Designing optimal rate allocation algorithms based on utility function in data networks

Number of pages: 205 File Format: word File Code: 32257
Year: 2004 University Degree: PhD Category: Electrical Engineering
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    Doctoral Dissertation in Electrical Engineering

    Abstract:

    The purpose of this thesis is to improve the performance of optimal rate allocation algorithms based on utility function in data networks
    The optimal rate allocation algorithm based on the utility function was first proposed by Dr. Golestani. Then Kelly showed that the problem of optimal rate allocation can be converted into two simpler sub-problems, one of which is solved by the network and the other by the users, and he showed that the network problem is actually a rate allocation problem with a proportional justice criterion and has many advantages, including similarity with the congestion control algorithm in TCP/IP (AIMD method), and also showed the stability and convergence of the algorithm in mathematical form. But at the same time, Kelly's algorithm also has some limitations, including the problem of scalability, low convergence speed, and high computational overheads. In this treatise, we will introduce two hierarchical algorithms, a fuzzy algorithm and a hybrid fuzzy-hierarchical algorithm with the aim of solving the above-mentioned defects in order to achieve rate allocation methods with higher convergence speeds while establishing proportional justice (W,a). In addition, the mathematical analysis of the stability of the proposed algorithms, the analysis of the behavior of hierarchical algorithms in the presence of background traffic with a variable rate, and the analysis of the phenomenon of users entering and exiting the system are among other things that will be examined in this thesis. rtl;">Introduction

    1-1 Introduction

    In general, quality of service is the capability that the network has in Distinguish between types of services and traffic classes so that users who are in a traffic class, depending on their needs, see different performance of the network compared to other types. Among the ways to support the quality of service, we can mention various methods of rate control and congestion control2.

    The methods of rate control and congestion control are used in computer networks in order to control the traffic in the networks and divide the bandwidth, taking into account the assumed criterion of justice.

    Rate control is a set of methods used by the network to control the input rate to the network, while Congestion control is the application of some controls on the inputs that have filled the network buffers.

    In a general classification, congestion control in data telecommunication networks is done in two ways. Window-based methods in which the number of packets in the network is set to a certain limit by intelligently controlling a window called the congestion window4 [6,5,4,3,2,1] and rate-based methods in which the traffic in the network is looked at as a liquid flow and with specific algorithms, an attempt is made to allocate rates to network users in such a way that the justice in Rate allocation to users should be respected [11,10,9,8,7].

    Several criteria have been introduced for the implementation of this justice, the most prominent of which are maximum-minimum1, proportionality2, and minimum potential delay3 justice criteria [14,13,12].

    Mo and Walrand in [13] have investigated the justice criterion (W,a) And they have shown that all the mentioned justice criteria can be obtained as special cases of the more general justice criterion (W,a).

    With the research that has been done in the field of congestion control and rate allocation algorithms, it has been concluded that any algorithm that is used for congestion control or rate allocation should be implemented in a distributed manner at the network level, as far as possible, because otherwise, if the algorithm is implemented centrally, as the network dimensions increase, a significant computational load will be applied to the central processor, and in addition, in case of a malfunction in this processor, the behavior of the entire system will be disturbed. And it becomes a mess, while in a distributed algorithm, the responsibility of rate allocation and congestion control is placed on all network nodes and end users, and the creation of an error or defect in a part of this distributed system will not have a great impact on the behavior of the entire algorithm. For this reason, researchers such as Bertsekas [15] and Gallager [16] have tried to push rate allocation algorithms towards distributed and widespread algorithms at the network level.

    The initial idea of ??implementing the rate control problem as a general optimization problem has been proposed by S.J. Golestani [17] and after him, many researchers have tried to develop existing methods for access of users at the network level to optimal rates with distributed methods. And.

    The work of these researchers can be generally divided into two main categories. In the first category, researchers such as S. Low in [18,19] have tried to turn the optimization problem into a widespread problem at the network level by using duality theory [15] in which end users and network links are able to solve the general optimization problem by exchanging some information with each other and even these researchers in [18] have tried to prove the stability of their distributed algorithms with the help of mathematical methods and in practice how to implement such algorithms in the ATM 5 network. [21,20] and for the ABR service available in it, it has been investigated and analyzed using the facilities provided by this service.

     

     

    Researchers who are in the second category of the above division try to solve the problem of optimal rate allocation with general optimization theory using methods based on the penalty function [15] sentence
    We can refer to the research conducted in [24,23,22,10,8,7].

    Of course, it is necessary to explain, there are also researchers who have tried to solve the problem of general optimization of rate allocation by using methods different from the above two general methods. For example, Ba?ar et al. T. in [25] and R. Srikant et al. In [8], they have tried to analyze the rate allocation optimization problem with the help of game theory.

    Among the most important methods of the second category, we can refer to the research results in [7]. Kelly et al. In [7], in addition to implementing an extensive algorithm at the network level, they have tried to achieve the criterion of proportional justice. Among the most important features of this criterion, its proximity to the well-known congestion control method in the Internet by Jacobson et al. It is presented in [26]. Among the other outstanding features of this algorithm, checking and proving its stability is appropriate by choosing Lyapunov functions.

    Since the time delay in the Kelly algorithm has received less attention, R.Johari and D.Tan have conducted extensive research in [11] to prove the stability of the Kelly algorithm in the presence of delay and under certain conditions, and have achieved significant results, and finally, the stability of the algorithm for a general network topology and arbitrary but limited delays by L. Massoulié is presented in [27] and S. Deb and R. Srikant in [28].

    The issue of user entry and exit in the Kelly algorithm is investigated in [10].

    One ??of the most effective methods applied to avoid congestion or control it is the use of costing methods2 on network links. Per the passing traffic is one of them [31,30,29], in these methods, each link imposes a fee on passing users for the accumulated traffic that passes through it, and this cost increases with the increase of passing cumulative traffic, and for example in [7], such costing methods have been used in order to achieve fair and optimal rates for elastic users [32] existing in the network.

  • Contents & References of Designing optimal rate allocation algorithms based on utility function in data networks

    List:

    Table of contents.. eight

    Abstract..1

    Chapter one: Introduction

    1-1 Introduction..2

    1-3 Explanation of the topic..5

    1-2 Order of content presentation..6

    Chapter two: Examining the concept of service quality in networks Data

    2-1 Introduction. 7

    2-2 Mechanisms in the network to create QoS. 8

    2-3 Queuing methods with continuous work. 9

    2-3-1 FIFO queuing method. 2-3-4 Round Robin queuing method.12

           2-3-5 Bitwise Round Robin method.

           2-3-6 practical method of fair bitwise round robin queuing. 2-3-9 Improved DRR method (DRR+) 15

    2-3-10 Weighted Fair Queuing (WFQ) method 15

    2-3-11 WF2Q method 15

    2-3-12 Delay-EDD and Jitter-EDD methods 16

    2-4 Queuing methods with work Non-persistent. 17

    2-4-1 Leaky Bucket method 18 2-4-2 Token Bucket method 18 2-5 Methods used to drop packets 18 2-5-1 Tail Dropping 19 2-5-2 Random Early Detection (RED) 19

    2-5-3 Weighted Random Early Detection (WRED). 19

    2-6 types of service classes in data networks. 20

    2-7 integrated services. ..25

    Chapter three: rate control and the concept of justice in data networks

    3-1 Introduction..26

    3-2 The concept of rate control and its goals. 27. 3-2-1 window-based methods 27. 3-2-2 rate-based methods 28. 3-3 division of existing traffic at the network level 29. 3-4 concept of fairness in rate allocation in data networks 31. 4-1 network model 32.

           3-4-2 maximum-minimum justice criterion.33

           3-4-3 proportional justice criterion..34

          3-4-4 minimum potential delay justice criterion.

           3-4-5 weighted bandwidth allocation.

           3-4-6 proportional justice criterion (W,a) 37. 3-5 Conclusion. 38. Chapter 4: Examining optimal rate allocation methods to network level users based on fluid flow perspective. 4-1 Introduction.

    4-3 Rate control in computer networks using the concept of cost.46

    4-3-1 Kelly algorithm for solving the network problem.49

    ..51

           4-3-5 Time delays ..52

           4-3-6 Matching users ..54

     

                                                                                                                                                                                                           Simultaneous optimization of the path and rate of users. Conclusion..60

    Chapter Five: Methods for Solving Constrained Convex Optimization Problems 1-5 Introduction ..61

    5-2 Constrained Convex Optimization ..62

    5-2-1 Gradient Image Method 63

    5-2-2 Weighted Gradient Image and Newton Algorithms 65

           5-2-3 Convergence check using slope method. 66

    5-2-7 penalty function method. ..74

    6-3 Proposed algorithms ..76

    6-3-1 Algorithm I ..82

           6-3-2 Algorithm II 96 6-3-4 Algorithm IV 100 6-4 Stability of algorithms with proportional justice in the presence of time delay IV with conventional algorithms 119 7-2-1 First example 120 7-2-2 Second example 129 7-2-3 Third example 140 7-2-4 Fourth example 151 7-2-5 Example Fifth (checking the mutual effect of bottlenecks). 158

    7-3 Simulation of user entry and exit. 161

    7-4 Simulation of other justice criteria in the fuzzy algorithm. 165

    7-5 Discrete event simulation. 166

    7-5-1 Part I. 168

    7-5-2 Part II. 7-5-3 Simulation of Hierarchical Algorithm II in the presence of background traffic. 7-5-4 Comparison of fuzzy algorithm with Kelly. 179

    8-2  Suggestions.184

    List of abbreviations.186

    References

     

    Appendices

    A-N) Supplementary figures related to computer simulation. . Attached CD

    Q) Some computer programs used in the simulation. CD attachment

    Source:

     

     

    [1] Tanenbaum, A.S., Computer Networks, 3rd edition, Prentice Hall, New Jersey, 1996.

    [2] Brakmo, L., TCP Vegas Release 0.8, Nov. 1994.

    http://www.cs.arizona.edu/protocols

    [3] Mitra, D. and Seery, J.B., “Dynamic adaptive window for high-speed data networks,” in Proc. ACM SIGCOMM'90 Conf., pp. 30-40, 1990.

    [4] Mitra, D. and Seery, J.B., “Dynamic adaptive windows for high-speed data networks with multiple paths and propagation delays,” Computer Networks and ISDN Systems, (25), pp. 663-679, 1993.

    [5] Floyd, S., “TCP and explicit congestion notification,” ACM Computer Communications Review, Vol. 24, No. 5, pp. 10-23, Oct. 1994.

    [6] Fall, K. and Floyd, S., “Simulation-based comparison of tahoe, reno and sack TCP,” ACM Compu. Commun. Rev., Vol. 26, No. 3, pp. 5-21, July 1996.

    [7] Kelly, F.P., Maulloo, A.K. and Tan, D.K.H., “Rate control for communication networks: shadow prices, proportional fairness and stability,” J. Oper. Res. Soc., Vol. 49, No. 3, pp. 237-252, Mar. 1998.

    [8] Kunniyur, S. and Srikant, R., “End-to-End Congestion Control Schemes: Utility Functions, Random Losses and ECN Marks,” IEEE INFOCOM Mar. 2000.

    [9] Fendick, K.W., Rodriguez, M.A. and Weiss, A., "Analysis of a rate-based feedback control strategy for long-haul data transport." Performance Evaluation, Vol. 16, pp. 67-84, 1992.

    [10] Tan, D.K.H., Mathematical Models of Rate Control for Communication Networks, Ph.D. dissertation, pp. 35-61, Cambridge university, Aug. 1999.

    [11] Johari, R. and Tan, D., “End-to-End congestion control for the Internet: Delays and Stability,” IEEE Trans. On Networking, Vol.9, No.6, pp. 818-832, Dec. 2001.

    [12] Massoulié, L. and Roberts, J., “Bandwidth sharing: objectives and algorithms,” in Proc. IEEE INFOCOM, Vol.3, 1999, pp. 1395-1403.

    [13] Mo, J. and Walrand, J., “Fair End-to-End Window-Based Congestion Control,” IEEE Transactions on Networking, Vol. 8, No. 5, pp. 556-567, Oct. 2000.

    [14] Hurley, P., Le Boudec, J.Y. and Thiran, P., "A note on the fairness of additive increase and multiplicative decrease," in Proc. ITC-16, Edinburg, Scotland, pp. 467-478, June 1999.

    [15] Bertsekas, D. and Tsitsiklis, J., Parallel and Distributed Computation. Englewood Cliffs, NJ: Prentice-Hall, 1989. [16] Gallagher, R.G. and Bertsekas, D., Data Networks, Prentice-Hall, NJ 1987. [17] Golestani, S.J., A Unified Theory of Flow Control and Routing in Data Communication Networks, Ph.D Dissertation, MIT, Jan. 1980. [18] Low, S.H. and Lapsley, D.E.

Designing optimal rate allocation algorithms based on utility function in data networks