The day after a snow storm, cars arrive at Mel's Auto-Wash at an average rate of 10 per hour according to a Poisson process. The automated car washing process takes exactly 5 minutes from start to finish.
a. What is the probability that an arriving car will find the car wash empty?
b. On average, how many cars are waiting for service?
c. On average, what is the total length of time (from arrival to departure) cars will spend at the car wash?© BrainMass Inc. brainmass.com October 17, 2018, 4:21 am ad1c9bdddf
Please see the attachment for solution. If you need any clarification please ask me. Thanks.
It is given that,
Arrival rate = 10 cars per hour
Service rate = 1 car ...
The solution provides detailed explanation of a queuing problem.
Queuing problem: Average time a customer spends in Queue
Customers arrive at Homestake Bank between the hours of 10 A.M. and 11 A.M. according to a Poisson distribution at a mean rate of 40 per hour. During the period from 10 A.M. to 11 A.M. the bank has 3 tellers working. The average time a teller spends with a customer is 3 minutes, and service time follows an exponential distribution. What is the average time a customer will spend waiting in line before seeing a teller?View Full Posting Details