Erlang C calculator

How the calculation works

Erlang C models a queue where contacts that find every agent busy wait for the next free agent.

• Contacts per hour: arrivals in the hour you plan for.
• Average handle time: seconds per contact, with wrap-up.
• Service level target and answer time: the share of contacts answered within that many seconds.
• Shrinkage: paid time not available for contacts.

Traffic is contacts per hour times handle time in seconds, divided by 3,600: the average number of busy agents, in Erlangs. The calculator tries agent counts upward from just above the traffic and stops at the first that meets the target. For each, the Erlang C formula gives the chance a contact waits, and the service level is 1 minus that chance times e raised to minus (agents minus traffic) times answer time, divided by handle time. Average speed of answer is the chance of waiting times handle time, divided by agents minus traffic. Occupancy is traffic divided by agents. Scheduled agents is agents times 100, divided by 100 minus shrinkage, rounded up.

Worked example

100 contacts an hour at 180 seconds each is 5.00 Erlangs. For 80% answered within 20 seconds, 8 agents reach 88.0% and 7 reach only 74.0%, so the queue needs 8. With 30% shrinkage, 8 x 100 / 70 = 11.43, rounded up to 12 scheduled agents.

What it leaves out

Erlang C assumes contacts arrive at random at a steady rate, nobody hangs up or leaves the chat while waiting, every agent handles one contact at a time, and handling times follow an exponential pattern. Chat agents who handle several chats at once, email and other non-queue work are not modelled. No service level target is suggested.