Scenario B.5
A trucking firm has five trucks that each requires service at an average rate of once every 50 hours,according to an exponential distribution.The firm has a mechanic who needs five hours to complete the average job with exponential service times.
-Use the information in Scenario B.5.What is the probability that there will be no trucks in the system?

Question

Quizplus · Accepted Answer

The probability that there will be no trucks in the system can be calculated using the formula for the probability of zero items in an M/M/1 queue: P0 = 1 - (λ/μ), where λ is the arrival rate (1/50 per hour per truck) and μ is the service rate (1/5 per hour). With five trucks, λ = 5*(1/50) = 0.1, and μ = 0.2. Thus, P0 = 1 - (0.1/0.2) = 0.5, which falls in the range greater than 0.60 but less than or equal to 0.70.

Scenario B.5 A Trucking Firm Has Five Trucks That Each Requires Service