Mazumdar, R., L. G. Mason and C. Doulgligeris (1991). Fairness in network optimal flow control: Optimality of product forms. IEEE Trans. Communications 39(5), 775--782.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....We next consider the problem of determining the available bandwidth, or appropriate communication rate for unicast video communication. One important criterion in determining the available bandwidth is the notion of fairness, which is well studied in networking and can assume several definitions [83, 65]. Several research groups have focused on developing packet switching disciplines that achieve fairness by requiring routers to store per flow information [35, 94, 95] Problems with applying such solutions to the current best e#ort Internet include high complexity and the required global ....

....and study the global implications of rate control algorithms. Since it has been shown that there exist rate allocations that optimize overall network throughput 167 while denying access to certain users [46] the goal of rate control is often to achieve some form of globally fair allocation [83]. It has recently been shown mathematically in [65] that in a scheme in which a network advertises the appropriate usage price to the senders, it is possible for uncooperative receivers to achieve a globally fair allocation. It is interesting to investigate how such a scheme may be implemented in ....

R. Mazumdar, L. Mason, and C. Douligeris. Fairness in network optimal flow control: Optimality of product forms. IEEE Trans. Comm., 39(5), pp. 775--82, May 1991.

.... in networks, along with decentralized implementations [9, 8, ll] The Nash Bargaining Solution (NBS) is a natural framework that allows us to define and design fair assignment of bandwidth between applications with different concave utilities and has already been used in networking problems [13, 7]. It is characterized by a set of axioms that are appealing in defining fair ness. As already recognized in [6] and later in [ proportional fairness agrees with NBS when the object that is shared fairly is the throughput (and the minimum required rate is zero) We use NBS to study the fairness ....

R. Mazumdar, L. G. Mason, and C. Douligeris. Fairness in network optimal flow control: optimality of product forms. IEEE Trans. on Comm., 39:775-782, 1991.

....environment. As increasing types of traffic with widely differing characteristics and widely differing quality of service (QoS) requirements are needed to be supported, efficient allocation of limited resources among all the traffic types is obviously a multiple objective optimization problem[2]. As a branch of analysis tool developed to provide a mathematical process for decision making in a conflict situation, the use of game theory concepts has been widely considered for resolving network optimization problems[3] From the game theory viewpoint, each separate class of traffic ....

R. Mazumdar, et.al, "Fairness in Network Optimal Flow Control: Optimality of Product Forms", IEEE Trans. on Commu., Vol.39,No.5,1991

....fairness: loosely, a set of rates is max min fair if no rate may be increased without simultaneously decreasing another rate which is already smaller. In a network with a single bottleneck resource max min fairness implies an equal share of the resource for each flow through it. Mazumdar et al. [14] have pointed out that from a gametheoretic standpoint such an allocation is not special, and have advocated instead the Nash bargaining solution, from cooperative game theory, as capturing natural assumptions as to what constitutes fairness. The need for networks to operate in a public (and ....

....(1) If w r = 1; r 2 R, then a vector of rates x solves NETWORK(A;C;w) if and only if it is proportionally fair. Such a vector is also the Nash bargaining solution (satisfying certain axioms of fairness [22] and, as such, has been advocated in the context of telecommunications by Mazumdar et al. [14]. A vector x is such that the rates per unit charge are proportionally fair if x is feasible, and if for any other feasible vector x 0: 2) The relationship between the conditions (1) and (2) is well illustrated when w r ; r 2 R, are all integral. For each r 2 R, replace the single user r ....

Mazumdar R, Mason LG and Douligeris C (1991). Fairness in network optimal flow control: optimality of product forms. IEEE Transactions on Communications, 39, 775--782.

....Fairness The previous definition of fairness puts emphasis on maintaining high values for the smallest rates. As shown in the previous example, this may be at the expense of some network inefficiency. An alternative definition of fairness has been proposed in the context of game theory [19]. Definition 31.2.3 (Proportional Fairness) An allocation of rates #x is proportionally fair if and only if, for any other feasible allocation #y, we have: y s x s 31.2. FAIRNESS 9 In other words, any change in the allocation must have a negative average change. Let us consider for ....

Mazumdar R., Mason L.G., and Douligeris C. Fairness in network optimal flow control: Optimality of product form. IEEE Transactions on Communication, 39:775--782, 1991.

....QoS requirements. Hence, it is necessary to decide which traffic streams should receive degraded service, either in terms of loss, delay or both. This is the problem of real time bandwidth scheduling. A common thread in the literature is to assign bandwidth fairly (see, for example, 2] 3] [7]) in which users with moderate bandwidth requirements are not penalized because of the excessive demands of others. This is the concept of fair queueing [10] 2] 3] 8] 9] in which the available bandwidth is shared equally among all competing sessions. As a result of equalizing the ....

R. Mazumdar, L. G. Mason and C. Douligeris, "Fairness in network optimal flow control: optimality of product forms," IEEE Trans. Commun., vol. 39, pp. 775--782, 1991.

....others. In either type of game, the goal of each player is to optimize their performance. Non cooperative games have the advantage of less player to player communication overhead [22] Nonetheless, the use of this information, in cooperative games, can result in a Pareto optimal allocation [12] [16]. A Pareto optimal allocation is one where no player can increase their allocation without someone else decreasing theirs. While optimal allocations can be achieved, it is difficult to apply this strategy to large networks and various types of traffic sources [22] Microeconomic flow control is ....

R. Mazumdar, L. G. Mason, and C. Douligeris. Fairness in Network Optimal Flow Control: Optimality of Product Forms. IEEE Transactions on Communications, 39(5):775 -- 782, May 1991.

....x, the aggregate of proportional changes is negative: X i x i Gamma x i x i 0: 6) In [19] Kelly et al. suggested a simple linear increase and multiplicative decrease algorithm that converges to the proportionally fair point. Recently, game theory has been applied to flow control [23, 7, 26]. These authors model users as players competing for common shared resources. The concept of Nash Equilibrium provides a framework for defining fairness and proper operating points for the network. In [7] the game is viewed as noncooperative. In [23] it is modeled as a cooperative game in which ....

....theory has been applied to flow control [23, 7, 26] These authors model users as players competing for common shared resources. The concept of Nash Equilibrium provides a framework for defining fairness and proper operating points for the network. In [7] the game is viewed as noncooperative. In [23], it is modeled as a cooperative game in which the users act to achieve better common utilities. Next, we generalize the concept of proportional fairness. Consider the following optimization problem: P ) maximize g = P i p i f(x i ) 7) subject to A T x c (8) over x 0 (9) where f is an ....

R. Mazumdar, L.G. Mason, and C. Douligeris. Fairness in network optimal flow control:optimality of product forms. IEEE Transactions on Communications, 39(5):775--782, May 1991.

....performance. According to this formulation, the network is a common resource shared and competed by selfish users. This is a typical scenario of a game [MYE91, FUD92] The application of game theoretic tools to networking problems has been gaining increasing interest within the past few years [HSIA91, MAZ91, ECO91, ZHA92, ORD93, KOR93, COC93]. Competition on network resources can be observed, for example, in AT T s customer specified routing [VAN92] and in networks implementing the Intelligent Network (IN) concept [GAR93] such as the Deutsche Bundespost Telekom [SCH92] A natural competition among users arises when they attempt to ....

Ravi Mazumdar, Lorne Mason, and Christos Douligeris, "Fairness in Network Optimal Flow Control: Optimality of Product Forms," IEEE Transactions on Communications, vol. 39, pp. 775--781, May 1991.

....networks and control in telecommunications. Among these are several papers that consider static control problems and thus use static games: Marchand [8] considers optimal input control to a queueing system; Hsiao and Lazar [4] Douligeris and Mazumdar [1, 2, 3] Mazumadar, Mason and Douligeris [11] consider the problem of optimal flow control in a multiclass telecommunications environment; Mason and Girard [9, 10] consider routing models; Shenker [12] studies the problem of optimal service allocation to several users. Kalai and Zemel [5] consider a problem in networks that yield a ....

R. Mazumdar, L. Mason and C. Douligeris, "Fairness in Network Optimal Flow Control: Optimality of Product Forms", preprint.

....below 10 . 3.1.1 Telecommunication networks GT concepts have been applied to formulate different resource problems in telecommunication networks. Examples are the routing problem in a telephone network [13] 26] flow control in computer networks [14] 37] flow control in multiclass [28] and general networks [14] routing in multiservice networks [9] call admission [27] and congestion control [38] in broadband networks. In addition, GT has been applied to model and solve some higher level issues (e.g. pricing) associated with telecommunication networks. For example, 11] ....

Mazumdar, R., Mason L.G., and Douligeris C., Fairness in Network Optimal Flow Control: Optimality of Product Forms, IEEE Trans on Communications vol. COM-39., May 1991 pp 775-782

....according to its own individual performance objectives. Such networks are henceforth called noncooperative, and game theory [MYE91, FUD92] provides the systematic framework to study and understand their behavior. Game theoretic models have been employed in the context of flow control [HSIA91, MAZ91, ZHA92, ALT93, ORD93, KOR93, ALT94], routing [ECO91, ORD93] and pricing [COC93] in modern networking. These studies mainly investigate the structure of the network operating points, i.e. the Nash equilibria of the respective games. Such equilibria are inherently inefficient [DUB86] and, in general, exhibit suboptimal network ....

Ravi Mazumdar, Lorne Mason, and Christos Douligeris, "Fairness in Network Optimal Flow Control: Optimality of Product Forms," IEEE Transactions on Communications, vol. 39, pp. 775--781, May 1991.

....and understand their behavior. The operating points of a noncooperative network are the Nash equilibria of the underlying game, i.e. the points where unilateral deviation does not help any user to improve its performance. Game theoretic models have been employed in the context of flow control [3, 4, 5, 6, 7], routing [8, 9, 10] and pricing [11] in modern networking. These studies mainly investigate the structure of the Nash equilibria and provide valuable insight into the nature of networking under decentralized and noncooperative control. The present work approaches noncooperative networking from a ....

R. Mazumdar, L. Mason, and C. Douligeris, "Fairness in Network Optimal Flow Control: Optimality of Product Forms," IEEE Transactions on Communications, vol. 39, pp. 775--781, May 1991.

....P k (fl k ; fl 0k ) attain their extreme values at the same points in the interior of the fl k strategy space. This property is used to overcome the difficulty arising from the fact that P k (fl k ; fl 0k ) is not concave 6 in fl k . A more general property of H k (fl k ; fl 0k ) derived in [MAZ91], is that it is actually concave in fl = fl k ; fl 0k ) fl k ) K k=1 . Convergence results for synchronous and asynchronous implementations of the greedy algorithm for this store and forward model are not available. The results from Theorems 3 6 Concavity of the players objective ....

....game, if the individual objective functions are twice differ Why is Flow Control Hard: Optimality, Fairness, Partial and Delayed Information 27 entiable, any extremum or inflexion point of their product is Pareto efficient. The arbitration selection scheme for this problem is studied in [MAZ91]. We will present this approach in the context of fairness, in section 4. The network power P c (fl) has a unique extremum, at which it is maximized: fl = fl k ) K k=1 ; fl k = fi k K P K i=1 fi i ; 1 k K: 3:8) This is a point in S, according to Proposition 1. A crucial question ....

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Ravi Mazumdar, Lorne Mason, and Christos Douligeris, "Fairness in Network Optimal Flow Control: Optimality of Product Forms," IEEE Transactions on Communications, vol. 39, pp. 775--781, May 1991.

....of multi controller network flow control problems. In particular, in [10] 2 uniqueness of the Nash equilibrium is established for a BCMP type queuing network, under a power based criterion. A thorough study of competitive multi class flow control to a single node (server) may be found in [12] [13] and the references cited therein. Yet another flow control analysis is given by Shenker[14] who considers an internetwork gateway problem. The approach there is to assume that users operate selfishly and it is the task of the designer to set the gateway parameters such that overall network ....

L. M. R. Mazumdar and C. Douligeris, "Fairness in network optimal flow control: Optimality of product forms," IEEE Transactions on Communications, vol. 39, pp. 775--782, MAy 1991.

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Mazumdar, R., L. G. Mason and C. Doulgligeris (1991). Fairness in network optimal flow control: Optimality of product forms. IEEE Trans. Communications 39(5), 775--782.

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Mazumdar, R., L. G. Mason and C. Douligeris (1991). Fairness in network optimal flow control: Optimality of product forms. IEEE Trans. Communications 39(5), 775--782.

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R. Mazumdar, L.G. Mason, C. Douligeris, Fairness in network optimal flow control: optimality of product forms, IEEE Trans. Commun. 39 (1991) 775--782.

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R. R. Mazumdar, L. Mason and C. Douligeris, "Fairness in network optimal flow control: Optimality of product forms," IEEE Trans. on Communications, vol. 39, no. 5, pp. 775--782, May 1991.

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Mazumdar R,Mason L,Douligeris C. Fairness in network optimal flow control: optimality of product forms. IEEE Transactions on Communications 1991;39(5):775--82.

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R. Mazumdar, L. Mason, and C. Douligeris, "Fairness in network optimal flow control: Optimality of product forms," IEEE Transactions on Communications, vol. 39, pp. 775--782, May 1991.

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R. Mazumdar, L. Mason, and C. Douligeris, "Fairness in network optimal flow control: Optimality of product forms," IEEE Trans. Commun., vol. 39, pp. 775--781, May 1991.

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