Question

The rental process for these cues is exhaustive and takes 75 minutes for each application. There are three employees that conduct these interviews, and on average, it is one hour between customer arrivals. What is the arrival rate? What is the service rate? On average, how many hours do customers wait to begin the application process? What is the probability all servers are idle?

Answer 1

Solution:

Arrival Rate = 1 customer/hour

Service Rate = 0.8 customer/hour

Number of servers = 3

Effective Service Rate = 3*0.8 = 2.4 customers/hour

The formulae are,

Hence,

a)
Arrival Rate = 1 customer/hour

b)
Service Rate = 0.8 customers/hour
Effective Service rate = 2.4 customershour -- (This will be the one used in all calculations)

c)

Hence, there will be 0.297 customers waiting in the queue.

d)

Hence, the probability that all the servers will be idle is 58.3%