Please I need the step of the solution Q)) From historical data, Harry’s Car Was
ID: 3178485 • Letter: P
Question
Please I need the step of the solution Q))From historical data, Harry’s Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Harry figures that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the A)Utilization rate of the car wash. B)Average time a car waits before it is washed. C)Average time a car spends in the service system.
Please I need the step of the solution Q))
From historical data, Harry’s Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Harry figures that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the A)Utilization rate of the car wash. B)Average time a car waits before it is washed. C)Average time a car spends in the service system.
Q))
From historical data, Harry’s Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Harry figures that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the A)Utilization rate of the car wash. B)Average time a car waits before it is washed. C)Average time a car spends in the service system.
From historical data, Harry’s Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Harry figures that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the A)Utilization rate of the car wash. B)Average time a car waits before it is washed. C)Average time a car spends in the service system.
From historical data, Harry’s Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Harry figures that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the A)Utilization rate of the car wash. B)Average time a car waits before it is washed. C)Average time a car spends in the service system.
Explanation / Answer
Harry's car wash Queuing Model M/M/s (Exponential Service Times) Input Data Operating Characteristics Arrival rate (l) 10 Average server utilization (r) 0.8333 Service rate (m) 12 Average number of customers in the queue (Lq) 4.1667 Number of servers (s) 1 Average number of customers in the system (L) 5.0000 Average waiting time in the queue (Wq) 0.4167 Average time in the system (W) 0.5000 Probability (% of time) system is empty (P0) 0.1667 Probabilities Number of Units Probability Cumulative Probability 0 0.1667 0.1667 1 0.1389 0.3056 2 0.1157 0.4213 3 0.0965 0.5177 4 0.0804 0.5981 5 0.0670 0.6651 6 0.0558 0.7209 7 0.0465 0.7674 8 0.0388 0.8062 9 0.0323 0.8385 10 0.0269 0.8654 11 0.0224 0.8878 12 0.0187 0.9065 13 0.0156 0.9221 14 0.0130 0.9351 15 0.0108 0.9459 16 0.0090 0.9549 17 0.0075 0.9624 18 0.0063 0.9687 19 0.0052 0.9739 20 0.0043 0.9783 Arrival rate 10 cars Per hour Service rate One car at every 5 minutes Service rate 12 cars per hour Number of servers (s) 1 Entering above values in the Excelmodules Queuing models---->M/M/s, we get following results: A) average number of cars in line Avg no of cars in line(Lq) 4.167 B) average time a car waits before it is washed Avg waiting time in queue(Wq) 0.417 hours Avg waiting time in queue(Wq) 25 Mins C) average time a car spends in the service system Avg time in service system(W) 0.5 hours Avg time in service system(W) 30 Mins D) utilization rate of the car wash Average utilization of service system 0.833 83.33 Percent E) probability that no cars are in the system Probability of no car in the system(P(0)) 0.167