A restaurant receives on average 1,000 customers per day (between 9am and 9pm). During peak times (12pm to 2pm and 7pm to 9pm), the restaurant receives around 700 customers in total and, on average, 70 customers can be found in the restaurant at a given point in time. At non-peak times, the restaurant receives 300 customers in total and, on average, 30 customers can be found in the restaurant at a given point in time. a. What is the average time that a customer spends in the restaurant during peak times? b. What is the average time that a customer spends in the restaurant during non-peak times?

A restaurant receives on average 1,000 customers per day (between 9am and 9pm). During peak times (12pm to 2pm and 7pm to 9pm), the restaurant receives around 700 customers in total and, on average, 70 customers can be found in the restaurant at a given point in time. At non-peak times, the restaurant receives 300 customers in total and, on average, 30 customers can be found in the restaurant at a given point in time. a. What is the average time that a customer spends in the restaurant during peak times? b. What is the average time that a customer spends in the restaurant during non-peak times?

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter20: Queuing Theory

Section20.6: The M/m/s/gd/∞/∞ Queuing System

Problem 2P

See similar textbooks

Similar questions

In a lake, the population of a particular fish species is about 1 million. Fish reproduce by 20% of the population each month, regardless of the season. In addition, fish die naturally after living for an average of 10 months. There are two separate companies (for example, A and B) fishing with 5 boats on the edge of this lake. According to current data, each boat catches 5000 fish per month. However, if the total number of boats caught in the lake increases, the number of fish to be caught by each boat decreases, as the boats will prevent each other from fishing. In addition, if the fish population in the lake increases, the fish caught per boat increases, and if the population decreases, the fish caught per boat decreases. As companies earn money from hunting, they want to buy new boats over time and enlarge their boat fleet.
In a lake, the population of a particular fish species is about 1 million. Fish reproduce by 20% of the population each month, regardless of the season. In addition, fish die naturally after living for an average of 10 months. There are two separate companies (for example, A and B) fishing with 5 boats on the edge of this lake. According to current data, each boat catches 5000 fish per month. However, if the total number of boats caught in the lake increases, the number of fish to be caught by each boat decreases, as the boats will prevent each other from fishing. In addition, if the fish population in the lake increases, the fish caught per boat increases, and if the population decreases, the fish caught per boat decreases. As companies earn money from hunting, they want to buy new boats over time and enlarge their boat fleet. Indicate the causal relationships in this system with arrows and signs. Show the causality loops in this system, at least 1 negative, at least 1 positive, and…
A local café has a single cash register, with a single assistant to work it, and three servers working to fill the customer orders. Customers arrive with exponential interarrivaltime an average of one every 2 minutes. The time to place their order and pay at theregister is normally distributed with mean 90 seconds and standard deviation 20 seconds. Each customer’s order is then passed to one of the servers who take on average5 minutes with standard deviation 1.5 minutes, also normally distributed, to fill the order.g. Estimate the expected time from the servers receiving an order to it being ready forthe customer (including any queueing time).
a. The average mobile user has 500 minutes of use per month; 90% of traffic occurs during work days. There are 20 week days per month. Assuming that in a given day, 10% of traffic occurs during the busy hour (BH), determine the traffic per subscriber per BH. b. During a busy hour, 1400 calls were offered to a group of trunks and 14 calls were lost. The average call duration has 3 minutes. Find Traffic offered, Traffic carried, Grade of Service (GOS) and the total duration of period of congestion.7. What is the height to width ratio that gives the highest performance in case implementing Multiple Input Multiple Output (MIMO) using Planar Arrays?
A local café has a single cash register, with a single assistant to work it, and three serversworking to fill the customer orders. Customers arrive with exponential interarrivaltime an average of one every 2 minutes. The time to place their order and pay at theregister is normally distributed with mean 90 seconds and standard deviation 20 seconds.Each customer’s order is then passed to one of the servers who take on average5 minutes with standard deviation 1.5 minutes, also normally distributed, to fill the order.a. Calculate the capacity of the register and the servers. What is the bottleneck inthis system?b. Calculate the average utilizations of the register and the serversc. What is the probability a customer is delayed at the register?d. What is the expected time from a customer’s arrival to the order being passed on tothe servers (including any queueing time)?e. Estimate the probability that there is a delay between a customer placing his orderand a server beginning to work on the…
A local café has a single cash register, with a single assistant to work it, and three servers working to fill the customer orders. Customers arrive with exponential interarrival time an average of one every 2 minutes. The time to place their order and pay at the register is normally distributed with mean 90 seconds and standard deviation 20 seconds. Each customer’s order is then passed to one of the servers who take on average 5 minutes with standard deviation 1.5 minutes, also normally distributed, to fill the order. a.) Calculate the capacity of the register and the servers. What is the bottleneck in this system? b.) Calculate the average utilizations of the register and the servers c.) What is the probability a customer is delayed at the register? d.) What is the expected time from a customer’s arrival to the order being passed on to the servers (including any queueing time)? e.) Estimate the probability that there is a delay between a customer placing his order and a server…
A local café has a single cash register, with a single assistant to work it, and three servers working to fill the customer orders. Customers arrive with exponential interarrival time an average of one every 2 minutes. The time to place their order and pay at the register is normally distributed with mean 90 seconds and standard deviation 20 seconds. Each customer’s order is then passed to one of the servers who take on average 5 minutes with standard deviation 1.5 minutes, also normally distributed, to fill the order. a.) Calculate the capacity of the register and the servers. What is the bottleneck in this system? b.) Calculate the average utilizations of the register and the servers c.) What is the probability a customer is delayed at the register?
A call center has 60 employees on‐line, each of whom make one phone call every 3 min on average, and talk on average for 2 min. Each call costs 15¢. What is the total traffic in erlangs? How many circuits are required for a GoS of 1%? How much should the yearly (250 working days, 8 working hours a day) lease price be for the company to make a 50% saving in its telephone bills over the first 3 years? Assume the lease set‐up fee of $30,000 should be paid over a period of 3 years.
Consider an emergency room. An average of 10 patientsarrive per hour (interarrival times are exponential). Uponentering, the patient fills out a form. Assume that this alwaystakes 5 minutes. Then each patient is processed by one oftwo registration clerks. This takes an average of 7 minutes(exponentially distributed). Then each patient walks 2 min-utes to a waiting room and waits for one of 4 doctors. Thetime a doctor takes to see a patient averages 20 minutes,with a standard deviation of 10 minutes. a On the average, how long does a patient spend in theemergency room? b On the average, how much of this time is spent wait-ing for a doctor? c What percentage of the time is each doctor busy?
In a cellular network, each cell has seven channels, two of which are dedicated solely for handoff calls. Assume that both new and handoff call arrivals are subject to a Poisson process. The average arrival rate of new calls and handoff calls is 1.5 and 0.3 calls per minute, respectively. The holding duration of a channel is exponentially distributed, with a mean of 2 minutes. Determine the blocking probability of new and handoff calls.
There are a number of plants in a garden. Each of the plants has been treated with some amount of pesticide. After each day, if any plant has more pesticide than the plant on its left, being weaker than the left one, it dies. You are given the initial values of the pesticide in each of the plants. Determine the number of days after which no plant dies, i.e. the time after which there is no plant with more pesticide content than the plant to its left. Example // pesticide levels Use a -indexed array. On day , plants and die leaving . On day , plant in dies leaving . There is no plant with a higher concentration of pesticide than the one to its left, so plants stop dying after day . Input Format The first line contains an integer , the size of the array .The next line contains space-separated integers . Constraints Sample Input 7 6 5 8 4 7 10 9 Sample Output 2 Explanation Initially all plants are alive. Plants = {(6,1), (5,2), (8,3), (4,4), (7,5),…
At the beginning of the first day (day 1) after grape harvesting is completed, a grape grower has 8000 kg of grapes in storage. On day n, for n = 1, 2, . . . ,the grape grower sells 250n/(n + 1) kg of the grapes at the local market at the priceof $2.50 per kg. He leaves the rest of the grapes in storage where each day they dryout a little so that their weight decreases by 3%. Let wn be the weight (in kg) ofthe stored grapes at the beginning of day n for n ≥ 1 (before he takes any to themarket).(a) Find the value of wn for n = 2.(b) Find a recursive definition for wn. (You may find it helpful to draw a timeline.)(c) Let rn be the total revenue (in dollars) earned from the stored grapes from thebeginning of day 1 up to the beginning of day n for n ≥ 1. Find a recursiveformula for rn.(d) Write a MATLAB program to compute wn and rn for n = 1, 2, . . . , num wherenum is entered by the user, and display the values in three columns: n, wn, rnwith appropriate headings.Run the program for num =…