Customers arrive at Best-Bank-in-Town’s (BBT) sole ATM location at a rate of 21 customers per hour. It is assumed that the arrival process is random. BBT recently hired an intern who estimated that the average service time is 2 minutes per customer with a standard deviation of 1.2 minutes. [Assume that the arrival rate is the same throughout the day without peak and off-peak considerations and that there is only one ATM machine at that location] 1. Calculate average waiting time for ATM user at the BBT location 2. Calculate average length of queue at the ATM location (i.e. average numbers of customers waiting for service)? 3. What is the probability that an arriving customer has no waiting time to use the ATM? 4. BBT wants to cut the average waiting time in half without necessarily adding another ATM machine. They are in discussions with their ATM software provider who has told them that their new software is very consistent with information retrieval and can greatly minimize the…

A tax consulting firm has 5 counters in its office to receive people who have problems concerning their income, wealth and sales taxes. On the average 75 persons arrive in an 8hour day. Each tax adviser spends 25 minutes on an average on an arrival. If the arrivals are Poissonly distributed and service times are according to exponential distribution, find The probability of there being no customer in the system              The average number of customers in the system                                       iii.          Average number of customers waiting to be served                                  iv.   Average time a customer spends in the system                                        v.         Average waiting time for a customer

A university is considering setting up an information desk manned by one employee. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 18 per hour.   It takes an average of 2 minutes to answer a question.   It is assumed that arrivals are Poisson and answer times are exponentially distributed. 3. Find the proportion of the time that the employee is busy. 4. Find the average number of people receiving and waiting to receive information. 5. Find the average number of people waiting in line to get information.

As my arrival rate is increasing, my Wq, W, Lq, L descrease, then become negative, then less negative over time. Why is that?

Doña Blanca plans to open a small car wash and must decide how much space to allocate to waiting cars. She estimates that customers will arrive randomly (Poisson process) at an average rate of 1 every 4 minutes, unless the waiting area is full, in which case the arriving customers will take their car elsewhere. The total time attributable to washing a car has exponential distribution with mean 3 minutes. Compare the fraction of potential customers lost due to lack of waiting space if a) 2 and b) 4 spaces (in addition to the wash location) are provided.

Answer the given question with a proper explanation and step-by-step solution. Use the information. A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poison distribution at the rate of 2.5 per minute. In serving themselves, customers take about 22 seconds, exponentially distributed.Use formulas to solve, no excel. Show all work. a. How many customers would you expect to see, on average, at the coffee urn? b.How long would you expect it to take to get a cup of coffee? c.What percentage of time is the urn being used? d. What is the probability that three or more people are in the cafeteria?

An average of 40 students per hour arrive at the MBAcomputing lab. The average student uses a computer for 20minutes. Assume exponential interarrival and service times.a If we want the average time a student waits for a PCto be at most 10 minutes, how many computers shouldthe lab have?b If we want 95% of all students to spend 5 minutesor less waiting for a PC, how many PCs should the labhave?

Please solve this in excel. Ray is planning to open a small car-wash operation for washing just one car at a time. He must decide how much additional space to provide for waiting cars. Ray estimates that customers would arrive according to a Poisson input process with a mean rate of 1 every 4 minutes, unless the waiting area is full, in which case the arriving customers would take their cars elsewhere. The time that can be attributed to washing one car has an exponential distribution with a mean of 2 minutes. Suppose that Ray makes an average $4 per served customers. Moreover, each car space rented for waiting costs $800 per month. Ray is planning to run the car-was for 200 hours every month. 2. How much space should Ray provide for the waiting cars in order to maximize his expected net profit? (By net profit, we mean profit from car-wash operations minus the rental cost)

The following data has been collected on the number of customers seen to arriveto a museum in a succession of 5-minute intervals: 5, 1, 3, 7, 5, 5, 6, 7, 5, 7, 4, 8, 1,5, 2, 3, and 5. Estimate the squared coefficient of variation of the arrival process. Ifthis data was known to come from a Poisson process, what would be your estimateof l, the rate of customer arrivals?