# Load Balancing and Switch Scheduling

Save this PDF as:

Size: px
Start display at page:

## Transcription

3 queue length at time slot and and denote the number of arrivals and departures in time slot, respectively. Note and only take binary values. For any queue, we have (1) The dynamics of the queue is not linear and it is often approximated as a linear system: (2) In a load balancing system, the load balancer controls the arrival to each queue while is given by the service discipline. On the other hand, switch scheduling algorithm determines the departures from each queue while is not controllable. Note the approximate system dynamics have an equivalent representation: (3) If we set, and, then we have (4) Note this is exactly the same as Equation 2. If we start with a bandwidth allocation problem that has system dynamics as in 2 and we need to determine, we arrive at a load balancing problem as in 4 and we need to determine, the equivalent of. This equivalence is achieved by considering a negative dual system. By negative, we mean that the new system has a state variable that is the negative of the original system. By dual system, we mean the arrival and departure processes are swapped. Essentially, one can imagine this as reversing all the arrows in Figure 1(b) and consider the bandwidth allocator as a token allocator. If a token arrives at queue, then one packet can leave that queue. Hence, the number of packets waiting in the queue is equal to the negative of the number of tokens in the queue. By doing this, we can cast the bandwidth allocation problem as a load balancing problem. Note this is only true for the approximate queue dynamics. We would need to verify how well this approximation works in the simulations. Another technical point is that the time indexes change when we swap the arrivals and departures. This is due to our convention that arrivals occur at the beginning of the time slot and departure occur at the end of the time slot. Between the measurement of and, there is one arrival and one departure. Thus we swap the arrival and the departure within the time of measuring and, we need to change their time indexes as well to conform with our assumption. By considering the negative dual system, we arrive at two identical systems except for the sign of the state of the system. Hence, the load balancing algorithm SQ (join the shortest queue) will lead to the bandwidth allocation algorithm LQF (Longest Queue First). Also due to the equivalence in the system dynamics, when a version of RAND, RAND(d) and RAND(d,m) is used in load balancing, the performance of the switch is similar to what can be achieved by the dual algorithm in switch scheduling.

5 cast load balancing as a switch scheduling problem since the scheduling is much better studied for the crossbar switch. However, there is some technicality. In a switch scheduling algorithm, an edge can be useless if there are no packets from its input port to its output port. However, the matching algorithms deal with this problem naturally. For load balancing, an edge is useless when there is no arrival to that input port at a given time slot. But this is not usually not taken care of in the matching algorithms. This can be easily fixed. At time, if there is no packet arriving at input port, we assume for all. Thus we can apply the MWM (Maximum Weight Matching) (and potentially many other scheduling algorithms) to load balancing and get a new load balancing algorithm. The counterpart of MWM is essentially a minimum weight matching with the appropriate queue lengths set to if no packets arrive in the current time slot. IV. ENTROPY RATE OF LOAD BALANCING AND SWITCH SCHEDULING In Section II and III, we have shown that load balancing and switch scheduling are dual systems of each other for the linear dynamics approximation. If the linear approximation proves itself to be an accurate one, we would expect the property of one system holds true for its dual system. In this section, we study the entropy rate of the randomized scheduling based on the knowledge of the entropy rate of randomized load balancing as studied in [5]. The one dimensional load balancing system as shown in Figure 1(a) is studied in [5]. In particular, it is assumed that all servers have identical service rates for. The class of the randomized load balancing algorithms that can be described by a coin toss model is considered. We review the coin toss model defined in [5] as follows. Let be the permutation of numbers of which arranges the queues in the increasing order in time slot right after departures. Let be a probability vector representing the probabilities of the outcome of the toss of a coin with sides and let. If a packet arrives in time slot, we toss an -sided coin distributed according to. If the outcome of the coin toss is, randomized algorithm SQ( ) can be identified with, then the packet joins the queue. The (5) The special case of can be identified with the vector. The main theorem gives a closed-form formula for the entropy rate of the load balancing algorithms that can be specified by the coin toss model. Theorem 1: Suppose the arrival process to the -queue system is stationary, ergodic and renewal. Let the service distribution be independent of the arrival process and i.i.d. Under mild technical conditions [5], the entropy rate of the queue-size process of any algorithm that belongs to the coin toss model is equal

6 to, where are random variables representing the inter-arrival time, the service time and the coin toss result respectively. The problem of the entropy rate of the bandwidth allocation problem shown in Figure 1 (b) can be similarly described as a coin toss model. We let be the permutation of and it arranges the queue sizes in decreasing order in time slot right after arrivals. The coin toss probability for LQF( ) 1 is the same as that of SQ( ). We toss a coin to decide which queue to serve. When all the queues are always non-empty, the linear queue dynamics are exact. Hence, the duality holds. We could use the negative dual transform shown in Section II and cast the bandwidth allocation problem in the language of load balancing. Let for, then the randomized bandwidth allocation problem is precisely a load balancing problem that can be described as follows. Let be the permutation of and it arranges the in the increasing order in time slot right after departures. Then we do the coin toss. Note this description is exactly the same as the coin toss model for the load balancing algorithm. We can also swap the arrival process and departure process since they have exactly the same properties. For example, with Poisson arrivals and exponential services, both inter-arrival and inter-departure times are exponential. Therefore, exchanging the arrivals and departures will not lead to inconsistency problems. Hence, we claim the entropy rate of the two systems are equal. This leads us to the following proposition. Proposition 1: If all the queues in the system are always non-empty, the entropy rate of the queue dynamics is the same for the load balancing and switch scheduling systems with correspondent parameters. Hence, the entropy rate of the load balancing system with i.i.d. arrivals of rate for each queue has the entropy rate of. However, Proposition 1 does not hold when the queues can be empty since the queue dynamics is no longer linear. We believe this is due to the loss of inter-changeability of the inter-arrival and interservice times. Let us assume Poisson arrivals and exponential services. For load balancing and bandwidth allocation systems, the inter-arrival times are exponential, but the inter-service times are exponential plus some potential idle time between services due to empty queues. However, when we consider the negative dual system of the bandwidth allocation, the new arrival process has an inter-arrival time of the sum of exponential random variable plus some random idle time. Thus, we no longer have the exact mapping. We denote the random time between serving the packet and the packet as. Note is always equal to zero when all the queues are always non-empty. The bijection that proves Theorem 1 no longer holds. However, we have two injections that give a lower bound and an upper bound on the entropy rate. Proposition 2: The entropy rate of the bandwidth allocation system is upper bounded by and lower bounded by. 1 In LQF( ), we randomly choose samples in each time slot and serve the longest queue among the samples. If all the queues are empty, no packet will be served in the current time slot.

9 Fraction of Queues with Load At Least i: s i (t) Performance of SQ(d), LQF(d) and the Joint Algorithm SQ(2) & RAND SQ(3) & RAND SQ(2) & LQF(2) RAND & LQF(2) RAND & LQF(3) Load i Fig. 4. Performance of Joint Load Balancing and Bandwidth Allocation ACKNOWLEDGMENTS The authors would like to thank Isaac Keslassy for his helpful discussions. REFERENCES [1] C.S. Chang, D.S. Lee, Y.S Jou, Load balanced Birkhoff-von Neumann Switches IEEE Workshop on High Performance Switching and Routing, [2] A. Czumaj and V. Stemann, Randomized Allocation Processes, FOCS, [3] Devavrat Shah, Balaji Prabhakar, The use of memory in randomized load balancing, ISIT [4] P. Giaccone, B. Prabhakar, D. Shah, Randomized Scheduling Algorithms for High Aggregate Bandwidth switches, Infocom [5] C. Nair, B. Prabhakar, D. Shah, The Randomness in Randomized Load Balancing, Proceedings of the 39th Annual Allerton Conference on Communication, Control and Computing, pp , October [6] N. McKeown, B. Prabhakar, EE384Y Lecture Notes, Stanford Unviersity 2003.

### Load Balancing with Migration Penalties

Load Balancing with Migration Penalties Vivek F Farias, Ciamac C Moallemi, and Balaji Prabhakar Electrical Engineering, Stanford University, Stanford, CA 9435, USA Emails: {vivekf,ciamac,balaji}@stanfordedu

### Hydrodynamic Limits of Randomized Load Balancing Networks

Hydrodynamic Limits of Randomized Load Balancing Networks Kavita Ramanan and Mohammadreza Aghajani Brown University Stochastic Networks and Stochastic Geometry a conference in honour of François Baccelli

Load Balancing with Memory Michael Mitzenmacher Harvard University michaelm@eecs.harvard.edu Balaji Prabhakar Stanford University balaji@stanford.edu Devavrat Shah Stanford University devavrat@cs.stanford.edu

### A QOS BASED LOAD BALANCED SWITCH

A QOS BASED LOAD BALANCED SWITCH Vishnu Prasath Badri narayanan, Manigandan S K Veltech Hightech Dr.RR and Dr.SR Engineering college,india ABSTRACT The simple architecture with high forwarding capacity

### 1212 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 16, NO. 5, OCTOBER 2008

1212 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 16, NO. 5, OCTOBER 2008 Padded Frames: A Novel Algorithm for Stable Scheduling in Load-Balanced Switches Juan José Jaramillo, Student Member, IEEE, Fabio

### Performance Analysis of a Practical Load Balanced Switch

Performance Analysis of a Practical Balanced Switch Yanming Shen, Shivendra S Panwar, H Jonathan Chao Department of Electrical and Computer Engineering Polytechnic University Abstract The load balanced

### How Useful Is Old Information?

6 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 11, NO. 1, JANUARY 2000 How Useful Is Old Information? Michael Mitzenmacher AbstractÐWe consider the problem of load balancing in dynamic distributed

### 2.3 Convex Constrained Optimization Problems

42 CHAPTER 2. FUNDAMENTAL CONCEPTS IN CONVEX OPTIMIZATION Theorem 15 Let f : R n R and h : R R. Consider g(x) = h(f(x)) for all x R n. The function g is convex if either of the following two conditions

### Chapter 1. Introduction

Chapter 1 Introduction 1.1. Motivation Network performance analysis, and the underlying queueing theory, was born at the beginning of the 20th Century when two Scandinavian engineers, Erlang 1 and Engset

### Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay

Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture - 17 Shannon-Fano-Elias Coding and Introduction to Arithmetic Coding

### This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

IEEE/ACM TRANSACTIONS ON NETWORKING 1 A Greedy Link Scheduler for Wireless Networks With Gaussian Multiple-Access and Broadcast Channels Arun Sridharan, Student Member, IEEE, C Emre Koksal, Member, IEEE,

### 6.6 Scheduling and Policing Mechanisms

02-068 C06 pp4 6/14/02 3:11 PM Page 572 572 CHAPTER 6 Multimedia Networking 6.6 Scheduling and Policing Mechanisms In the previous section, we identified the important underlying principles in providing

### Per-flow Re-sequencing in Load-Balanced Switches by Using Dynamic Mailbox Sharing

Per-flow Re-sequencing in Load-Balanced Switches by Using Dynamic Mailbox Sharing Hong Cheng, Yaohui Jin, Yu Gao, YingDi Yu, Weisheng Hu State Key Laboratory on Fiber-Optic Local Area Networks and Advanced

### Change Management in Enterprise IT Systems: Process Modeling and Capacity-optimal Scheduling

Change Management in Enterprise IT Systems: Process Modeling and Capacity-optimal Scheduling Praveen K. Muthusamy, Koushik Kar, Sambit Sahu, Prashant Pradhan and Saswati Sarkar Rensselaer Polytechnic Institute

### STABILITY OF LU-KUMAR NETWORKS UNDER LONGEST-QUEUE AND LONGEST-DOMINATING-QUEUE SCHEDULING

Applied Probability Trust (28 December 2012) STABILITY OF LU-KUMAR NETWORKS UNDER LONGEST-QUEUE AND LONGEST-DOMINATING-QUEUE SCHEDULING RAMTIN PEDARSANI and JEAN WALRAND, University of California, Berkeley

### Quantitative Analysis of Cloud-based Streaming Services

of Cloud-based Streaming Services Fang Yu 1, Yat-Wah Wan 2 and Rua-Huan Tsaih 1 1. Department of Management Information Systems National Chengchi University, Taipei, Taiwan 2. Graduate Institute of Logistics

### ECE 358: Computer Networks. Solutions to Homework #4. Chapter 4 - The Network Layer

ECE 358: Computer Networks Solutions to Homework #4 Chapter 4 - The Network Layer P 4. Consider the network below. a. Suppose that this network is a datagram network. Show the forwarding table in router

### princeton univ. F 13 cos 521: Advanced Algorithm Design Lecture 6: Provable Approximation via Linear Programming Lecturer: Sanjeev Arora

princeton univ. F 13 cos 521: Advanced Algorithm Design Lecture 6: Provable Approximation via Linear Programming Lecturer: Sanjeev Arora Scribe: One of the running themes in this course is the notion of

### Smart Queue Scheduling for QoS Spring 2001 Final Report

ENSC 833-3: NETWORK PROTOCOLS AND PERFORMANCE CMPT 885-3: SPECIAL TOPICS: HIGH-PERFORMANCE NETWORKS Smart Queue Scheduling for QoS Spring 2001 Final Report By Haijing Fang(hfanga@sfu.ca) & Liu Tang(llt@sfu.ca)

### Decentralized Utility-based Sensor Network Design

Decentralized Utility-based Sensor Network Design Narayanan Sadagopan and Bhaskar Krishnamachari University of Southern California, Los Angeles, CA 90089-0781, USA narayans@cs.usc.edu, bkrishna@usc.edu

### Xiaoqiao Meng, Vasileios Pappas, Li Zhang IBM T.J. Watson Research Center Presented by: Payman Khani

Improving the Scalability of Data Center Networks with Traffic-aware Virtual Machine Placement Xiaoqiao Meng, Vasileios Pappas, Li Zhang IBM T.J. Watson Research Center Presented by: Payman Khani Overview:

### Pull versus Push Mechanism in Large Distributed Networks: Closed Form Results

Pull versus Push Mechanism in Large Distributed Networks: Closed Form Results Wouter Minnebo, Benny Van Houdt Dept. Mathematics and Computer Science University of Antwerp - iminds Antwerp, Belgium Wouter

### Analysis of a Production/Inventory System with Multiple Retailers

Analysis of a Production/Inventory System with Multiple Retailers Ann M. Noblesse 1, Robert N. Boute 1,2, Marc R. Lambrecht 1, Benny Van Houdt 3 1 Research Center for Operations Management, University

### LECTURE 16. Readings: Section 5.1. Lecture outline. Random processes Definition of the Bernoulli process Basic properties of the Bernoulli process

LECTURE 16 Readings: Section 5.1 Lecture outline Random processes Definition of the Bernoulli process Basic properties of the Bernoulli process Number of successes Distribution of interarrival times The

### Analysis of an Artificial Hormone System (Extended abstract)

c 2013. This is the author s version of the work. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purpose or for creating

### Adaptive Batch Scheduling for Packet Switching with Delays

1 Adaptive Batch Scheduling for Packet Switching with Delays Kevin Ross and Nicholas Bambos 1 University of California Santa Cruz, kross@soe.usc.edu Stanford University, bambos@stanford.edu We discuss

### IEEE/ACM TRANSACTIONS ON NETWORKING 1 1063-6692/\$26.00 2009 IEEE

IEEE/ACM TRANSACTIONS ON NETWORKING 1 Feedback-Based Scheduling for Load-Balanced Two-Stage Switches Bing Hu, Student Member, IEEE, and Kwan L. Yeung, Senior Member, IEEE Abstract A framework for designing

### CMSC 858T: Randomized Algorithms Spring 2003 Handout 8: The Local Lemma

CMSC 858T: Randomized Algorithms Spring 2003 Handout 8: The Local Lemma Please Note: The references at the end are given for extra reading if you are interested in exploring these ideas further. You are

### Keywords: Dynamic Load Balancing, Process Migration, Load Indices, Threshold Level, Response Time, Process Age.

Volume 3, Issue 10, October 2013 ISSN: 2277 128X International Journal of Advanced Research in Computer Science and Software Engineering Research Paper Available online at: www.ijarcsse.com Load Measurement

### UNIT 2 QUEUING THEORY

UNIT 2 QUEUING THEORY LESSON 24 Learning Objective: Apply formulae to find solution that will predict the behaviour of the single server model II. Apply formulae to find solution that will predict the

### Minimizing Probing Cost and Achieving Identifiability in Probe Based Network Link Monitoring

Minimizing Probing Cost and Achieving Identifiability in Probe Based Network Link Monitoring Qiang Zheng, Student Member, IEEE, and Guohong Cao, Fellow, IEEE Department of Computer Science and Engineering

### The Exponential Distribution

21 The Exponential Distribution From Discrete-Time to Continuous-Time: In Chapter 6 of the text we will be considering Markov processes in continuous time. In a sense, we already have a very good understanding

### Performance Analysis of a Telephone System with both Patient and Impatient Customers

Performance Analysis of a Telephone System with both Patient and Impatient Customers Yiqiang Quennel Zhao Department of Mathematics and Statistics University of Winnipeg Winnipeg, Manitoba Canada R3B 2E9

### Deployment of express checkout lines at supermarkets

Deployment of express checkout lines at supermarkets Maarten Schimmel Research paper Business Analytics April, 213 Supervisor: René Bekker Faculty of Sciences VU University Amsterdam De Boelelaan 181 181

### Stochastic Processes and Queueing Theory used in Cloud Computer Performance Simulations

56 Stochastic Processes and Queueing Theory used in Cloud Computer Performance Simulations Stochastic Processes and Queueing Theory used in Cloud Computer Performance Simulations Florin-Cătălin ENACHE

### A QUEUEING-INVENTORY SYSTEM WITH DEFECTIVE ITEMS AND POISSON DEMAND. bhaji@usc.edu

A QUEUEING-INVENTORY SYSTEM WITH DEFECTIVE ITEMS AND POISSON DEMAND Rasoul Hai 1, Babak Hai 1 Industrial Engineering Department, Sharif University of Technology, +98-1-66165708, hai@sharif.edu Industrial

### Transportation Polytopes: a Twenty year Update

Transportation Polytopes: a Twenty year Update Jesús Antonio De Loera University of California, Davis Based on various papers joint with R. Hemmecke, E.Kim, F. Liu, U. Rothblum, F. Santos, S. Onn, R. Yoshida,

### Cloud Computing. Computational Tasks Have value for task completion Require resources (Cores, Memory, Bandwidth) Compete for resources

Peter Key, Cloud Computing Computational Tasks Have value for task completion Require resources (Cores, Memory, Bandwidth) Compete for resources How much is a task or resource worth Can we use to price

### Scaling 10Gb/s Clustering at Wire-Speed

Scaling 10Gb/s Clustering at Wire-Speed InfiniBand offers cost-effective wire-speed scaling with deterministic performance Mellanox Technologies Inc. 2900 Stender Way, Santa Clara, CA 95054 Tel: 408-970-3400

### CURTAIL THE EXPENDITURE OF BIG DATA PROCESSING USING MIXED INTEGER NON-LINEAR PROGRAMMING

Journal homepage: http://www.journalijar.com INTERNATIONAL JOURNAL OF ADVANCED RESEARCH RESEARCH ARTICLE CURTAIL THE EXPENDITURE OF BIG DATA PROCESSING USING MIXED INTEGER NON-LINEAR PROGRAMMING R.Kohila

### Appendix: Simple Methods for Shift Scheduling in Multi-Skill Call Centers

MSOM.1070.0172 Appendix: Simple Methods for Shift Scheduling in Multi-Skill Call Centers In Bhulai et al. (2006) we presented a method for computing optimal schedules, separately, after the optimal staffing

### Hyper Node Torus: A New Interconnection Network for High Speed Packet Processors

2011 International Symposium on Computer Networks and Distributed Systems (CNDS), February 23-24, 2011 Hyper Node Torus: A New Interconnection Network for High Speed Packet Processors Atefeh Khosravi,

### Probabilities and Random Variables

Probabilities and Random Variables This is an elementary overview of the basic concepts of probability theory. 1 The Probability Space The purpose of probability theory is to model random experiments so

### IEOR 6711: Stochastic Models, I Fall 2012, Professor Whitt, Final Exam SOLUTIONS

IEOR 6711: Stochastic Models, I Fall 2012, Professor Whitt, Final Exam SOLUTIONS There are four questions, each with several parts. 1. Customers Coming to an Automatic Teller Machine (ATM) (30 points)

### Path Selection Methods for Localized Quality of Service Routing

Path Selection Methods for Localized Quality of Service Routing Xin Yuan and Arif Saifee Department of Computer Science, Florida State University, Tallahassee, FL Abstract Localized Quality of Service

### FPGA Implementation of IP Packet Segmentation and Reassembly in Internet Router*

SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol. 6, No. 3, December 2009, 399-407 UDK: 004.738.5.057.4 FPGA Implementation of IP Packet Segmentation and Reassembly in Internet Router* Marko Carević 1,a,

### Optical interconnection networks with time slot routing

Theoretical and Applied Informatics ISSN 896 5 Vol. x 00x, no. x pp. x x Optical interconnection networks with time slot routing IRENEUSZ SZCZEŚNIAK AND ROMAN WYRZYKOWSKI a a Institute of Computer and

### Using median filtering in active queue management for telecommunication networks

Using median filtering in active queue management for telecommunication networks Sorin ZOICAN *, Ph.D. Cuvinte cheie. Managementul cozilor de aşteptare, filtru median, probabilitate de rejectare, întârziere.

### Modelling the performance of computer mirroring with difference queues

Modelling the performance of computer mirroring with difference queues Przemyslaw Pochec Faculty of Computer Science University of New Brunswick, Fredericton, Canada E3A 5A3 email pochec@unb.ca ABSTRACT

### Effective Bandwidth of Multiclass Markovian Traffic Sources and Admission Control With Dynamic Buffer Partitioning

1524 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 51, NO. 9, SEPTEMBER 2003 Effective Bandwidth of Multiclass Markovian Traffic Sources and Admission Control With Dynamic Buffer Partitioning Yu Cheng, Student

### Performance of networks containing both MaxNet and SumNet links

Performance of networks containing both MaxNet and SumNet links Lachlan L. H. Andrew and Bartek P. Wydrowski Abstract Both MaxNet and SumNet are distributed congestion control architectures suitable for

### Fairness in Routing and Load Balancing

Fairness in Routing and Load Balancing Jon Kleinberg Yuval Rabani Éva Tardos Abstract We consider the issue of network routing subject to explicit fairness conditions. The optimization of fairness criteria

### Congestion-Dependent Pricing of Network Services

IEEE/ACM TRANSACTIONS ON NETWORKING, VOL 8, NO 2, APRIL 2000 171 Congestion-Dependent Pricing of Network Services Ioannis Ch Paschalidis, Member, IEEE, and John N Tsitsiklis, Fellow, IEEE Abstract We consider

### Quality of Service versus Fairness. Inelastic Applications. QoS Analogy: Surface Mail. How to Provide QoS?

18-345: Introduction to Telecommunication Networks Lectures 20: Quality of Service Peter Steenkiste Spring 2015 www.cs.cmu.edu/~prs/nets-ece Overview What is QoS? Queuing discipline and scheduling Traffic

### 4 The M/M/1 queue. 4.1 Time-dependent behaviour

4 The M/M/1 queue In this chapter we will analyze the model with exponential interarrival times with mean 1/λ, exponential service times with mean 1/µ and a single server. Customers are served in order

### BRAESS-LIKE PARADOXES FOR NON-COOPERATIVE DYNAMIC LOAD BALANCING IN DISTRIBUTED COMPUTER SYSTEMS

GESJ: Computer Science and Telecommunications 21 No.3(26) BRAESS-LIKE PARADOXES FOR NON-COOPERATIVE DYNAMIC LOAD BALANCING IN DISTRIBUTED COMPUTER SYSTEMS Said Fathy El-Zoghdy Department of Computer Science,

### Notes V General Equilibrium: Positive Theory. 1 Walrasian Equilibrium and Excess Demand

Notes V General Equilibrium: Positive Theory In this lecture we go on considering a general equilibrium model of a private ownership economy. In contrast to the Notes IV, we focus on positive issues such

### Modeling and Simulation of Queuing Scheduling Disciplines on Packet Delivery for Next Generation Internet Streaming Applications

Modeling and Simulation of Queuing Scheduling Disciplines on Packet Delivery for Next Generation Internet Streaming Applications Sarhan M. Musa Mahamadou Tembely Matthew N. O. Sadiku Pamela H. Obiomon

### CSC2420 Fall 2012: Algorithm Design, Analysis and Theory

CSC2420 Fall 2012: Algorithm Design, Analysis and Theory Allan Borodin November 15, 2012; Lecture 10 1 / 27 Randomized online bipartite matching and the adwords problem. We briefly return to online algorithms

### Sprinklers: A Randomized Variable-Size Striping Approach to Reordering-Free Load-Balanced Switching

Sprinklers: A Randomized Variable-Size Striping Approach to Reordering-Free Load-Balanced Switching Weijun Ding Jim Xu Jim Dai Yang Song Bill Lin June 7, 2014 Abstract Internet traffic continues to grow

### Notes on Determinant

ENGG2012B Advanced Engineering Mathematics Notes on Determinant Lecturer: Kenneth Shum Lecture 9-18/02/2013 The determinant of a system of linear equations determines whether the solution is unique, without

### AN EFFICIENT DISTRIBUTED CONTROL LAW FOR LOAD BALANCING IN CONTENT DELIVERY NETWORKS

Available Online at www.ijcsmc.com International Journal of Computer Science and Mobile Computing A Monthly Journal of Computer Science and Information Technology IJCSMC, Vol. 3, Issue. 9, September 2014,

### 6.254 : Game Theory with Engineering Applications Lecture 5: Existence of a Nash Equilibrium

6.254 : Game Theory with Engineering Applications Lecture 5: Existence of a Nash Equilibrium Asu Ozdaglar MIT February 18, 2010 1 Introduction Outline Pricing-Congestion Game Example Existence of a Mixed

### Lecture 15: Congestion Control. CSE 123: Computer Networks Stefan Savage

Lecture 15: Congestion Control CSE 123: Computer Networks Stefan Savage Overview Yesterday: TCP & UDP overview Connection setup Flow control: resource exhaustion at end node Today: Congestion control Resource

### Queueing Networks with Blocking - An Introduction -

Queueing Networks with Blocking - An Introduction - Jonatha ANSELMI anselmi@elet.polimi.it 5 maggio 006 Outline Blocking Blocking Mechanisms (BAS, BBS, RS) Approximate Analysis - MSS Basic Notation We

### An Asymptotically Minimal Node-degree Topology for Load-Balanced Architectures

An Asymptotically Minimal ode-degree Topology for Load-Balanced Architectures Zhenhua Liu, Xiaoping Zhang, Youjian Zhao, Hongtao Guan Department of Computer Science and Technology, Tsinghua University

### Offline sorting buffers on Line

Offline sorting buffers on Line Rohit Khandekar 1 and Vinayaka Pandit 2 1 University of Waterloo, ON, Canada. email: rkhandekar@gmail.com 2 IBM India Research Lab, New Delhi. email: pvinayak@in.ibm.com

### Towards Optimal Firewall Rule Ordering Utilizing Directed Acyclical Graphs

Towards Optimal Firewall Rule Ordering Utilizing Directed Acyclical Graphs Ashish Tapdiya and Errin W. Fulp Department of Computer Science Wake Forest University Winston Salem, NC, USA nsg.cs.wfu.edu Email:

### Partitioning edge-coloured complete graphs into monochromatic cycles and paths

arxiv:1205.5492v1 [math.co] 24 May 2012 Partitioning edge-coloured complete graphs into monochromatic cycles and paths Alexey Pokrovskiy Departement of Mathematics, London School of Economics and Political

### 5 Performance Management for Web Services. Rolf Stadler School of Electrical Engineering KTH Royal Institute of Technology. stadler@ee.kth.

5 Performance Management for Web Services Rolf Stadler School of Electrical Engineering KTH Royal Institute of Technology stadler@ee.kth.se April 2008 Overview Service Management Performance Mgt QoS Mgt

### Further Analysis Of A Framework To Analyze Network Performance Based On Information Quality

Further Analysis Of A Framework To Analyze Network Performance Based On Information Quality A Kazmierczak Computer Information Systems Northwest Arkansas Community College One College Dr. Bentonville,

### M/M/1 and M/M/m Queueing Systems

M/M/ and M/M/m Queueing Systems M. Veeraraghavan; March 20, 2004. Preliminaries. Kendall s notation: G/G/n/k queue G: General - can be any distribution. First letter: Arrival process; M: memoryless - exponential

### Assignment #3 Routing and Network Analysis. CIS3210 Computer Networks. University of Guelph

Assignment #3 Routing and Network Analysis CIS3210 Computer Networks University of Guelph Part I Written (50%): 1. Given the network graph diagram above where the nodes represent routers and the weights

### The Basics of Graphical Models

The Basics of Graphical Models David M. Blei Columbia University October 3, 2015 Introduction These notes follow Chapter 2 of An Introduction to Probabilistic Graphical Models by Michael Jordan. Many figures

### USING ADAPTIVE SERVER ACTIVATION/DEACTIVATION FOR LOAD BALANCING IN CLOUD-BASED CONTENT DELIVERY NETWORKS

USING ADAPTIVE SERVER ACTIVATION/DEACTIVATION FOR LOAD BALANCING IN CLOUD-BASED CONTENT DELIVERY NETWORKS Darshna Dalvadi 1 and Dr. Keyur Shah 2 1 School of Computer Studies, Ahmedabad University, Ahmedabad,

### Analyzing Mission Critical Voice over IP Networks. Michael Todd Gardner

Analyzing Mission Critical Voice over IP Networks Michael Todd Gardner Organization What is Mission Critical Voice? Why Study Mission Critical Voice over IP? Approach to Analyze Mission Critical Voice

### Concurrent Round-Robin-Based Dispatching Schemes for Clos-Network Switches

830 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 10, NO. 6, DECEMBER 2002 Concurrent Round-Robin-Based Dispatching Schemes for Clos-Network Switches Eiji Oki, Member, IEEE, Zhigang Jing, Member, IEEE, Roberto

### Examining Self-Similarity Network Traffic intervals

Examining Self-Similarity Network Traffic intervals Hengky Susanto Byung-Guk Kim Computer Science Department University of Massachusetts at Lowell {hsusanto, kim}@cs.uml.edu Abstract Many studies have

### Competitive Analysis of On line Randomized Call Control in Cellular Networks

Competitive Analysis of On line Randomized Call Control in Cellular Networks Ioannis Caragiannis Christos Kaklamanis Evi Papaioannou Abstract In this paper we address an important communication issue arising

### Multi-service Load Balancing in a Heterogeneous Network with Vertical Handover

1 Multi-service Load Balancing in a Heterogeneous Network with Vertical Handover Jie Xu, Member, IEEE, Yuming Jiang, Member, IEEE, and Andrew Perkis, Member, IEEE Abstract In this paper we investigate

### IN THIS PAPER, we study the delay and capacity trade-offs

IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 15, NO. 5, OCTOBER 2007 981 Delay and Capacity Trade-Offs in Mobile Ad Hoc Networks: A Global Perspective Gaurav Sharma, Ravi Mazumdar, Fellow, IEEE, and Ness

### Probability and Random Variables. Generation of random variables (r.v.)

Probability and Random Variables Method for generating random variables with a specified probability distribution function. Gaussian And Markov Processes Characterization of Stationary Random Process Linearly

### Software Performance and Scalability

Software Performance and Scalability A Quantitative Approach Henry H. Liu ^ IEEE )computer society WILEY A JOHN WILEY & SONS, INC., PUBLICATION Contents PREFACE ACKNOWLEDGMENTS xv xxi Introduction 1 Performance

### Quality of Service (QoS) on Netgear switches

Quality of Service (QoS) on Netgear switches Section 1 Principles and Practice of QoS on IP networks Introduction to QoS Why? In a typical modern IT environment, a wide variety of devices are connected

### Structure Preserving Model Reduction for Logistic Networks

Structure Preserving Model Reduction for Logistic Networks Fabian Wirth Institute of Mathematics University of Würzburg Workshop on Stochastic Models of Manufacturing Systems Einhoven, June 24 25, 2010.

### Cloud Storage and Online Bin Packing

Cloud Storage and Online Bin Packing Doina Bein, Wolfgang Bein, and Swathi Venigella Abstract We study the problem of allocating memory of servers in a data center based on online requests for storage.

### Sources: Chapter 6 from. Computer Networking: A Top-Down Approach Featuring the Internet, by Kurose and Ross

M ultimedia Communication Multimedia Systems(Module 5 Lesson 3) Summary: Beyond Best-Effort Motivating QoS Q uality of Service (QoS) Scheduling and Policing Sources: Chapter 6 from Computer Networking:

### Load Balancing in Ad Hoc Networks: Single-path Routing vs. Multi-path Routing

Balancing in d Hoc Networks: Single-path Routing vs. Multi-path Routing Yashar Ganjali, btin Keshavarzian Department of Electrical Engineering Stanford University Stanford, C 9435 Email:{yganjali, abtink}@stanford.edu

### Section 1.1. Introduction to R n

The Calculus of Functions of Several Variables Section. Introduction to R n Calculus is the study of functional relationships and how related quantities change with each other. In your first exposure to

### The Joint Distribution of Server State and Queue Length of M/M/1/1 Retrial Queue with Abandonment and Feedback

The Joint Distribution of Server State and Queue Length of M/M/1/1 Retrial Queue with Abandonment and Feedback Hamada Alshaer Université Pierre et Marie Curie - Lip 6 7515 Paris, France Hamada.alshaer@lip6.fr

### Resource Provisioning and Network Traffic

Resource Provisioning and Network Traffic Network engineering: Feedback traffic control closed-loop control ( adaptive ) small time scale: msec mainly by end systems e.g., congestion control Resource provisioning

### Cost Model: Work, Span and Parallelism. 1 The RAM model for sequential computation:

CSE341T 08/31/2015 Lecture 3 Cost Model: Work, Span and Parallelism In this lecture, we will look at how one analyze a parallel program written using Cilk Plus. When we analyze the cost of an algorithm

### Big, Fast Routers. Router Architecture

Big, Fast Routers Dave Andersen CMU CS 15-744 Data Plane Router Architecture How packets get forwarded Control Plane How routing protocols establish routes/etc. 1 Processing: Fast Path vs. Slow Path Optimize

### Multi-layer Structure of Data Center Based on Steiner Triple System

Journal of Computational Information Systems 9: 11 (2013) 4371 4378 Available at http://www.jofcis.com Multi-layer Structure of Data Center Based on Steiner Triple System Jianfei ZHANG 1, Zhiyi FANG 1,

### Performance of Cloud Computing Centers with Multiple Priority Classes

202 IEEE Fifth International Conference on Cloud Computing Performance of Cloud Computing Centers with Multiple Priority Classes Wendy Ellens, Miroslav Živković, Jacob Akkerboom, Remco Litjens, Hans van

### Using Generalized Forecasts for Online Currency Conversion

Using Generalized Forecasts for Online Currency Conversion Kazuo Iwama and Kouki Yonezawa School of Informatics Kyoto University Kyoto 606-8501, Japan {iwama,yonezawa}@kuis.kyoto-u.ac.jp Abstract. El-Yaniv

### Routing in packet-switching networks

Routing in packet-switching networks Circuit switching vs. Packet switching Most of WANs based on circuit or packet switching Circuit switching designed for voice Resources dedicated to a particular call

### Can We Beat DDoS Attacks in Clouds?

GITG342 Can We Beat DDoS Attacks in Clouds? Shui Yu, Yonghong Tian, Song Guo, Dapeng Oliver Wu IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 25, NO. 9, SEPTEMBER 2014 정보통신대학원 49기 정보보호 전공