erlang metric remains a foundation, translating raw telemetry into actionable capacity metrics that align with SI timekeeping standards.

Historical Perspective

Agner Krarup Erlang, a Danish engineer and mathematician at the Copenhagen Telephone Company, introduced the concept in the early twentieth century. His 1909 paper on telephone exchange capacity analysed call arrivals as a Poisson process and laid the groundwork for modern queueing theory. The erlang unit quickly became indispensable for dimensioning circuit-switched networks as telephony expanded throughout Europe and North America. Mid-century innovations such as crossbar and electronic switching systems continued to rely on erlang-based traffic forecasts for investment and operations planning.

With the advent of digital telephony, mobile networks, and packet switching, the erlang concept adapted to new technologies. While IP networks often use bits per second to describe traffic, erlang analysis still informs voice and video capacity planning, especially where guaranteed quality of service is required. Contact centres and cloud telephony services adopt erlang calculations to staff agents, allocate virtual trunks, and meet service-level agreements.

Key Concepts for Practitioners

Grade of Service Targets

Grade of Service (GoS) quantifies acceptable blocking or waiting probabilities. Public switched telephone networks traditionally target 1% to 2% blocking (GoS = 0.01 to 0.02) during busy hour conditions. Designers use erlang charts or software to determine the number of circuits required to meet these targets given forecast traffic.

Busy Hour and Traffic Measurements

Traffic is usually measured in the busy hour, the one-hour period with the highest average load over a day. Time-of-day variations, seasonality, and promotional campaigns can shift busy-hour demand, so analysts monitor multiple intervals and update erlang forecasts accordingly. Accurate time synchronisation ensures that call detail records and network counters align with timekeeping standards.

Multimedia and Packet Networks

In Voice over IP (VoIP) and multimedia systems, erlangs coexist with throughput metrics. Engineers map erlang occupancy to bandwidth using codec bit rates, packetisation intervals, and overhead factors. This integration enables unified capacity planning that considers both channel occupancy and data throughput.

Applications

Mobile Networks: Operators design radio access networks and core switching with erlang-based demand forecasts, balancing spectrum efficiency with quality requirements. Small cell deployments and distributed antenna systems rely on local erlang estimates to justify investments and optimise handover performance.

Contact Centres: Workforce management teams convert call volume forecasts into erlangs to calculate staffing needs using Erlang C models, factoring in target service levels and shrinkage. Cloud-based contact centres allocate virtual agents and licenses based on erlang demand, ensuring cost-effective scaling.

Cloud and API Services: Although measured in requests per second, these services adopt erlang-like utilisation metrics to quantify concurrency. Engineers translate utilisation into erlangs to apply familiar queueing formulas when designing autoscaling policies and resilience strategies.

Importance for Modern Network Planning

The erlang remains relevant because it expresses service demand independently of specific technology implementations. It enables apples-to-apples comparison between legacy TDM systems and modern IP-based architectures. Reporting utilisation in erlangs fosters clear communication between network engineers, finance teams, and regulators overseeing service quality.

Incorporating erlang metrics into dashboards and capacity reviews helps organisations anticipate congestion, allocate capital efficiently, and maintain customer satisfaction. When combined with signal level and voltage measurements, erlang analysis supports holistic performance management.

Further Resources

Expand your telecommunications toolkit with the joule, watt, and siemens explainers. These resources reinforce how energy, power, and conductance intersect with traffic intensity in communication networks.