Question

Suppose the inter-arrival time of calls to a call center is 10 seconds on average and each service representative can answer 1 call per minute on average. What is the minimum number of service representatives required so that the queue is stable?

Answer 1

We have a call center where the inter-arrival time of calls is 10 seconds on average and the service rate is 1 call per minute.

We have to find the minimum number of representatives required so that the queue is stable.

We can start by expressing the arrival rate of calls as:

$\lambda=\frac{1}{\#\text{calls per minute}}=\frac{1}{6\min }$

The service rate is:

$\mu=1\frac{1}{\min }$

For stability