The Evolution of Erlang Formulas in Workforce Management

 For more than a century, Erlang formulas have been at the heart of call center planning, traffic engineering, and workforce management.

Developed by Danish mathematician A.K. Erlang in the early 1900s, these models help us answer a critical question: How many agents or lines do we need to handle demand while maintaining service quality?

Over time, the formulas have evolved to reflect changes in customer behavior, technology, and the complexity of service operations. Let’s break down the journey from Erlang B to O.

Erlang B – Blocked Calls Are Lost
Use case: Telephone networks and trunk sizing.
Assumption: If all lines are busy, the next call is blocked and lost (no waiting).
Why it matters: Useful for telecom engineering, emergency lines, and systems without queuing.

Erlang C – Everyone Waits
Use case: Traditional call centers.
Assumption: Calls never get blocked, customers wait indefinitely, and no one abandons.
Why it matters: Helps forecast staffing to achieve service levels (e.g., 80% of calls answered in 20 seconds).

Erlang A – Abandonment Model
Use case: Modern contact centers with measurable abandonment rates.
Assumption: Customers may leave the queue after waiting too long.
Why it matters: More realistic than Erlang C, avoiding overstaffing by accounting for customer patience.

Erlang X – The Extended Model
Use case: Omnichannel, complex environments.
Assumption: Extends Erlang A by including retries, redials, and multi-channel interactions.
Why it matters: Reflects today’s customer behavior across calls, chat, and digital channels.

Erlang O – Overhead Volatility Optimization
Use case: Volatility caused by unpredictability in today's contact centers.
Assumption: The Power of One shows the significant impact of having one less agent on service levels, wait times, abandonments, occupancy, telecom load, EX and CX, thus plan for life's surprises by staffing to higher levels of overhead to account for business volatility and unplanned shrinkage, and deploying real-time automation to transform agent idle time into productive learning and development time.
Why it matters: A new staffing model that addresses the limitations of traditional models like Erlang-C and Erlang-A, which often break down under the operational realities of today's contact centers.

The progression from Erlang B to Erlang O reflects the evolution of our industry from simple telephone lines to today’s omnichannel, digital-first ecosystems.

Each model brings us closer to realism:

B = Busy signals
C = Unlimited waiting
A = Abandonment included
X = Asynchronous & concurrency
O = Overhead volatility optimization

In your professional opinion, which Erlang model is most important for WFM planning?