Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Speedy Oil provides a single-server automobile oil change and lubrication service. Customers provide an arrival rate of 2.5 cars per hour. The service rate is 5 cars per hour. Assume that arrivals follow a Poisson probability distribution and that service times follow an exponential probability distribution. What is the average number of cars in the system

Sagot :

nuhulawal20

Answer:

the average number of car(s) in the system is 1

Step-by-step explanation:

Given the data in the question;

Arrival rate; λ = 2.5 cars per hour

Service time; μ = 5 cars per hour

Since Arrivals follows Poisson probability distribution and service times follows exponential probability distribution.

Lq = λ² / [ μ( μ - λ ) ]

we substitute

Lq = (2.5)² / [ 5( 5 - 2.5 ) ]

Lq = 6.25 / [ 5 × 2.5 ]

Lq = 6.25 / 12.5

Lq = 0.5

Now, to get the average number of cars in the system, we say;

L = Lq + ( λ / μ )

we substitute

L = 0.5 + ( 2.5 / 5 )

L = 0.5 + 0.5

L = 1

Therefore, the average number of car(s) in the system is 1

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.