2021-07-17 , updated 2023-12-02
Written by: Robert
Keywords: Erlang-C, PBX
For the description of queuing systems, a notation called Kendall’s notation is used. A queue system is defined by, AP/STD/c where AP is the arrival process, ST is the service time distribution, and c is the number of servers. AP and STD are often modeled by a Markovian process M.
An additional set of standard parameters is used to describe the request rate and the number of serving agents:
| Parameter | Description |
|---|---|
| h | Average request time |
| λ | Average request rate |
| A | The load of the system: A = λh |
| μ | Reciprocal of request time (hμ = 1). |
To find the probability to be placed in a queue in PBX and call center systems, a M/M/c / (Erlang C) model can be used.
Assuming an average request rate (incoming call rate) of λ, and an average call time h, the load is defined as A = λh. The load is a measure of the request traffic on a system.
Below is a calculation for 3 different loads, using an average call time h = 2.5 minutes (hμ = 1):
image:
As can be seen from the first plot, with the lowest traffic of 8 requests per minute, the call center should preferably have > 25-30 agents (operators) in order to ensure a good quality of service. With higher traffic, 14 incoming calls per minute, >40 agents are required.
Similarly, from the second plot, waiting time W in minutes, decreases to < 10 seconds when >25 agents are available, at λ = 8 per minute.