Customers arrive at a video rental desk at the rate of one per minute (exponential interarrival times). Each server can handle 0.4 customers per minute (exponential service times).
-If there are 4 servers,what is the average time it takes in minutes to rent a videotape?
A)2
B)3
C)4
D)5
E)6

Question

Customers arrive at a video rental desk at the rate of one per minute (exponential interarrival times). Each server can handle 0.4 customers per minute (exponential service times).
-If there are 4 servers,what is the average time it takes in minutes to rent a videotape?
A)2 
B)3 
C)4 
D)5 
E)6

Quizplus · Accepted Answer

We can model this problem using a queuing system with M/M/4 notation (exponential distribution for interarrival times, exponential distribution for service times, and 4 servers). 
Using Little's Law, we know that the average number of customers in the system (waiting and being served) is equal to the arrival rate multiplied by the average time in the system. 
So, using the formula for the M/M/4 system, we can calculate the average time in the system to be:
Average time in system = (1/4)/(0.4-1/4) = 2.5 minutes
Since the customer is only being served for 0.4 minutes, the remaining 2.5-0.4 = 2.1 minutes is the average waiting time in the queue. 
Therefore, the average time it takes to rent a videotape is 2.5 minutes. 
The best choice is B.

Customers Arrive at a Video Rental Desk at the Rate