All trucks traveling on Interstate 40 between Albuquerque and Amarillo are required to stop at a weigh station. Trucks arrive at the weigh station at a rate of 120 per eight-hour day (Poisson distributed), and the station can weigh, on the average, 140 trucks per day (Poisson distributed). Suppose arriving truck drivers look to see how many trucks are waiting to be weighed at the weigh station. If they see four or more trucks in line, they will pass by the station and risk being caught and ticketed. What is the probability that a truck will pass by the station?

Pasquist Water Company (PWC) operates a 24-hour facil-ity designed to efficiently fill water-hauling tanker trucks.Trucks arrive randomly to the facility and wait in line to ac-cess a wellhead pump. Since trucks vary in size and the filling operation is manually performed by the truck driver, the timeto fill a truck is also random.a. If the manager of PWC uses the multiple-server modelto calculate the operating characteristics of the facility’swaiting line, list three assumptions she must make regard-ing the behavior of waiting trucks and the truck arrivalprocess.b. Suppose an average of 336 trucks arrive each day, thereare four wellhead pumps, and each pump can serve anaverage of four trucks per hour.▪ What is the probability that exactly 10 trucks will arrivebetween 1:00 p.m. and 2:00 p.m. on any given day?▪ How likely is it that once a truck is in position at a well-head, the filling time will be less than 15 minutes?c. Contrast and comment on the performance differencesbetween:▪…

The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the rate of two jobs per 8-hour day. The company's repair facility is a single-server system operated by a repair technician. The service time varies, with a mean repair time of 3.0 hours and a standard deviation of 2.1 hours. The company's cost of the repair operation is $26 per hour. In the economic analysis of the waiting line system, Robotics uses $37 per hour cost for customers waiting during the repair process. (a) What are the arrival rate and service rate in jobs per hour? (Round your answers to four decimal places.) λ = μ = (b) Show the operating characteristics. (Round your answers to four decimal places. Report time in hours.) L = 9 L = W₁ = Wa W = h Show the total cost per hour. (Express the total cost per hour in dollars. Round your answer to the nearest cent.) TC = $ (c) The company is considering purchasing a computer-based equipment repair system that would…

Assume trucks arriving for loading/unloading at a truck dock from a single server waiting line. The mean arrival rate is three trucks per hour, and the mean service rate is five trucks per hour. Use the Single Server Queue Excel template to answer the following questions. Do not round intermediate calculations. Round your answers to three decimal places. What is the probability that the truck dock will be idle?   What is the average number of trucks in the queue?   truck(s) What is the average number of trucks in the system?   truck(s) What is the average time a truck spends in the queue waiting for service?   hour(s) What is the average time a truck spends in the system?   hour(s) What is the probability that an arriving truck will have to wait?   What is the probability that more than two trucks are waiting for service?

Assume trucks arriving for loading/unloading at a truck dock from a single server waiting line. The mean arrival rate is three trucks per hour, and the mean service rate is six trucks per hour. Use the Single Server QueueExcel template to answer the following questions. Do not round intermediate calculations. Round your answers to three decimal places.   What is the probability that the truck dock will be idle?   What is the average number of trucks in the queue?  truck(s) What is the average number of trucks in the system?  truck(s) What is the average time a truck spends in the queue waiting for service?  hour(s) What is the average time a truck spends in the system?  hour(s) What is the probability that an arriving truck will have to wait?   What is the probability that more than two trucks are waiting for service?

1.)The arrival rate is the     rate of arrivals to the service facility     all of these     rate items arrive at the server after being in the queue     time between arrivals to the service facility 2.) what is "queue discipline"?

A mom and pop car wash with 1 drive through lane gets an average of 4 cars per hour, with a Poisson distribution. The washing and drying process has a mean of 12 minutes, M= exponentially distributed, and a car cannot enter the lane until the car in front of it is finished drying (there can only be one car in the lane at one time). Due to the location, there is only space enough to hold 5 cars in line waiting to get washed. However, they rent space from the empty lot next door that is large enough to hold as many cars as needed. They decided to rent a section that will hold only 3 cars. a) If they decide to rent a section that will hold 3 cars, what will you solve for to determine the probability that they will still turn cars away? b) They promise each customer their money back ($10) if it takes longer than 30 minutes to get their car washed (from the time they enter). They are open 8 hours per day. How much money can they expect to give away per day?

A Covid-19 vaccine clinic in downtown area of a large city opens 24 hours a day and residents from all over the city may come to the clinic for service. Assume that the arrival process follows Poisson distribution with an average of 5 arrivals per hour. The average time required to give the vaccine is 8 minutes and the service time follows exponential distribution. Use the standard single channel single stage queuing model introduced in class and equations given below to calculate corresponding values in answering the following questions. 1) Estimate the number of hours that the staff at the clinic are busy in a 12 hour time period 2) Estimate the time a person coming to the clinic is expected to wait to get served after he/she arrives. 3) Estimate the time a person is expected to spend in the clinic (including waiting and being served) after he/she arrives. 4) There is a seat in the clinic for the patient/person to sit down when he/she is treated. The clinic decided that at least 75%…

Consider a Poisson queue with random arrivals at the rate of 12 customers per hour and the following steady- state probabilities: po = 1/3, p1 = 1/2, p2 = 1/6, and p, = 0 for n = 3,4,5, ... . What is the mean (or effective) arrival rate in customers per hour for this queuing system? Consider drawing a rate diagram to assist in your solution. O 10 12 O none of the other choices O 2

How does an event improve the smooth queue management?