Consider a call center with three agents that receives 25 calls/hr during regular hours. We observe 3.5 people on hold on average. Also, calls take an average of 6 minutes. What is the inter-arrival time, the utilization of the system, and the queue and system waiting times during normal hours?

2.4 minutes ; 0.8333 ; 8.4 minutes ; 14.4 minutes

Explanation:

Given that:

Number of agents (n) = 3

Mean calls per hour (λ) = 25calls/hr

Average Number of calls in queue (Q) =3.5

Service time (E) = 6 minutes ;

Hence, mean service rate (μ) = 60/ 6 = 10 calls/hr

A.) The inter-arrival time :

1 /λ = 1 / 25 = 0.04 hours = (0.04 * 60) = 2.4 mins

The utilization of the system :

Mean calls per hour /(number of agents * mean service rate)

λ / (n * μ) = 25/ (3 * 10)

= 25 / 30

= 0.8333

Queue waiting time :

Q / λ

= 3. 5 * 0.04

= 0.14 hour = (0.14 * 60) = 8.4 minutes

System waiting time :

Queue waiting time + service time

8.4 minutes + 6 minutes = 14.4 minutes