An ice cream truck is parked at a local beach and customers queue up to buy ice creams at a rateof one per minute. The arrival pattern of people buying ice cream is essentially random. It takes40 seconds on average to serve a customer ice cream, with a standard deviation of 20 seconds.Find the following expected measures of performance for this system: the expected time in thequeue for ice cream, the expected total time to get an ice cream, and the expected number ofcustomers waiting for ice cream.

Given - Customer Arrival Rate (λ) = 1 per minute Service Rate (μ) = 40 seconds Standard…

Answered: An ice cream truck is parked at a local…

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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The BPD has three tellers to provide service. Each teller, on average, serves one customer in three minutes per customer, the latter arriving 50 every hour. Due to complaints received, an evaluation of the system has been requested:(a) Give the average utilization of the service system with the three tellers.b) What is the probability of arriving at the bank with no one there?c) What is the average number of customers waiting in line?d) On average how long does a customer wait in line to be served?e) On average how many customers would be served at a teller and waiting in line?
A single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 9 customers per hour and an average service rate of 13 customers per hour. The probability of 6 customers in the system is : a. 0.9661 b. 0.8899 c. 0.3077 d. 0.03388
You are the manager of a local bank where three tellers provide services to customers. On average, each teller takes four minutes to serve a customer. Customers arrive, on average, at a rate of 40 per hour. Having recently received complaints from some customers that they waited a long time before being served, your boss asks you to evaluate the service system. Specifically, you must provide answers to the following questions: a. The average utilization of the three-teller service system is p= 0.8889. (Enter your response rounded to four decimal places.) b. The probability that no customers are being served by a teller or are waiting in line is Po= 0.0280. (Enter your response rounded to four decimal places.) c. The average number of customers waiting in line is L₁ = customers. (Enter your response rounded to one decimal place.)
There is only one copying machine in the student lounge of the business school. Students arrive at the rate of λ=40 per hour (according to a Poisson distribution). Copying takes an average of 50 seconds, or μ=72 per hour (according to a negative exponential distribution). a) The percentage of time the machine is used = percent (round your response to the nearest whole number). b) The average length of the queue = enter your response here students (round your response to two decimal places). c) The average number of students in the system = students (round your response to two decimal places).
Joe’s market is a small grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane at an average rate of 15 customers per hour and that the average order takes 3 minutes to ring up and bag. If Joe does not want the average waiting time in the queue to exceed 5 minutes, what would you tell Joe about his current system? Back up your statement with quantitative information and assumptions.
Car owners fill up when their tanks are exactly half full. At the present time, an average of 8.5 cars/hr arrive at a single-pump gas station. It takes an average of 3.68 minutes to service a car. Suppose that a gas shortage occurs and panic buying takes place. All car owners now purchase gas when their tanks are exactly 3/4 full. Since each car is putting less gas into the tank for each visit, the average service time has been reduced to 2.54 minutes. Assume that arrival and departure rates are both exponential. What is the difference in length of queue before and after the shortage scenario, in terms of vehicles? answer an absolute value, and in four decimal places.
please answer in 30 mins.
A car mechanic, Carlos, can install new mufflers at an average rate of 3 every hour (following an exponential distribution). Customers needing this service arrive at the shop (following a Poisson distribution) on an average of 2 per hour. They are served on a first-in, first-out basis and come from the very large (almost infinite) population of possible buyers. Calculate the following operating characteristics of the service system: a. The probability there are no cars in the system. b. The average number of cars waiting in line. c. The average number of cars in the system. d. The average time a car spends waiting in line. e. The average time a car spends in the system.
A single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 6 customers per hour and an average service rate of 15 customers per hour. The average length of time customers will spend in the system is: O a. 2.667 minutes O b. 0.1111 minutes O c. 6.667 minutes O d. 0.04444 minutes
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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