You are considering to invest in a franchise fora coffee shop in your neighborhood. Tounderstand the revenue potential, you decideto visit a coffee shop from the same chain nextto your neighborhood. In the next few months,you visit this coffee shop at random timesbetween 6am and 9am. You observe that theline (queue) averages about 9 customers and ittakes about 3 minutes to get in and out of thecoffee shop. Assuming this is a typicalexperience and each customer spends about$5 per visit, what is the revenue potential perhour of this coffee shop?Hint: Calculate the number of customersarriving per minute (i.e., λ). Convert this tocustomers per hour. Then, calculate therevenue from these customers (each customerspends about $5, on average)

From the above given information, 9 customers arrive in the queue and takes at about 3 minutes to…

Answered: You are considering to invest in a…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 11P

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Please do not give solution in image formate thanku. To support National Heart Week, the Heart Association plans to install a free blood pressure testing booth in El Con Mall for the week. Previous experience indicates that, on average, 10 persons per hour request a test. Assume arrivals are Poisson distributed from an infinite population. Blood pressure measurements can be made at a constant time of five minutes each. Assume the queue length can be infinite with the FCFS discipline. What average number of persons can be expected to be in the system? What is the average amount of time that a person can expect to spend in line? On average, how much time will it take to measure a person’s blood pressure, including their waiting time?
Customers arrive at a bank counter at an average rate of 3customers per hour.a) Suggest a suitable distribution to model the number ofcustomers arriving at the counter, X, per minute.b) State clearly any assumptions you have made by suggestingthis model.c) Using your model,I. Find the probability that no customer arrive in a givenminute.II. Find the probability that at most 4 customers arrive in agiven minute.III. In any given 4 minutes period, find ? such that?(? > ?) = 0.0487.IV. Check the answer of part I and part ii using RStudio.
Compute the expected queueing time in an M/G/1 queue with an arrival rate of 10 per hour and the following service time distributions, all with mean 5 minutes: (1) exponential;(2) uniform over (0,a);(3) deterministic. Which distribution produces the smallest Wq and which the largest?
A company is using a carrier to deliver goods to a major customer. The annualdemand is $2,500,000, and the average transit time is 10 days. Another carrier promises to deliver in 7 days. What is the reduction in transit inventory?
Consider a D/D/1 queue, where D represents a deterministic (or degenerate) distribution. The interarrival times and service times do not have to be the same constant, of course. Find all five of the steady-state queueing metrics, and state parameter conditions for your results to be valid.
Netflix is a DVD movie rental company. They stock 50 DVDs of a recent blockbuster movie available for rental. Their rental fee is $4 per DVD per day. The inter-arrival time between rental requests for this movie is 2.5 hours, on average, with a standard deviation of 2.5 hours. Demand is steady throughout a 24-hour day (there is no evidence of other arrival patterns). Assume that if all copies of the DVD are rented, then customers are willing to wait for the next one to become available. Also, assume shipping is instantaneous (the shipping time is zero days). A DVD is rented, on average, for 5 days with a standard deviation of 3 days. What is the average number of unrented DVDs in Netflix’s warehouse? Hint: consider the average utilization.
A small grocery store has a single cashier lane where groceries line up to pay for their purchases. Interarrival time of customers is exponentially distributed with mean of 3 mins. Due to the variety in type and number of items purchased, transaction time is approximately exponentially distributed with mean 2.5 mins. a. Compute for the average number of customers in the cashier lane. b. Find the probability that there are at most 4 customers in the lane. c. What is the proportion of time that the cashier is idle? d. Find the average time a customer spends in the cashier, including queuing time and transaction time. e. Buying a POS machine will help reduce average transaction time to only 2 mins. (20% reduction) with the aid of a barcode reader - eliminating the need to type item codes manually. If implemented, find the percent reduction in the average time a customer spends in the cashier.
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
A. Know some of the basic queue performance measure B. Identify the relationships between queues and some statistical distribution
29) is essentially a method used by manufacturers and wholesalers, to accelerate cash receipts and avoid waiting thirty days or more, to collect for goods delivered to their customers. Cash management Cycle billing Factoring O Invoice discounting
Based on the concepts of Production Modeling and Simulation, do the following:a) Given a model of a simple queue, describe, in a simplified way, what is a source of customers.
Traffic lights placed at highway on-ramps which alternate between stop (red light) and go(green light) at fixed time intervals; e.g., every 10 seconds, A. convert the arriving traffic from following a normal distribution to following an exponentialdistribution.B. convert the arriving traffic from following an exponential distribution to following a normaldistribution.C. convert the arriving traffic from following a uniform distribution to following a Poissondistribution.D. convert the arriving traffic from following a Poisson distribution to following a uniformdistribution

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