Assume that for a gas and car wash station one car can be serviced at a time. Th
ID: 3253984 • Letter: A
Question
Assume that for a gas and car wash station one car can be serviced at a time. The arrivals follow a Poisson probability distribution, with an arrival rate of 1 car every 12 minutes and the service times follow an exponential probability distribution, with a service rate of 10 cars per hour.
What is the probability that the station will be idle?
What is the average number of cars that will be waiting for service?
What is the average time a car will be waiting for service?
What is the average time a car will be at the gas and wash station?
Please show how to get the answers based on the below excel template that I have to use.
Multiple-Channel Waiting Line Model Assumptions Poisson Arrivals Exponential Service Times Number of Channels Arrival Rate 0 Service Rate For Each Channel operating Characteristics Probability that no customers are in the system, Po #NAME? Average number of customers in the waiting line, Lq #DIV/0! #DIV/0! Average number of customers in the system, L Average time a customer spends in the waiting line, Wq #DIV/0! Average time a customer spends in the system, W #DIV/O! #DIV/0! Probability an arriving customer has to wait, PwExplanation / Answer
Solution:
Assume that for a gas and car wash station one car can be serviced at a time. The arrivals follow a Poisson probability distribution, with an arrival rate of 1 car every 12 minutes and the service times follow an exponential probability distribution, with a service rate of 10 cars per hour.
arrival rate of 1 car every 12 minutes
arrival rate of 5 car every hour
service rate of 10 cars per hour
What is the probability that the station will be idle?
probability that the station will be idle = 1-5/10
=0.5
What is the average number of cars that will be waiting for service?
=5*5/(10(10-5)) =2
What is the average time a car will be waiting for service?
=5/(10(10-5)) =0.1 hour or 6 minutes.
What is the average time a car will be at the gas and wash station?
=1/(10-5) =0.2 hour or 12 minutes