Erlang A (also known as the Abandonment Model) is an extension of the Erlang C queuing model, designed to account for customer abandonment in call centres or similar service environments. Unlike Erlang C, which assumes customers will wait indefinitely in a queue, Erlang A incorporates the reality that some customers may abandon their calls if their waiting time exceeds their patience.
Named after Danish mathematician Agner Krarup Erlang, who laid the foundation of queuing theory, Erlang A is a more advanced tool for workforce planning and service management, particularly in environments where abandonment is a significant concern.
Historical Development of Erlang Models
The Erlang models were pioneered by Agner Krarup Erlang in the early 20th century while studying telephone networks for the Copenhagen Telephone Company. Erlang’s research focused on understanding how to optimise the resources needed to handle fluctuating call volumes. His work formed the basis of queuing theory and introduced models like Erlang B (for systems without waiting queues) and Erlang C (for systems with waiting queues).
Conny Palm, a Swedish mathematician, extended Erlang’s work in the 1940s by introducing customer patience and abandonment into the queuing theory. Palm’s contributions marked a significant evolution of the Erlang C model, leading to the creation of Erlang A. By accounting for human behaviour—specifically, the tendency of callers to abandon their calls—Palm made the model more applicable to real-world situations, particularly in call centres and customer service operations.
Key Features of Erlang A
Erlang A builds upon Erlang C by incorporating customer patience, typically modelled as an exponential distribution. This allows it to calculate metrics like:
- Abandonment Rate: The percentage of customers who leave the queue before being served.
- Queue Length with Abandonment: The adjusted queue size after considering that some customers will not wait.
- Average Waiting Time: The expected waiting time for customers who remain in the queue.
- Service Levels: The percentage of calls answered within a specific time frame, factoring in the likelihood of abandonment.
Inputs to Erlang A
Erlang A requires the following inputs:
- Call Arrival Rate (λ): The number of calls arriving per unit of time.
- Average Handling Time (T): The average duration of an interaction with an agent.
- Number of Agents (N): The number of agents available to answer calls.
- Patience Rate (θ): The rate at which customers abandon the queue, typically derived from historical data.
Outputs of Erlang A
The model provides several useful outputs for planning and decision-making:
- Probability of Abandonment: A measure of how many customers will leave the queue before being served.
- Average Queue Length: The number of customers waiting in the system after factoring in abandonment.
- Agent Utilisation: The proportion of time agents spend actively engaged with customers.
- Service Levels: An adjusted view of service level performance, considering both served and abandoned calls.
Limitations of Erlang A
- Complexity: Compared to simpler models like Erlang C, Erlang A involves more parameters and assumptions, making it harder to implement.
- Patience Data Requirements: Accurate modelling requires reliable data on customer patience, which can be challenging to collect.
- Limited Scope: While Erlang A addresses abandonment, it does not account for other real-world factors like varying call arrival rates, multitasking, or agent inefficiencies.
Why Erlang A Underestimates Agent Requirements
While Erlang A is a more realistic model than Erlang C due to its inclusion of customer abandonment, it often underestimates the number of agents needed to meet service level targets. This tendency arises because the model assumes that customer abandonment helps reduce the overall workload in the system. However, in real-world scenarios, this can lead to suboptimal staffing levels and service issues.
- Abandonment is Not Always Beneficial:
Erlang A assumes that when customers abandon the queue, it reduces the system’s workload. However, abandonment is often a symptom of poor service. Customers who abandon may call back later, increasing the overall call volume and adding unpredictability to the system. - Overly Simplistic Patience Assumptions:
The model typically uses an exponential distribution to represent customer patience, but actual patience varies greatly. For instance, some customers abandon quickly, while others hold on longer, particularly for critical queries. Erlang A may fail to capture this variability, leading to overly optimistic predictions of queue lengths and waiting times. - Agent Occupancy Underestimation:
When abandonment reduces the queue size, Erlang A predicts a lower agent utilisation rate. However, if the actual abandonment rate is lower than expected, agents may become overwhelmed, resulting in higher occupancy than planned. This can lead to agent fatigue and diminished service quality. - Indirect Costs of Abandonment:
Abandonment can hurt customer satisfaction and loyalty. While the model treats it as a system efficiency, the real-world implications—such as reputational damage and repeat calls—are not accounted for, meaning the required staffing levels may be underestimated.