Kameda, H., J. Li, C. Kim and Y. Zhang (1997). Optimal Load Balancing in Distributed Computer Systems. Springer. Kelly, F. P. (1991). Network routing. Phil. Trans. R. Soc. Lond. A 337, 343--367.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....are jobs. An individual job can be processed in any of several interconnected nodes (computers) and the routing decision is taken so as to minimize its expected delay in the system (composed of both communication as well as processing delay) Much material on that application can be found in [20]. The most widely studied concept of equilibrium in telecommunications networks is, however, the Nash equilibrium applied to the case of nitely many decision makers. The decision makers typically represent service providers, each of whom can determine how to route the ow generated by its ....

H. Kameda, J. Li, C. Kim and Y. Zhang, Optimal Load Balancing in Distributed Computer Systems, Springer, 1997.

....model and introduce the concept of Nash equilibrium and the best reply algorithm or ESS. In Section 3, we consider a network made up of two processors and a communication bus between them, this network is shared by two users, each one being associated to a processor, this model was introduced in [6]; we show that the sequence generated by the algorithm is monotone, then we establish the convergence to Nash equilibrium of this sequence. In Section 4, we consider a network of N processors arranged in loop, each processor is in communication with its successor, as in the rst model to each ....

H. Kameda, J. Li, C. Kim and Y. Zhang, Optimal Load Balancing in Distributed Computer Systems, Springer, 1997.

....of its next execution. In [10] they use the above prediction scheme to develop four prediction based heuristics, two centralized and two distributed, which are compared against random scheduling and two effective nonprediction based heuristics, using trace driven simulations. Kameda et al. in [15] study the problem of optimal load balancing in tree networks with two way traffic. It is proven that the tree hierarchy optimization problem can be solved by solving much simpler star sub optimization problem iteratively. A decomposition algorithm to solve the optimal static load balancing ....

H. Kameda, J. Li, C. Kim, and Y. Zhang, "Optimal Load Balancing in Distributed Computer Systems", Springer-Verlag, 1997.

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Kameda, H., J. Li, C. Kim and Y. Zhang (1997). Optimal Load Balancing in Distributed Computer Systems. Springer. Kelly, F. P. (1991). Network routing. Phil. Trans. R. Soc. Lond. A 337, 343--367.

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Kameda, H., J. Li, C. Kim and Y. Zhang (1997). Optimal Load Balancing in Distributed Computer Systems. Springer.

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H. Kameda, J. Li, C. Kim and Y. Zhang, Optimal Load Balancing in Distributed Computer Systems, Springer, 1997.

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H. Kameda, J. Li, C. Kim and Y. Zhang, Optimal Load Balancing in Distributed Computer Systems, Springer, 1997.

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H. Kameda, J. Li, C. Kim and Y. Zhang, Optimal Load Balancing in Distributed Computer Systems, Springer, 1997.

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H. Kameda, J. Li, C. Kim and Y. Zhang, Optimal Load Balancing in Distributed Computer Systems, Springer, 1997.

....of the overall, individual, and class optima for this model are established in [8] 9] Remark 1 Note that, there is no mutual forwarding in overall and individual optima. That is, in overall and individual optima, either one of x ij (i 6= j) must be zero as shown in [18] and Section 2.2. 2 of [12]. Thus, when one of x ij (i 6= j) say x ij is non zero, T i (xxxx) decreases and T j (xxxx) increases with the change of t as shown in Theorems 2.5 and 2.7 of [12] Consequently no Braess type paradox occurs for individual and overall optima. Let us define three types of symmetries with respect ....

....optima. That is, in overall and individual optima, either one of x ij (i 6= j) must be zero as shown in [18] and Section 2.2.2 of [12] Thus, when one of x ij (i 6= j) say x ij is non zero, T i (xxxx) decreases and T j (xxxx) increases with the change of t as shown in Theorems 2.5 and 2. 7 of [12]. Consequently no Braess type paradox occurs for individual and overall optima. Let us define three types of symmetries with respect to the system parameter setting. Individual symmetry] If the following condition holds ; 5) it can be proved from definition (3) that at the individual ....

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H. Kameda, J. Li, C. Kim and Y. Zhang, Optimal Load Balancing in Distributed Computer Systems, Springer, 1997.

.... the original Braess paradox (for the Wardrop equilibrium) was in fact obtained [11] 12] In parallel to these studies, it has been observed that increased capacity of a part of a system may lead to the degradation of the overall performance measure, in a model of distributed computer system [7], 6] 18] in Wardrop and Nash equilibria. We call it the weaker Braess like paradox. Furthermore, Kameda et al. 6] found a seemingly anomalous case where in a Nash equilibrium each of two processing nodes (servers) forwards the same type of jobs mutually to be processed by the other node, thus ....

....are innite) For the existence and uniqueness of those optima see [5] Remark II.1: Note that there should be no mutual forwarding in overall and individual optima. That is, in overall and individual optima, either one of x ij (i 6= j) must be zero in case (A) due to [17] or to Section 2.2. 2 of [7] and in case (B) due to [13] And thus, when one of x ij (i 6= j) say x ij , is non zero, T i (xxxx) decreases and T j (xxxx) increases with the increase of as shown in Theorems 2.5 and 2.7 of [7] 6 III. The numerical experiments We examined the cases of the following parameter values of ....

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H. Kameda, J. Li, C. Kim and Y. Zhang, Optimal Load Balancing in Distributed Computer Systems, Springer, 1997. 10

....of virtual paths or virtual connections. Our framework thus allows us to handle routing both in a packet switching as well as in a circuit switching environment. We consider three different frameworks: i) Overall optimization criterion, where a single controller makes the routing decisions [9] [10], 12] 17] ii) Individual optimality, in which each routed individual chooses its own path so as to minimize its own cost. An individual is assumed to have an infinitesimally small impact on the load in the network and thus on costs of other individuals. This framework has been extensively ....

....to have an infinitesimally small impact on the load in the network and thus on costs of other individuals. This framework has been extensively investigated in transportation science [5] 8] 16] and was also considered in the context of telecommunication [11] and in distributed computing [9] [10], 11] The suitable optimization concept for this setting is of Wardrop equilibrium [18] it is defined as a set of routing decisions for all individuals such that a path is followed by an individual if and only if it has the lowest cost for that individual. iii) Class optimization; a class may ....

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H. Kameda, J. Li, C. Kim and Y. Zhang, Optimal Load Balancing in Distributed Computer Systems, Springer, 1997.

....equilibrium [22] This concept was very much studied (e.g. 3] 5] 6] 9] 20] and references therein) Most of the work with this optimization approach has been done in the framework of road traffic. However, this concept has been also useful in the area of distributed computing [14] [15], and in telecommunication networks [7] In the context of road traffic, an individual user (a job in our terminology) may correspond to a single driver, and the class may correspond to all the drivers of a given type of vehicle that have a given source and destination. In the context of ....

H. Kameda, J. Li, C. Kim and Y. Zhang, Optimal Load Balancing in Distributed Computer Systems, Springer, 1997.

....static load balancing policy depends only on the average behavior of the system in order to balance the workload of the system. This makes dynamic policy necessarily more complex than static one. But, dynamic load balancing policies have been believed to have better performance than static ones [3]. In this paper, we consider dynamic and static overall optimal policies whereby job scheduling is determined so as to minimize the system mean response time. The goal of this paper is to examine to what extent the optimal dynamic load balancing policy outperforms the static one by an exhaustive ....

....the arrival rate is near the processing rate of the Mainframe node. Meanwhile there have been some studies of performance comparison of dynamic vs. static policies in more sophisticated models where overheads are considered but the truly optimal dynamic policy is not accurately obtained than ours [3, 9]. 1 This paper is organized as follows. Section 2 describes the system model of this paper. Section 3 presents two optimal load balancing policies: static and dynamic. Section 4 describes the results of numerical examination. Finally, Section 5 summarizes this paper. 2 The System Model We ....

H. Kameda, J. Li, C. Kim and Y. Zhang, Optimal Load Balancing in Distributed Computer Systems, Springer, 1997.

....of all classes at the same time in a Wardrop equilibrium in the same environment. In the background of this work, it has been observed that increased capacity of a part of a system may lead to somewhat awkward behavior in terms of a system wide measure, in a model of distributed computer system [9, 10, 21]. The methods and algorithms for obtaining the optima and the equilibria are described in 2 [10, 12, 13, 16, 20] In this paper, we present an analytic study of a model of static load balancing among identical nodes each of which has an identical arrival. The results look quite counterintuitive ....

.... this work, it has been observed that increased capacity of a part of a system may lead to somewhat awkward behavior in terms of a system wide measure, in a model of distributed computer system [9, 10, 21] The methods and algorithms for obtaining the optima and the equilibria are described in 2 [10, 12, 13, 16, 20]. In this paper, we present an analytic study of a model of static load balancing among identical nodes each of which has an identical arrival. The results look quite counterintuitive and show that the ratio of the performance degradation in the paradoxical cases can be unlimitedly large. We ....

H. Kameda, J. Li, C. Kim and Y. Zhang, Optimal Load Balancing in Distributed Computer Systems, Springer, 1997.

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Kameda, H., J. Li, C. Kim, and Y. Zhang. (1997). Optimal Load Balancing in Distributed Computer Systems. Springer.

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H. Kameda, J. Li, C. Kim, and Y. Zhang. Optimal Load Balancing in Distributed Computer Systems. Springer, 1997.

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Kameda H,Li J,Kim C,ZhangY. Optimal load balancing in distributed computer systems. Berlin: Springer; 1997.

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C. Kim H. Kameda, J. Li and Y. Zhang. Optimal Load Balancing in Distributed Computer Systems. Springer, 1997.

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C. Kim H. Kameda, J. Li and Y. Zhang. Optimal Load Balancing in Distributed Computer Systems. Springer, 1997.

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C. Kim H. Kameda, J. Li and Y. Zhang. Optimal Load Balancing in Distributed Computer Systems. Springer, 1997.

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H. Kameda, J. Li, C. Kim, and Y. Zhang. Optimal Load Balancing in Distributed Computer Systems. Springer, 1997.

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H.Kameda H.Kameda, J.Li, C.Kim and Y.Zhang, Optimal Load Balancing in Distributed Computer Systems. Springner, 1996

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