When a growing business sets up a customer support line or scales its contact center for a new product launch, someone inevitably opens a spreadsheet and does simple division. If the team expects 180 calls during a busy hour and each call takes an average of three and a half minutes to resolve, total call workload is 630 minutes, or 10.5 hours of work per hour. Rounding up, management schedules 11 agents and expects every caller to be answered immediately.
On day one, the phone queues explode. Callers wait several minutes on hold, abandonment rates spike, and the eleven agents on duty are completely exhausted from taking back-to-back calls without a single second to breathe. The arithmetic was right, yet the staffing plan failed completely.
Why Simple Division Always Understaffs a Queue
Simple division assumes that customers call in a polite, evenly spaced line: one call arriving every twenty seconds on the dot, each lasting exactly 210 seconds. Real human behavior never works that way. Customer calls follow a Poisson arrival distribution. Five minutes go by with only two calls, and then twelve customers dial in at the exact same moment because a mobile banking app slowed down or a promotional SMS just went out.
When arrival spikes hit a team staffed right at bare workload capacity, a queue forms instantly. Because there is no spare capacity above the average arrival rate, the backlog cannot clear itself until call volume drops at the end of the shift.
How the Erlang C Model Solves the Queueing Problem
For over a century, telecommunications engineers and contact center planners have used the Erlang C formula, developed by Danish mathematician A.K. Erlang, to model random call arrivals accurately. Instead of looking only at average workload, Erlang C connects four operational variables:
- Traffic Intensity (Erlangs): One Erlang represents one continuous hour of call handling workload per hour. In our example of 180 calls per hour at 210 seconds Average Handle Time (AHT), traffic intensity is 10.5 Erlangs.
- Target Service Level (SLA): Defined as the percentage of calls answered within a target number of seconds, such as answering 80 percent of calls within 20 seconds.
- Maximum Agent Occupancy: Occupancy is the percentage of logged-in time an agent spends actively handling calls. When occupancy exceeds 85 percent over long shifts, agent burnout, errors, and turnover rise sharply.
- Roster Shrinkage: No employee sits at their headset for 100 percent of their paid shift. Breaks, team briefings, coaching, training, annual leave, and sick days typically reduce available desk time by 25 to 35 percent.
When you run 180 calls per hour at 210 seconds AHT through the Erlang C formula for an 80/20 service level, you find that you need 14 active agents logged in at their desks, not 11. Once you account for 30 percent shrinkage, you need 20 total rostered staff to cover that peak hour reliably.
Calculate Your Own Staffing Plan
You do not need complex spreadsheet macros to run Erlang C math. Use our Contact Center Staffing Calculator to enter your call volume, handle time, service level target, and shrinkage rate. It outputs active seats, total rostered staff, Average Speed of Answer, and a headcount sensitivity table directly in your browser.
If you want to reduce Average Handle Time through better agent tooling, omnichannel routing, or a faster internal knowledge base, book a consultation with KODA. We help support teams build connected operations that serve customers faster without burning out staff.