Workforce Management & Queue Engineering Lab

Erlang C Call Center Staffing Lab

Calculate call center staffing, Erlang C wait times, service level SLA probabilities, and shrinkage-adjusted roster headcount.

Queue Model Shrinkage & Roster Erlang Theory FAQ

Contact Center Presets

Load calibrated queue benchmarks.

Step 1: Inbound Traffic & Service Level Targets

Erlang C Queue & SLA Configuration

1. Inbound Volume & Handle Time

sec
Includes talk time + hold + after-call wrap-up.

2. Service Level Agreement (SLA) Targets

sec
%
Frontline agents actively logged in taking calls.

3. Workforce Shrinkage & Roster Staffing

%
$
Achieved SLA
83.4% in 20s
7.8s Avg Wait (ASA)
Agent Occupancy
89.7% Occupancy
46.7 Erlangs Workload
Total Roster Needed
75 Total Roster
52 on-seat + 30% shrinkage
Direct Cost / Call
$1.63 / contact
Agent labor per handled contact

Queuing Theory & Operations Research

Erlang C Mathematics & Workforce Sizing

The Erlang C model is the worldwide mathematical standard for sizing multi-server customer contact centers with queuing buffers ($M/M/c$ queuing model).

  • Workload ($A$ in Erlangs): Calculated as $lambda imes ext{AHT}$. One Erlang represents one full hour of continuous customer conversation.
  • The Occupancy Trap: Running agents above 88% occupancy causes severe queue spikes and agent turnover. A small 5% increase in call volume when occupancy is high causes an exponential surge in queue wait times.
  • Shrinkage Multiplier: Scheduled on-seat agents only represent a fraction of total employed staff. Incorporating 25% to 35% shrinkage ensures proper hiring and budget forecasting.

Explore broader queuing in the Queuing Theory Lab.

Contact Center Formulas

Essential workforce management formulas

Traffic Intensity A (Erlangs) = (Call Volume ÷ Interval Sec) × AHT Sec

Agent Occupancy = Traffic Intensity A ÷ Scheduled Agents N

Service Level SLA % = 1 - Pw × e^(-(N - A) × (Target Sec ÷ AHT Sec))

Average Speed of Answer (ASA) = (Pw × AHT Sec) ÷ (N - A)

Total Roster Headcount = Scheduled Agents ÷ (1 - Shrinkage %)

Benchmark retention ROI in the Turnover Cost Lab.

FAQ

Erlang C call center staffing questions

What is the Erlang C formula in call center staffing?

Erlang C is a mathematical formula that calculates the probability that an incoming caller will have to wait in queue given traffic intensity (Erlangs) and number of on-seat agents.

What is the standard 80/20 service level rule?

The 80/20 rule is an industry benchmark stating that 80% of incoming customer calls should be answered by an agent within 20 seconds of entering the queue.

Why should agent occupancy be kept below 88%?

Agent occupancy above 88% causes cognitive fatigue, chronic burnout, elevated turnover, and degraded customer satisfaction because agents have zero idle buffer between calls.

How does workforce shrinkage affect total required roster size?

Shrinkage accounts for non-productive paid time including breaks, training, PTO, and illness. Total Roster = Scheduled On-Seat Agents ÷ (1 - Shrinkage %). A 30% shrinkage requires 1.43× more total staff.

Can I export Erlang C staffing models to CSV?

Yes. You can export complete traffic Erlangs, SLA probabilities, ASA wait times, occupancy rates, and shrinkage-adjusted rosters as a UTF-8 CSV spreadsheet with formula injection defense.

Is this tool certified professional labor advice or contact center software?

No. This tool provides educational Erlang C queuing simulations for business analysis without certified employment, legal, or contact center SLA contractual warranties.

Continue Exploring Staffing & Capacity Tools

Explore our Staffing & Capacity Hub, analyze labor turnover in the Turnover Cost Lab, model general queues in the Queuing Theory Lab, or calculate warehouse labor in the Warehouse Capacity Lab.