Testing Customer Patience with the Erlang A Formula

In our last blog, we went into detail on Erlang C; the formula commonly used for calculating the number of agents needed to service a queue of a given size. Erlang C is at the heart of contact center service levels, but there’s another formula that adds another level of depth to our analysis; the Erlang A formula.

In short, Erlang A goes one step further than Erlang C, in that it adds additional depth to its portrait of the customer. It measures customer patience.

How is this done, how does it interact with the original Erlang C calculation, and how can you integrate its insights into your contact center operations? Is the sequel, for once, better than the original? Read on to discover more.

Before we continue, optimizing contact center performance depends on more than Erlang A. To go in-depth on contact center performance metrics, download Content Guru’s whitepaper: Keeping Up With the KPIs: The Contact Center KPIs Key to Outstanding CX.

What is Erlang A?

Erlang A was developed thirty years after the original Erlang C, in 1946, by Swedish mathematician, Cony Palm. (In addition to Erlang A and C, there is also a secret sibling, Erlang B, though this is not relevant to the operation of modern contact centers.)

Erlang C, whilst essential, missed out on a critical aspect of customer behavior; customer patience. It assumed that, once a customer queued up, they would remain in the queue until their call was answered. This is obviously not true for the real world. Customers run out of patience and abandon their calls. (A stands for abandons. See? Now we’re starting to appreciate the mystery of the thing.)

Erlang A offers a number of crucial benefits that Erlang C fails to account for:

  • By factoring in customer patience, you can better tailor contact center performance to your specific industry and need. Different types of organizations will experience different kinds of customer behavior – Erlang A allows you to account for that.

  • Erlang A represents to first step toward a focus on Customer Experience (CX). Where Erlang C assumed that customers would sit in queues, suffering as they must, Erlang A appreciates that customers are individuals, who’ll abandon calls when they feel ignored.

Erlang A, then, is a staple of the modern contact center. But how do we go about calculating it?

Calculating the Erlang A Formula

To factor abandon rate into the Erlang C formula, Cony Palm brought together the original formula with the mathematics of Andrey Markov. Markov had discovered a number of formulae surrounding ‘birth and death’ processes. In this case, ‘birth’ is joining the queue, ‘death’ leaving it.


The major difference between C and A is that Erlang A requires you to enter an ‘average patience’ value, in order to calculate the likelihood of a customer dropping out of the queue.

Average Patience

Average patience is the value at which 50% of your customers abandon their calls. This is simple to calculate; simply plot the percentage of abandoned calls against time, and you’ll get a value to input here.

This is where Erlang A allows for personalization; each contact center will have a different average patience value. A retailer, for instance, would likely see customers with less willingness to queue than a government agency.

Tools for Calculating Erlang A

If you thought Erlang C was difficult, Erlang A adds another level of complexity on top of that.

Even when you understand the mathematics behind the formula, calculating the additional value of Average Patience would prove an extra challenge. The best way to approach Erlang A is through an automatic calculator, letting you input the basic values, in order to calculate customer patience.

Such a solution would offer:

  • Predictive demand, using historic data on average customer patience to calculate abandon rates, then building on that data to create an accurate prediction of contact demand.

  • Automatic scheduling, leveraging the Erlang A to schedule enough agents to meet a given level of customer demand, ensuring that no customer has to wait longer than their average patience, reducing abandon rates.

  • Flexible reports, combining Erlang A and Erlang C with other metrics of customer experience quality, for a complete overview of contact center performance.

Moving Beyond Erlang A

Erlang A is a step beyond C. It offers a new level of complexity to demand forecasting, but it’s not the only contact center performance metric. To get a complete overview of your customer contact, you need to combine Erlang A with metrics that measure the quality of Customer Experience.

  • Customer Satisfaction (CSAT) - Customer satisfaction begins with a simple question, ‘How satisfied are you with your experience?’ From here, customers respond on a scale from ‘very dissatisfied’ to ‘very satisfied’. These results fall on a scale of 1 to 10, from which you can calculate an average score across various populations, anywhere between 1 and 100.

  • Net Promoter Score (NPS)Net Promoter Score doesn’t just measure customer satisfaction, it measures customer advocacy. By asking which customers are likely to recommend your business, it serves as an effective indicator of which customers are likely to stick by your side in the long run.

  • Value Enhancement Score (VES) – A relatively new metric, VES asks two questions, ‘How successfully were you able to use our product/service?’, and, ‘How confident are you with your purchase?’ In answering these questions, the customer gives their opinion on both your business and the impression conveyed by your customer service.

  • Customer Effort Score (CES)CES measures how much effort a customer had to put in to reach a solution to their problem. Friction within your customer service estate, confusion on the part of agents, or a failure to resolve a problem all lead to poor Customer Effort Score.

Every metric offers something different; a new perspective on a complex problem. And the more viewpoints you get, the deeper an insight you can draw. To truly perfect customer contact, you need complete contact center transparency.

Erlang A Made Easy with storm®

Erlang A is just one step toward true contact center transparency. To achieve that, you need a complete reporting solution. storm® VIEW™ brings every metric of contact center performance into a single, flexible interface. Users can pick from a pre-made range of metrics, or design their own custom KPIs. This data can be displayed on real-time dashboards and wallboards, or brought into shareable reports.

Content Guru’s Workforce Engagement Management (WFM) solution, storm WFM™ takes this one step further to offer automated scheduling, AI-backed demand prediction, and deep contact center performance insights, down to the level of the individual agent. WFM removes the complex formula, democratizing CX and giving you direct control of your Customer Experience. 

Want to learn more about key Customer Experience metrics and contact center KPIs? Download Content Guru’s whitepaper: Keeping Up With the KPIs: The Contact Center KPIs Key to Outstanding CX.