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Optimizing Call Center Staffing with Queue Theory: Traditional and Modern Approaches

Nick Farrell

November 14, 2024
Operational Solutions

Call center workforce management heavily relies on queue theory to ensure optimal staffing, efficient scheduling and streamlined call handling processes. Queue theory provides mathematical models that help predict and manage customer wait times, service times and overall operational efficiency. As call centers face increasing complexity with fluctuating call volumes and growing customer expectations, understanding and leveraging these models’ unique use cases and advantages is more important than ever.

But here’s the thing–the more you learn about queuing, the more nuanced and complex the subject becomes.

Before we continue, don’t worry–if you’re looking for a call center partner that can help you tackle these challenges and make smart decisions, AnswerNet has you covered! If you want to stop reading here and just get help, click here and a member of our solutions team will be happy to help guide you through the jargon and math to the other side where you’re getting the best possible customer experience out of your call center program budget.

What is queue theory?

Queueing theory is the mathematical study of resource demand and availability focusing on predicting how long queues will be and the waiting times involved. It is often part of operations research because its findings help businesses make decisions about the resources they need to provide efficient service. This is especially important in the call center industry as it forms the basis of modern workforce management (WFM) and scheduling strategies where forecasting models are becoming more entrenched in call center metrics, performance data, tech/human variables (ex: shrink in brick and mortar vs. WFH environments) and team behavioral patterns that tend to be unique to each service provider.

“But why don’t you just increase staffing to guarantee better answer times?”

Simple–MONEY!

Queueing theory and strong WFM frameworks help us understand how and when to increase budgets to scale up staffing when we can demonstrate it will be a profitable decision for the business that creates measurable positive impact for the customer experience.

Here are some other examples of queues you may have encountered in your life:

Supermarkets and Retail Stores: Customers waiting at checkout counters form queues, managed to optimize service time and minimize waiting.
Banks: Customers lining up to see tellers or use ATMs are examples of queues that can be analyzed to allocate resources efficiently.
Hospitals and Clinics: Patients waiting for services, such as emergency room treatment or scheduled appointments, represent queues that impact service efficiency.
Airports: Lines at check-in counters, security checks, and boarding gates are queues that require effective management to ensure smooth passenger flow.
Theme Parks: Rides and attractions often have long lines, where queue management helps balance visitor satisfaction and ride capacity.
Traffic Signals: Cars waiting at traffic lights or toll booths create queues, with traffic flow often studied to reduce congestion.
Fast-Food Restaurants: Both physical queues at the counter and virtual queues for drive-through services can be optimized for faster service.
Public Transport: People waiting for buses, trains, or subways form queues that are often studied for improving scheduling and service frequency.

What are some others that come to mind?

What each of these scenarios above have in common is that they can all be tuned to be more efficient, balancing cost and customer experience. But striking the optimal balance isn’t something you can just guess. It’s actually a highly technical process that requires some level of basic understanding to navigate (yes, even if your CCAAS platform performs the calculations for you).

Here are links and details regarding core foundational reading on queue theory for those who want to dive deep into the subject (warning–it’s dense):

Halfin, Shlomo, and Ward Whitt. “Heavy-Traffic Limits for Queues with Many Exponential Servers” (PDF available) This seminal paper, published in Operations Research (1981), focuses on heavy-traffic limit theorems for queueing systems with many servers.
Kleinrock, Leonard. Queueing Systems (PDF available) This classic work, published in 1975-1976, is fundamental in the field of queueing theory and discusses in-depth the mathematics behind queues, applied in various operations research contexts.
Kelly, Frank P. Reversibility and Stochastic Networks (PDF available) This 1979 book provides insights into stochastic processes and their reversibility, which is applicable in network and telecommunications queueing models. This text is a staple for those studying complex networked systems.
Chen, Hong, and David Yao. Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization. (available to purchase) Published in 2001, this book covers queueing networks, emphasizing their performance and optimization. It is a crucial resource for understanding advanced applications in modern systems.

Did you click through any of the links above? If you did, you now have an appreciation for the level of technical detail and research/rigor behind the staffing calculators and platform automations we use to staff our centers. But these are the foundational mathematics texts for anyone studying or applying queueing theory, particularly in fields like call centers, telecommunications, and network band research. What’s amazing about the time that we are in, leading into 2025 is that the research and discoveries being made today in this subject area will lead to new discoveries and applications (integrating behavioral analysis data points) thanks to AI.

Key Queue Theory Principles in Call Centers

Now let’s explore key queue theory principles, common frameworks like the Erlang models (Specifically Erlang C and Erlang A) and emerging approaches such as skill-based routing and customer patience modeling to help call centers improve performance and service quality.

Arrival Patterns (Poisson Process): Most call centers use the Poisson distribution to model call arrival patterns. This assumes that calls arrive randomly but with a predictable average rate. Understanding this arrival pattern helps call center managers plan for fluctuating call volumes and anticipate peak hours, ensuring they have enough agents scheduled during busy times.
Service Time Distribution (Exponential Service Times): Call centers often use the exponential distribution to model the time it takes to handle a call. This principle is based on the idea that shorter calls are more common, but longer calls still occur. By predicting average handle time (AHT), workforce managers can estimate how many agents will be available to handle calls at any given time.
Queue Discipline (First-Come, First-Served or Priority Queuing): In a typical call center environment, calls are handled on a First-Come, First-Served (FCFS) basis, ensuring that the first customer in the queue is the first to be served. However, some departments, such as tech support or VIP service lines, use priority queuing systems, where high-priority calls are served faster. These models help manage high-value customers or urgent issues more effectively.
Multi-Server Queues (Erlang Models): Developed by A.K. Erlang, the Erlang-C model is one of the most widely used frameworks in call center management. It calculates staffing needs based on the number of agents, call arrival rates, and service time distribution. With this model, call centers can estimate:
1. Expected wait times
2. Service levels (e.g., answering 80% of calls within 20 seconds)
3. The required number of agents to handle call volumes efficiently

Another important variation, the Erlang-A model, incorporates caller abandonment rates, allowing managers to predict the likelihood that a customer will hang up before being answered. This is crucial for high-volume call centers where long wait times might lead to abandoned calls.

Common Queueing Frameworks in Call Centers

1. Erlang-C Model: The Classic Framework

The Erlang-C model is the go-to tool for many call centers when it comes to predicting staffing needs. It allows workforce managers to calculate:

How many agents are needed to meet service-level agreements (SLAs), such as answering 80% of calls within 20 seconds.
The expected number of calls waiting in a queue at any given time.
How to optimize shift patterns to match expected call volumes.

Use Case:

If a call center needs to ensure a specific service level for handling a high volume of customer inquiries, the Erlang-C model helps them adjust staffing to meet these targets efficiently without overstaffing.

2. Erlang-A Model: Adjusting for Caller Patience

While Erlang-C assumes that customers will stay on the line until they are served, the Erlang-A model introduces the concept of caller abandonment. This model is more accurate for high-volume call centers where customers might hang up if they experience long wait times. By predicting abandonment rates, managers can:

Adjust staffing during peak periods to reduce wait times.
Estimate the potential cost of lost calls due to abandonment, which is especially critical in sales or customer support environments.

Q: What about Erlang B? What about Merlang? Stay tuned for blogs in the coming weeks on each of these model variations.

3. Markovian Models: Multi-Stage Queuing Systems

In more complex call centers where calls pass through multiple stages—such as routing from an IVR system to an agent or escalating an issue to a specialized department—Markov processes are often employed. These models assume that the future state of a system (e.g., a customer being routed to a specific agent) depends only on the current state, not the history of the interaction. This allows call centers to:

Model more complex interactions where different service levels are needed at different stages.
Optimize multi-tier support environments where call routing is based on customer inquiries and agent expertise.
Decide where cross-training and escalations should occur to reduce the number of segments in a communication chain.

Emerging and More Nuanced Approaches

As the complexity of call center operations increases, new queueing models have emerged that incorporate AI and advanced analytics to provide deeper insights into agent performance and customer behavior.

1. Skill-Based Routing (SBR)

Traditional queueing models assume that any agent can handle any call. However, with skill-based routing (SBR), calls are routed based on agent expertise. This more complex model has shifted the focus to:

Optimizing staffing by distributing calls to agents with the right skill sets.
Dynamic queuing models that adjust routing in real time based on agent performance and call complexity.

Use Case:

In a tech support center, an AI-driven SBR system might route a call to a specialist agent based on the caller’s specific issue, ensuring that the customer receives the most efficient service possible.

2. Customer Patience Modeling

Modern variations of the Erlang models incorporate customer patience. These models include balking (when customers refuse to enter the queue due to perceived long waits) and reneging (when customers leave the queue after joining it). This approach is particularly helpful in high-pressure environments like financial services or healthcare, where wait times directly impact customer satisfaction.

3. Predictive Analytics and AI

Predictive analytics and AI-driven models are revolutionizing call center workforce management by allowing real-time adjustments to staffing and routing based on historical trends and live data. With these tools, call centers can:

Predict call volumes based on past trends and external factors (e.g., seasonal spikes).
Optimize call routing by factoring in agent performance and customer sentiment (using real-time sentiment analysis tools).

Use Case:

An AI system might predict an increase in call volumes during a product launch and automatically adjust agent schedules, ensuring adequate staffing during peak times without the need for last-minute changes.

Merging Traditional and Emerging Models for Optimal Performance

The integration of traditional queue theory models like Erlang-C and Erlang-A with AI-driven predictive analytics and skill-based routing enables call centers to optimize their workforce and enhance customer satisfaction. By understanding customer behavior, agent performance, and leveraging both mathematical models and modern technology, call centers can improve service levels, reduce wait times, and better manage workforce efficiency.

The risk of not taking action is that you may end up depending solely on technology to make decisions for you without the ability to guide the outcomes or understand how your variable inputs influence the results. This could impact your ability to produce accurate forecasts, control budgets and deliver excellent, cost-effective service.

Do you struggle to schedule the right number of resources for your call center queues? Do you have call metric reports you’re struggling to interpret? Or is your current call center services provider unable to make informed recommendations regarding the optimal way you should schedule your resources and apply your budget? Our BPO solutions experts and WFM analysts would be happy to help.