In order to reduce the average time customer spends waiting in the queue, the Swedish Bakery considersreplacing Tim Gonzales (their current server) by John Thunderbolt who can serve faster. John Thunderbolt canserve a customer in 4 minutes on average (exponentially distributed). What would the new average waiting timein the queue (in minutes) be? If your answer is not an integer, keep two decimal points.QUESTION 12John Thunderbolt's weekly salary is $200 higher than Tim's salary. For each minute of reduction in the averagewaiting time in the queue, the Swedish Bakery avoids a loss of S60 per week. Determine whether the fallewingstatement is true or false:Swedish Bakery should replace Tim Gonzales by John Thunderbolt.O True The Swedish Bakery gets an average of 8 customers per hour. Tim Gonzales, the server, can serve a customerin 5 minutes on average. The arrival rate follows a Poisson distribution, and service time is exponentiallydistributed.What is the average number of customers in the system? If your answer is not an integer, keep two decimalpoints.What is the average waiting time in the queue (in minutes)? If your answer is not an integer, keep two decimalpoints.

Given, in the swedish bakery, Arrival rate of customers, λ =8 per hour = 8÷60 =0.13 customers per…

Answered: The Swedish Bakery gets an average of 8…

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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Suppose you’re designing a toll bridge for vehicle traffic over the Cache la Poudre River. Cars are expected to arrive at the central toll plaza at a rate of 400 per hour. You will have five toll booths, which can each process cars at a rate of 120 cars per hour. Assume cars arrive into the toll plaza according to a Poisson distribution with a mean rate of 400 units per period. Assume car processing times are exponentially distributed with a mean service rate of 120 units per period. 1. What is the probability that two channels are busy and no units are waiting in the queue? 2. What is the steady-state average length of the queue (waiting line)? 3. What is the mean number of units in the system (queue and 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 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?
A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed. Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with a mean of 37 calls per hour. The service rate per line is 24 calls per hour. (a) What is the probability that 0, 1, 2, and 3 access lines will be in use? (Round your answers to four decimal places.) P(0)=P(1)=P(2)=P(3)= (b) What is the probability that an agent will be denied access to the…
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"?
Consider two identical queuing systems except for the service time distribution. In the first system the service time is random and Poisson distributed. The service time is constant in the second system. How would the waiting time differ in the two systems?
In improving services to consumers, Limited Company Prima conducted a study of the queue time spent by consumers during the payment process with one available payment service.The average arrival of consumers in 1 hour is 8 consumers, while every hour the number of customers who can be served is 10 consumers. Count: a. The average length of time the customer is in the storeb. Average number of consumers who are being servedc. If the waiter fee is 500 and the subscription fee is waiting for 100, calculate the hourly amount
Customer interarrival times at a store are exponentially distributed with rate 8 customers per hour. Customers are served by a single customer service representative (CSR), at a rate of 10 customers per hour. Service times are also exponentially distributed. Which of the following statements are true? O The probability of having exactly three customers in the store is 0.128. O None of the answers are correct. The store has customers waiting for a CSR 80.0% of the time. The average number of customers in the store is 3.2. O The average wait time for the CSR is 24 minutes.
Please do not give solution in image format thanku Average Arrival Rate (Ri) 20 Customers/Hr Arrival Standard Deviation is 2 customers/hr Average Processing Time 12 minutes Process Time Standard Deviation 3 minutes 5 Servers 1) What is Server Utilization? 2) Average Queue Length?
Town Taxi uses three dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to Town Taxi use a common number. When all dispatchers are busy, the caller hears a waiting song until the first dispatchers becomes available. The telephone system will assign available dispatcher to the waiting callers according to FCFS. Assume that the arrival of calls follows a Poisson distribution, with an average of 35 calls per hour. Also assume that the time that each dispatcher spends with a customer follows Exponential distribution and each dispatcher takes an average of 3 minutes with each caller. 15.What is the average time in minutes that a customer spends in the system? 3.8 mins 7 mins 4.8 mins 8.9 mins
A post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks. How long does the average person spend waiting for a clerk? 1.143 minutes 3.429 minutes 1.929 minutes 0.643 minute

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