Solution:
Given that:
customers arrive at a fast-food restaurant .In that restaurant three workers taking food orders at independent service stations.
Customer rate 120/-
7.4 During lunch hour, customers arrive at a fast-food restaurant at the rate of T20 customers...
7.5 For the fast-food restaurant chain of the previous exercise, assume that customers turn away from the store if all three service stations are busy. Let Y, denote the number of service stations busy at time . Then, (Yo is a continuous-time Markov chain. Exhibit the generator matrix.
3. A fast food restaurant has a drive-thru window. On average 40 customers arrive at the window every hour. It takes 1 minute on average to serve a customer. a. What is the average number of customers that will be in line and in service at any time? b. On average, how long will a customer spend in the system?
Problem 1. Consider a fast food restaurant where customers arrive and get in line according to a Poisson process with an average rate of 120 customers per hour. The restaurant has one line and the amount of time it takes the cashier to serve a customer is exponentially distributed with a mean of 2 minutes. Let X_t denote the number of customers in line at time t. 1. Give the state space of the chain (X_t)t≥0. 2. For each state...
During lunchtime at a certain fast food restaurant, customers arrive at an average rate of 7 customers every 5 minutes. assume a poisson distribution to find the probability that: A) exactly 12 customers arrive in a given 10 minute interval (perform this calculation using an appropriate formula, showing the setup.) b) between 5 and 10 customers (inclusive) arrive in a given 5 minute interval (show how you can answer this from the table) c) after a customer arrives, find the...
Queuing theory question: At a restaurant during the lunch hour 4 customers enter per minute and spend an average of 5 minute ordering and waiting to pick up their food. 35% take their food to go and 65% sit down. Those that down spend an average of 24 minutes sitting. a. How many people on average are in the restaurant? b. How many on average are sitting?
Queuing theory question: At a restaurant during the lunch hour 4 customers enter per minute and spend an average of 5 minute ordering and waiting to pick up their food. 35% take their food to go and the rest sit down. Those that is down spend an average of 24 minutes. How many people on average are in the restaurant and how many are in the dining area?
3. Customers arrive at the drive-through lane of a fast food restaurant at a rate of one every 3 minutes. Use the Poisson probability distribution to answer the following (12 Marks) a. What is the expected number of customers in one hour? b. What is the probability that exactly two customers arriving at the drive-through lane in a nine-minutes interval? c. What is the probability that less than two customers arrive at the drive through lane a nine-minutes interval? d....
The waiting time until a customer is served at a fast food restaurant during lunch hours has a skewed distribution with a mean of 2.4 minutes and a standard deviation of 0.4 minute. Suppose that a random sample of 44 waiting times will be taken. Compute the probability that the mean waiting time for the sample will be longer than 2.5 minutes. Answer: (Round to 4 decimal places.)
Please answer using stochastic operations principles Cars arrive at a rate of 10 per hour in a single-server drive-in restaurant. Assume that the teller serves vehicles with a rate exponentially distributed with a mean of 4 minutes per car (ie, a rate of 1 car every 4 minutes). Answer the following questions: (a) What is the probability that the teller is idle? (b) What is the average number of cars waiting in line for the teller? (A car that is...
The Yum and Yee food truck near the business school serves customers during lunch hour by taking orders and making fresh batches of stir-fry. Customers have only one choice during the lunch hour so that Y&Y can maximize the number of customers served. Assume that each customer places just one lunch order, and all lunch orders are the same size: one unit of stir-fry. The stir-fry cooking works in this manner. First, one person cooks a batch of orders in...