6. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive according to a Poissonprocess at a mean rate of 2 per minute. However, business is growing and management projects that the meanarrival rate will be 3 per minute a year from now. The transaction time between the teller and customer has anexponential distribution with a mean of 1 minute.Management has established the following guidelines for a satisfactory level of service to customers. Theaverage number of customers waiting in line to begin service should not exceed 1. At least 90 percent of thetime, the number of customers waiting in line should not exceed 3.(a) Use the Excel sheet to evaluate how well the guidelines will be satisfied a year from now if no change ismade in the number of tellers.

Find the Given details below: Current system: Arrival time λ 120 Service time μ 60 Future…

Answered: The Security & Trust Bank employs 4…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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LF Bank has 3 tellers serving customers through a shared line where the next customer in line goes to the first available teller. Each teller can serve 30 customers per hour with exponential service times and the customers arrive at a rate of 74 per hour, according to a Poisson distribution. On average, how many customers are in the system? (Note: carry all your results to at least 4 decimal places) Round your final answer to 2 decimal places. Answer: Check
The Clip Joint is a hairstyling salon at University Mall. Four stylists are always available toserve customers on a first-come, first-served basis. Customers arrive at an average rate of fiveper hour, and the stylists spend an average of 35 minutes on each customer Determine the average number of customers in the salon, the average time a customer must wait, and the average number waiting to be served.
United Raiders Drive-In Market has one checkout counter where one employee operates the cash register. The combination of the cash resister and the operator is the server in this queuing system; the customers who line up at the counter to pay their selections form the waiting line. Customers arrive at a rate of 24 per hour according to a Poisson distribution, and service times are on average equal to 2 minutes per customer. What is the number of customers waiting in the queue on average?
Please do not give solution in image formate thanku. A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed. Required: (g) Assume that the information desk employee earns $10 per hour. The cost of waiting time, in terms of customer unhappiness with the mall, is $12 per hour of time spent waiting in line. Find the total expected costs over an 8-hour day.
The VBO grocery store has a checkout counter with a full-time cashier. Customers arrive randomly with an average rate of 20 per hour. The distribution of service time is exponential with an average of 2 minutes. Occasionally, this situation causes a long queue and customer complaints. Since there is no room for another cashier, the manager plans to hire another person to help pack the groceries and reduce the expected service time to 1.5 minutes, still with exponential distribution. The manager wants the percentage of time when there are more than 2 customers at the cash register to be less than 25%. He also wants no more than 5% of customers to have to wait 5 minutes or more before starting service or 7 minutes or more before finishing service. a) Use the formulas from the M/M/1 model to calculate L, Lq, W and Wq, π0, π1 and π2 of the current transaction. What is the probability that there are more than 2 customers at the cash register? (b) Repeat (a) for the helper alternative.
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During the evening hours, an average of 52 customers can be found in Sachi’s Sports Bar. About 40 customers arrive each hour. Using Little’s Law, how long does each customer stay at Sachi’s?
Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that one customer is receiving a haircut and two customers are waiting? If required, round your answer to four decimal places.P3 = fill in the blank 4 What is the probability that more than two customers are waiting? If required, round your answer to four decimal places.P(More than 2 waiting) = fill in the blank 5 What is the average time a customer waits for service? If required, round your answer to four decimal places.Wq = fill in the blank 6 hours
A call centre operates with two customer service representatives. Customers call the centre according to a Poisson process with an average rate of 10 calls per hour. The service times follow an exponential distribution with a mean service rate of 6 calls per hour per representative. The goal is to analyse the performance of this queuing system and determine key metrics.
The local Burger Doodle fast-food restaurant has a drive-through window. Customers in cars arriveat the window at the rate of 10 per hour (Poisson distributed). It requires an average of4 minutes (exponentially distributed) to take and fill an order. The restaurant chain has a servicegoal of an average waiting time of 3 minutes. During the 2-hour lunch period, the arrival rate of drive-in customers increases to 20 per hour. Will the two-window system be able to achieve the restaurant’s service goal during this rush period?
. At a car washing service facility customers arrive at the rate of 8 cars per hour. The service can manage an average of 12 cars per hour. The arrivals follow a Poisson distribution and the service follows a Exponential distribution. Calculate a) Utilization of the system b) Average number of customers in the system c) Average time customers spend in the system
Students arrive randomly at the help desk of the computer lab. There is only one service agent, and the time required for inquiry varies from student to student. Arrival rates have been found to follow the Poisson distribution, and the service times follow the negative exponential distribution. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. On average, how long (in minutes) does it take to service each student?

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