...Queuing Theory Queuing Theory • Queuing theory is the mathematics of waiting lines. • It is extremely useful in predicting and evaluating system performance. • Queuing theory has been used for operations research. Traditional queuing theory problems refer to customers visiting a store, analogous to requests arriving at a device. Long Term Averages • Queuing theory provides long term average values. • It does not predict when the next event will occur. • Input data should be measured over an extended period of time. • We assume arrival times and service times are random. • • • • Assumptions Independent arrivals Exponential distributions Customers do not leave or change queues. Large queues do not discourage customers. Many assumptions are not always true, but queuing theory gives good results anyway Queuing Model Q W λ Tw Tq S Interesting Values • Arrival rate (λ) — the average rate at which customers arrive. • Service time (s) — the average time required to service one customer. • Number waiting (W) — the average number of customers waiting. • Number in the system (Q) — the average total number of customers in the system. More Interesting Values • Time in the system (Tq) the average time each customer is in the system, both waiting and being serviced. Time waiting (Tw) the average time each customer waits in the queue. Tq = Tw + s Arrival Rate • The arrival rate, λ, is the average rate new customers arrive measured in arrivals per time period....
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...Table of contents 1. Introduction 2. Arrival Pattern of customers 3. Service Patterns 4. System Capacity 5. Number of Service Channels 6. Queue Discipline 7. Queuing Cost 8. The Four Models 9. Model-1(Single Channel Queuing Model) 10. Model-2 (Multiple-Channel Queuing) 11. Model-3 (Constant-Service-Time) 12. Model-3 (Constant-Service-Time) 13. Simulation 14. Conclusion Abstract This report is about queuing theory, it’s application and analysis. Queuing theory has a vast number of applications starting from the simplest day to day life examples to complicated computer algorithms. To further explain the queuing theory analysis we have used simulation of an example from our case study. We have done an in depth analysis of the four queuing theory models and chosen one of them for the simulation. The results can be helpful in improving the overall performance of the manufacturing facility. Introduction According to U. Narayan Bhat waiting line are a phenomena through which businesses and facilities can be helped in an orderly manner. There are several ways to forma queue (waiting line), for instance when people wait to get a boarding pass from an airline counter, there can be 3 service stations (airline counters) and hence 3 waiting lines, or there can be one service station and hence one queue. These days we mostly see one counter for airline services as this benefit the passengers and airline best. This conclusion...
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...IEEE Globecom 2010 Workshop on Broadband Wireless Access Joint Admission Control and Resource Allocation with GoS and QoS in LTE Uplink Oscar Delgado ECE, Concordia University Montreal, Qc, H3G 1M8, Canada Email: o delgad@encs.concordia.ca Brigitte Jaumard CIISE, Concordia University Montreal, Qc, H3G 1M8, Canada Email: bjaumard@ciise.concordia.ca Abstract—In this paper, an admission control (AC) scheme is proposed for handling multiclass Grade of Service (GoS) and Quality of Service (QoS) in Uplink Long Term Evolution (LTE) systems. GoS requirement in conjunction with QoS has been seldom taken into account in previous admission control and resource allocation algorithms for LTE uplink. We propose a novel algorithm for handling the priorities while fulfilling the QoS objective of all granted requests. It corresponds to a solution that combines resource allocation and admission control properties to satisfy the GoS and QoS objectives. Call blocking probability, call outage probability, system capacity and number of effectively served requests are used as performance metrics. Numerical results show that it is possible to manage a priority scheme which satisfies the QoS constraints of all granted requests without any system capacity loss, when comparing to previous algorithms. Furthermore, the proposed AC algorithm gain, for the most sensitive traffic, can be around 20% over the reference AC algorithm. Index Terms—QoS, Priority, Admission Control, Scheduling, LTE, Uplink...
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...LAB 8 Task 1 Dfnalskfj;aslja;sf Asfasfasfasf Asfasf Asfasf Asfasff Gjfgjfgdhjd Dgdrd Task 2 #include<stdio.h> //#include<conio.h> main(){ int i, j, k, n, so, tq, sob, sum, swt, stat, tata, temp, count; int bt[10], bth[10], wt[10], tat[10]; float awt=0.0, atat=0.0; char new; printf("\n\n\n\n To start round robin scheduling press any key: "); k = 0; new = getchar(); system("cls"); while(k < 7){ j = 0; sob = 0; count = 0; sum = 0; swt = 0; stat = 0; tata = 0; printf("\n\n\n\t\t\t ROUND-ROBIN SCHEDULING"); printf("\n\t\t\t ======================"); printf("\n\n\n\n\n Enter number of processes: "); scanf("%d", &n); printf("\n"); for(i = 0; i < n; i++){ printf("\n Enter burst time for Process P%d: ", i+1); scanf("%d", &bt[i]); bth[i] = bt[i]; } printf("\n\n Enter time quantum: "); scanf("%d", &tq); system("cls"); printf("\n\n\n\t\t\t ROUND-ROBIN SCHEDULING"); printf("\n\t\t\t ======================"); printf("\n\n\n\n\n Time quantum: %d", tq); for(i = 0; i < n; i++){ if(bth[i] % tq == 0){ so = bth[i] / tq; } else{so = (bth[i] / tq) +1;} sob = sob + so; } int gc[sob], gcps[sob]; ...
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...Optimal Power Allocation and Scheduling for Two-Cell Capacity Maximization ∗ Dept. Anders Gjendemsjø∗, David Gesbert†, Geir E. Øien∗ , and Saad G. Kiani† of Electronics and Telecom., Norwegian Univ. of Science and Technology, 7491 Trondheim, Norway, Email: {gjendems, oien}@iet.ntnu.no † Mobile Communications Department, Institute Eur´ com, e 06560 Sophia-Antipolis, France, Email: {gesbert, kiani}@eurecom.fr maximize the network capacity for the case of individual link power constraints [8] and a sum power constraint [9]. In [10] it is assumed that each base station, when it transmits, transmits with maximum power Pmax . Which base stations that should be active at each time slot is decided according to a rate maximization objective. However, no proof of optimality is given for the on/off power allocation. In [11] transmit power allocation for a downlink two-user interference channel is studied under a sum transmit power constraint and the assumption of symmetric interference. The derived power allocation depends on the level of interference; when the inference is above a certain threshold the total power is allocated to the best user. For interference less than the threshold, the available power is divided among the two users according to a water-filling principle. However, due to the sum power constraint and symmetry of interference assumption these results are not readily applicable for two-cell power allocation, where it is more reasonable to assume individual power constraints...
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...A Distributed Joint Channel-Assignment, Scheduling and Routing Algorithm for Multi-Channel Ad Hoc Wireless Networks Xiaojun Lin and Shahzada Rasool School of Electrical and Computer Engineering, Purdue University West Lafayette, IN 47907, U.S.A. {linx,srasool}@ecn.purdue.edu Abstract— The capacity of ad hoc wireless networks can be substantially increased by equipping each network node with multiple radio interfaces that can operate on multiple non-overlapping channels. However, new scheduling, channelassignment, and routing algorithms are required to fully utilize the increased bandwidth in multi-channel multi-radio ad hoc networks. In this paper, we develop a fully distributed algorithm that jointly solves the channel-assignment, scheduling and routing problem. Our algorithm is an online algorithm, i.e., it does not require prior information on the offered load to the network, and can adapt automatically to the changes in the network topology and offered load. We show that our algorithm is provably efficient. That is, even compared with the optimal centralized and offline algorithm, our proposed distributed algorithm can achieve a provable fraction of the maximum system capacity. Further, the achievable fraction that we can guarantee is larger than that of some other comparable algorithms in the literature. I. I NTRODUCTION Multi-channel multi-radio ad hoc wireless networks have recently received a substantial amount of interest, especially under...
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...Great Zimbabwe University Faculty of Agriculture and Natural Sciences Department of Mathematics and Computer Science Student: Sigwadhi Teddy M149125 Research Project (HSOR 460) Proposal Presentation in partial fulfilment of BSc. 4th Year Special Honours Degree in Operations Research and Statistics Supervisor: Mr. R. Mawonike Research Topic Queuing theory based approach to the analysis of sales checkout at Montagu Spar supermarket Location: Avenues Area, Harare, Zimbabwe Background of the study • Zimbabwe is an important emerging country among the developing countries. • The Spar Montagu has been chosen to be the research object primarily because of its clientele which have different buying behaviors. There are a mix of customers, low to high class customers and it has been seen to provide interesting results on the busy and non busy periods. • The main purpose of this project is to study the application of queuing theory and to evaluate the parameters involved in the service unit for the sales checkout operation in Spar Montagu supermarket Background of the study continued… • Queuing theory is the theory of waiting lines and service provision • A mathematical model is to be developed to analyse the performance of the checking out service unit • Two parameters need to be determined from the data collected in the supermarket through the mathematical model to the service point. • One parameter is the customer arrival rate to the service point per hour • The other is the...
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...NETW320 -- Converged Networks with Lab Lab #3 Title: IPv4 TOS and Router Queuing Objectives In this lab, you will work with an intranet for an organization that will encompass four different site locations in different cities. The subnets of these locations will be connected by a backbone IP network. The organization will be using a converged network that allows data and real-time voice traffic to traverse the same packet-switched network. The data traffic will consist of FTP (file transfer protocol) and email traffic and the voice traffic will be a VoIP (Voice over Internet Protocol) implementation. You will experiment with various router queuing policies to see how routers within a TCP/IP network can be utilized to support QoS (Quality of Service) within a converged network that is based on TCP/IP. Explanation and Background Traditional voice and data applications have been kept on separate networks. The voice traffic is confined to a circuit-switched network while data traffic is on a packet-switched network. Often, businesses keep these networks in separate rooms, or on different floors, within buildings that they own or lease (and many still do). This requires a lot of additional space and technical manpower to maintain these two distinct infrastructures. Today’s networks call for the convergence of these circuit-switching and packet-switching networks, such that voice and data traffic will traverse a common network based on packet switching. A common WAN technology...
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...Overview In this lab, we will compare the speed and accuracy of different traffic representations: explicit traffic, background traffic, and hybrid traffic. The network used in the lab is a model of a company that provides video-on-demand services to 100 users. The company would like to introduce three classes of service for its clients: gold (ToS = 3), silver (ToS = 2) and bronze (ToS = 1). To provide differentiated treatment for the different service classes, Weighted Fair Queuing (WFQ) has been configured on the access router. In this lab, we will predict the delay for each class of service and compare the results obtained using the different traffic modeling approaches. Objectives and Methodology * Create a simple network with explicit traffic and run a simulation. * Replace explicit traffic with background traffic and rerun the simulation. * Replace background traffic with hybrid traffic and rerun the simulation. * Assess and compare the speed and accuracy of the three traffic-modeling approaches. Explanation and Background In the real world, one of the most important jobs a network manager can do is manage the traffic on the network. If the traffic doesn’t flow, the network is not exactly a credit to its operators. In addition, we now deal with many different types of traffic that are particular to certain applications and architectures, the most obvious examples being voice and video traffic. In these applications, the number one demand is for low delay...
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...Queuing Theory Significance There is a very significant reason why Queuing Theory exists. Not only does it apply to a wide variety of topic, many within the business and supply chain industries, it also helps prove cause and effect. In addition to this, it provides a very logical idea of what a solution to a problem it has discovered should be. Measuring and understanding both order rate and service rate can potentially be the difference between business success and business failure. For example, if a company has too slow of a service rate, it is going to lose business because of the long wait times. On the opposite end of the spectrum, if a company focuses too much on improving its service rate instead of understanding its ratio compared to order rate, it will be misusing its very valuable resources. It is also important to have knowledge of all different types of queuing systems. Importance of Queuing Configuration As one can imagine, the importance of a queuing system configuration is very significant as well. As stated above, there are several different types of queuing systems and queuing configurations. If a business uses an improper queuing system or queuing configuration, it can suffer from one of many different negative consequences. Some examples of different types of queuing systems/queuing configurations are First Come First Served, First In First Out, Round Robin, Service in Random order, and many more. Queuing systems and configurations also vary by the number...
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...Queuing Theory Queuing Theory Waiting in lines is a social phenomenon that people face on a daily basis. Queues of people form when checking in at the airport, purchasing items at a cash register, and getting on rides in amusement parks. Waiting in lines can have both economic costs and psychological costs when customers perceive it as a negative experience. Waiting too long in line can be extremely frustrating for customers and staff. Analyzing and understanding queuing systems for service businesses involves finding and managing the best level of service that will keep customers happy and costs under control. The problem for managers in most queuing situations is the trade-off decision between adding costs of providing more rapid service against the inherent cost of waiting. To analyze a queuing system one must look at arrival characteristics including the pattern in which customers arrive at the facility, customer behaviors once they are in line, and the size of the customer population. Service characteristics, such as, the configuration of the service system and the pattern of service times must also be considered in the mathematical model (Render, Stair, Hannah, & Hail, 2015). In this paper, I will discuss the advantages and disadvantages of queuing theory for an organization in the service industry and the benefits provided by the constant service time model Queuing Systems for Service Businesses Queuing systems are put in place to serve customers in an orderly...
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...* Management optimization of bank’s queuing system * Abstract Nowadays the queue phenomenon in the bank offices is a common and troublesome issue that nearly occurs everyday in the banks of China. The rapid tempo of life makes people pay much attention to the time management, they don’t willing to spend much time on queuing and gradually lose confidence in banks. In order to improve the efficiency and the satisfy degree of customers and finally increase the profit of banks, the banks have to do something about their current queuing system. This proposal aims at analyzing the current queuing system of the China banks, finding out existing problems and carrying out some effective measures based on the previous researches, the principle of queuing and statistic method. Under the premise of less increasing the operation cost of the banks to improve the service efficiency in order to realize the win-win result of customers satisfaction and banks profit. Background Every person no matter he is young or old may have some painful experiences waiting in the banks of China. Customers still have to wait for a period of time even when they avoid the busy hours of the banks. Not alone the busy operation time or the peak period of the banks people have to wait for ages. I also had the similar experiences when I was an undergraduate student. As a student we need to pay our tuition fee through a certain bank such as Bank of China before a semester begins. However so many students...
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...Queuing Theory Queuing Theory is generated from the service industries such as shops and retail dealers that need to pay much attention to the feeling of the customers and, at the mean time, to the cost with that the service was offered. As a retailer manager, one of the important things he or she might focus on is that the queue line length which could not be too long or too short. If the queue line is too long, the customer would be impatient and complain about the service quality the shop offers while if the shop gives too many counters to deal with the customers transaction further to reduce the length of the queue, it is definitely to increase the cost of the operation. Queue Theory is a kind of tool that could help the managers who need to analyze the queue line and estimate the cost of controlling it to understand the situation and make a decision on it. The prerequisite of Queue Theory is that the customers, services and other factors in the systems are discrete. In other words they are independent with each other since the rate of the customer coming and the rate of the service provided would not affect each other. Then these factors could meet the demand of Poisson Distribution. There are four models about Queuing Theory according to our textbook: MM1- Single-Server Queuing Model, MMS- Multiple-Server Queuing Model, MD1- Constant-Service-Time Model and Limited-Population Model. They are very useful in the different areas in the business. The first model single-server...
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...Quantitative Modules: I Love Coffee (ILC) illustrate a waiting-line system. The Queuing theory is a very important aspect of operations at ILC, and plays as vital tool to ILC’s operations manager. I Love Coffee drive through, implements a queuing system with its customers, having customers wait in line for the product. Characteristics of the waiting –line system at the I Love Coffee drive through. First using the arrivals or input in the systems of all the customers of (ILC) this will help build a database to better understand aspects of the ILC’s customers, such as the size or number of customers in given period of time, and certain patterns that emerge to help demonstrate a better understanding an example would be statistical distribution. With respect to the size of the population at I Love Coffee, it has an unlimited population. Patterns of customer arrivals at (ILC) show a rise in arrivals between 07:00AM – 11:00AM and 6:00PM – 12:00AM with intervals varying from 3:00 to 5:00 minutes per arrival or customer. Moreover, with regards to the waiting line characteristics ILC has a limited queuing system that can take 6 vehicles at one certain time period, more over the drive through also acts as the service facility, supplying the coffee through designated collection windows. Additionally, to have a better quantitative understanding of the arrival rate with regards to the queuing theory, a discrete Poisson distribution can be established by the following: x: 3 P(x)=...
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...Queuing Theory Most restaurants want to provide an ideal level of service wherein they could serve their customers at the least minimum time. However, as the restaurant established its name to the public, it makes a great queuing or waiting line that most of the customers do not want. Not all restaurants desire for queue since it could make confusions to them and because of their losses from the customers who go away and dissatisfied. For some time, adding chairs and tables are not enough to solve the queuing problem. In the case of Tamagoya Noodle House, they have this principle of serving the customer with their high quality ramen regardless of the number of customers. In short, they are more on the quality than the quantity; not on the profit side but rather on the quality side. But because they really want to serve more customers especially those ramen lovers who came from far places, they want to solve these queuing problems. Service time distribution Arrivals Customer 3 Customer 2 Customer 1 Service Facility Queue Fig. 1 Queuing System Configuration Assumptions of the model: Since Tamagoya Noodle House uses a Single-Channel, Single-Phase model in order to avoid confusion of customer’s order. The model we used assumes that seven conditions exist: 1. Arrivals are served on a First-in, First-out basis. Though some of customers who ordered less and or senior citizens were prioritized to be served first. 2. Every customer...
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