An average of 10 cars/hour arrive at a car repair station with two servers. Assume that the average service for each customer is 4 minutes and both interarrival and service times are exponentially distributed. If this car repair station has a capacity of 4 cars a. Write the steady-state equations and solve them. Compare the results with those calculated in question 1 and draw a conclusion. b. What is the probability that the car repair station is idle? c. What is the average number of cars waiting in the line? d. What is the average amount of time a customer spends in the car repair station? e. On average, how many customers will be served by the repair station in an hour?
At the Zero th state, p1 = ( / ) p0 ; p1 /p0 = /
Considering the actual service rate = 60 mins /4 mins of service = the station can handle 15 cars in 1 hr
An average of 10 cars/hour arrive at a car repair station with two servers. Assume that the avera...
Please answer using stochastic operations principles Cars arrive at a rate of 10 per hour in a single-server drive-in restaurant. Assume that the teller serves vehicles with a rate exponentially distributed with a mean of 4 minutes per car (ie, a rate of 1 car every 4 minutes). Answer the following questions: (a) What is the probability that the teller is idle? (b) What is the average number of cars waiting in line for the teller? (A car that is...
An average of 40 cars per hour (interarrival times are exponentially distributed) are tempted to use the drive-in window at the Hot Dog King restaurant. If a total of more than 4 cars are in line (including the car at the window) a car will not enter the line. It takes an average of 4 minutes (exponentially distributed) to serve a car. (a) What is the average number of cars waiting for the drive-in window (not including a car at...
**LOOKING FOR FORMULAS, ANSWERS PROVIDED. Problem-1: At a single-phase, multiple-channel service facility, customers arrive randomly. Statistical analysis of past data shows that the interarrival time has a mean of 20 minutes and a standard deviation of 4 minutes. The service time per customer has a mean of 15 minutes and a standard deviation of 5 minutes. The waiting cost is $200 per customer per hour. The server cost is $25 per server per hour. Assume general probability distribution and no...
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 10 minutes and the service times follow an exponential probability distribution, with a service rate of 8 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...
An average of 90 cars per hour arrive at a single-server toll booth. The average service time for each customer is a half minute, and both interarrival times and service times are exponential. For each of the following questions, show your work, including the formula that you are using. 1) On average, how many cars per hour will be served by the server
175-5.* A service station has one gasoline pump. Cars wanting gasoline arrive according to a Poisson process at a mean rate of 15 per hour. However, if the pump already is heing used, these po- tential customers may balk (drive on to another service station). In particular, if there are n cars already at the service station, the prob- ability that an arriving potential customer will balk is n/3 for n 1. 2, 3. The time required to service a...
Star Car Wash estimates that dirty cars arrive at the rate of 15 per hour all day and at the wash line, the cars can be cleaned at the rate of one every 4 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) average time a car spends in the service system. (b) average number of cars in line. (c) average time a...
Cars arrive at a toll booth at average rate of 60 per hour. The standard deviation of the time between arrivals is 0.8 minutes. What is the coefficient of variation of the interarrival times of cars?
A car wash has one automatic car wash machine. Cars arrive according to a Poisson process at an average rate of 5 every 30 minutes. The car wash machine can serve customers according to a Poisson distribution with a mean of 0.25 cars per minute. What is the probability that there is no car waiting to be served?
1. A new shopping mall is considering setting up a car wash manned by six employees. From past data, Regal Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Regal 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. It is assumed that arrivals are...