L.Fratta, M.Gerla, and L.Kleinrock. The Flow Deviation Method: An Approach to Storeand -forward Network Design. In Networks 3, pages 97--133, 1973. 11  Home/Search   Document Not in Database   Summary   Related Articles   Check

....maximum concurrent flow problems [22] A good overview of routing algorithm design using MCFs is given by Bertsekas and Gallager [8] while Ahuja et al. 7] give a more general treatment of MCFs. One of the first MCF formulations of the routing algorithm design problem is given by Fratta et al. [23] where the cost function approximates the queuing delay of a particular routing algorithm. Other early work by Ros Peran [24] uses maximum channel load as a cost function. The work presented in the paper introduces two new cost functions, worst case and average case throughput. The convexity of ....

L. Fratta, M. Gerla, and L. Kleinrock, "The flow deviation method --- an approach to the store-and-forward communication network design," Networks, vol. 3, pp. 97--133, 1973.

.... network state information into the routing decision is considered in [15] in the context of all optical networks, while previous work on state dependent routing with trunk reservation in traditional telecommunications networks is considered in [14] It is also known that flow deviation methods [5], although computa tionally demanding, can be used to find the optimal routing that minimizes the maximum link load for a given network topology. Because global changes of the logical topology and or routing scheme can be disruptive to the network, algorithms that are based on a sequence of ....

L. Fratta, M. Gerla, and L. Kleinrock. The flow deviation method: An approach to store-and-forward communication network design. Networks, 3:97-133, 1973.

....eq (35) 1 (3.2t) Hence aT(f) i c. I, 8f y 2 1 (Ci f i) 3.22) Given the traffic requirements yk the optimal flow vector f (and hence route assignments) can be determined by a downhill search technique using any feasible flow vector as a starting point. The reader is referred to [11,13] for details Finalty we comment that in practice instead of doing capacity assignment and optimal routing as separate problems, it is desirable to do both optimizations together The resulting problem is much more difficult than each of the above and one must resort to heuristic search ....

L. Fratta M. Gerla and L. Kleinrock, The Flow Deviation Method: An Approach to Store-and-Forward Network Design Networks 3 (1973) 97-133.

.... network state information into the routing decision is considered in [15] in the context of all optical networks, while previous work on state dependent routing with trunk reservation in traditional telecommunications networks is considered in [14] It is also known that flow deviation methods [5], although computationally demanding, can be used to find the optimal routing that minimizes the maximum link load for a given network topology. Because global changes of the logical topology and or routing scheme can be disruptive to the network, algorithms that are based on a sequence of small ....

L. Fratta, M. Gerla, and L. Kleinrock. The flow deviation method: An approach to store-and-forward communication network design. Networks, 3:97--133, 1973.

....problems are closely related to each other, it is inappropriate to separate them. Papers where the routing and capacity assignment problems are treated simultaneously include [11] 10] 13] 23] 19] 20] 2] Gerla and Kleirock [11] presented heuristic methods based on the flow deviation algorithm [7]. As pointed out by Gavish [10] the weakness of this approach is that there is no means to evaluate the solution quality. Gavish and Neuman [10] formulated the problem as a non linear integer programming problem, and proposed a Lagrangean relaxation based approach. The networks studied in ....

L. Fratta, M. Gerla, and L. Kleinrock. The Flow Deviation Method: An Approach to Storeand -Forward Communication Network Design. Networks, 3(2):97--133, Mar. 1973.

....608] and use this formulation in order to identify a few properties of the problem. The methodology used by Gerla et al. 12] and Pazos Rangel and Gerla [20] is used in order to develop an optimal scatternet capacity assignment algorithm which is similar to the well known flow deviation algorithm [11]. The main difference between the algorithms is that at each iteration This model conforms to the model presented in [14] in which the inter piconet scheduling algorithm deals with capacity allocation requests from applications or forwarding functions. there is a need to solve a maximum weight ....

....capacity assignment algorithm for finding an optimal solution of Problem SCA, defined in Section 3.2, is introduced .The algorithm is based on the conditional gradient method also known as the Frank Wolfe method [2, p. 215] which was used for the development of the flow deviation algorithm [11]. Therefore, we refer to the algorithm as the scatternet capacity deviation (SCD) algorithm. Gerla et al. 12] and Pazos Rangel and Gerla [20] have used the Frank Wolfe method in order to develop bandwidth allocation algorithms for ATM networks. Following their approach, we shall now describe the ....

[Article contains additional citation context not shown here]

L.Fratta,M.GerlaandK.Kleinrock,"The Flow Deviation Method: an Approach to Store-and-Forward Communication Network Design", Networks, Vol. 3, pp. 97-133, 1973.

.... network state information into the routing decision, is considered in [8] in the context of all optical networks, while previous work on state dependent routing with trunk reservation in traditional telecommunications networks is considered in [7] It is also known that flow deviation methods [2], although computationally demanding, can be used to find the optimal routing that minimizes the maximum link load for a given network topology. Because global changes of the logical topology and or routing scheme can be disruptive to the network, we consider algorithms that are based on a ....

L. Fratta, M. Gerla, and L. Kleinrock. The flow deviation method: An approach to store-and-forward communication network design. Networks, 3:97--133, 1973.

....(i.e. the sequence of lightpaths used to reach a destination node from a source node) have been specified. Under the assumption that traffic flows can be arbitrarily partitioned and routed on different lightpaths, efficient algorithms for finding the optimal routing on a given topology are known [4, 18]. If this assumption is not valid, other algorithms can be used to route flows in the network. Among them, we chose shortest path routing, because of its simplicity and its effectiveness in minimizing the network congestion level [19] 2.1 Formulation of the problem Several different Mixed ....

L.Fratta, M.Gerla, L.Kleinrock, "The Flow Deviation Method: An Approach to Store-and-Forward Communication Network Design" Networks, Vol.3, n.2, pp.97-133, March 1973.

....NP complete [3] thus typically the two problems are solved separately [4] If each node is only equipped with a single transceiver port, only a single path exists between each pair of nodes, thus there is no routing problem. In the case of multiple transceivers per node, flow deviation methods [5] can be used to find the optimal routing that minimizes the maximum link load for a given topology configuration. For simplicity, however, we focus on minimum hop routing. In addition to simplicity, minimum hop routing is attractive because it minimizes the total network load and is commonly used ....

L. Fratta, M. Gerla, and L. Kleinrock, "The flow deviation method: An approach to store-and-forward communication network design," Networks, vol. 3, pp. 97--133, 1973.

.... network state information into the routing decision is considered in [14] in the context of all optical networks, while previous work on state dependent routing with trunk reservation in traditional telecommunications networks is considered in [13] It is also known that flow deviation methods [4], although computationally demanding, can be used to find the optimal routing that minimizes the maximum link load for a given network topology. Because global changes of the logical topology and or routing scheme can be disruptive to the network, we consider algorithms that are based on a ....

L. Fratta, M. Gerla, and L. Kleinrock. The flow deviation method: An approach to store-and-forward communication network design, 1973.

....traffic into several different paths. Many analyses have shown that it tends to distribute traffic into multiple paths: both network throughput and message delay can be improved [CR97, JG93, JL92] Solution techniques for multi path routing include heuristic methods [FC71] as well as optimal ones [CG74, FCK73, G77, SC76]. Some ideas of these routing algorithms have been absorbed in recent versions of Internet protocols. For example, OSPF distributes traffic over paths that have (almost) equal length [M94a] IGRP goes even further. It quantifies the notion of almost equality by introducing variance coefficient ....

L. Fratta, M. Cerla, and L. Kleinrock. The Flow Deviation Method: An Approach to Store-and-Forwad Communication Network Design. Networks, Vol 3, 1973.

....are not applicable to Concave TCFA problems and are not considered further in this paper. In [26] and [20] Kleinrock and Gerla assumed link cost functions to be linear or concave to reflect the effects of economies of scale in the pricing of link capacity. By using a flow deviation technique [15], linearisation of concave link cost functions and continuous approximations to discrete capacity variables, Kleinrock and Gerla develop a Concave Branch Elimination (CBE) procedure to solve the TCFA problem. A similar, design procedure called the Cut Saturation (CS) technique is also presented in ....

....capacity variables, Kleinrock and Gerla develop a Concave Branch Elimination (CBE) procedure to solve the TCFA problem. A similar, design procedure called the Cut Saturation (CS) technique is also presented in [26] and [6] Like the CBE procedure it employs the flow deviation technique from [15] to route traffic in the network. The CBE procedure is shown to be superior to CS in [26] Gavish et al. 16] 17] 18] 19] develop a TCFA design procedure using a Lagrangian relaxation of a Mixed Integer Linear Programming (MILP) formulation of the problem. Gavish et al. assume that links are ....

L. Fratta, M. Gerla, and L. Kleinrock. The flow deviation method: An approach to store-andforward computer-communication network design. Networks 3, (1972) 97--133.

....cuts (columns) are made up of indicator vectors of paths on a network, the problem is sparse. By exploiting sparsity, accpm could solve [32, 40] extremely large instances, with up to 5000 arcs and or 10000 commodities. The survey paper [73] investigates several methods such as the flow deviation [28], a primal dual proximal method [64] and the projection method [8] on large nonlinear multicommodity flow problems. The most striking result is that accpm is not always the fastest, but it is constantly good and is by far the most stable one. 6 At least on problems of medium to large size, but ....

L. Fratta, M. Gerla and L. Kleinrock, "The flow deviation method : an approach to storeand -forward communication network design", Networks, 3 (1973), pp. 97-133.

.... (ELS) where the overflow traffic is equally shared among the overflow paths; Optimal overflow Load Sharing (OLS) where overflow traffic is shared among the overflow paths according to the optimal load distribution determined solving a multicommodity flow problem by the flow deviation method [FGK]. Note that in case of complete symmetric network ELS and OLS coincide. All this routing differ just for the determination of the second choice route. 3. A case study: traffic scenarios, evaluation comparison of the routing schemes #For the comparison, we consider the four node full connected ....

L. Fratta, M. Gerla, L. Klainrock "The flow deviation method: an approach to store-and-forward communication network design" Networks (1973), 3: 97-133.

....yields optimal flow assignments on fixed topologies. Since the genetic algorithm is much better suited for discrete optimization problems, it will be used to solve the connectivity problem. The flow assignment problem will be solved on fixed topologies with minimum hop routing and flow deviation [21]. The overall algorithm is: create initial population of topologies while stopping criterion is not met evaluate each topology using minimum hop routing mate individuals to create new generation mutate generation The division of the problem reduces the size of the solution space that each ....

....matrix is built as the shortest paths are found. This allows the algorithm to choose the least used path, when alternate paths exist. Still, minimum hop routing is not adequate because it does not allow flows to be split between alternate paths. To overcome this deficiency, flow deviation is used [21]. The flow deviation method works with a flow assignment algorithm, in this case minimum hop routing. Given a flow assignment, the flow deviation method removes the most heavily used link and then the assignment problem is solved on the resulting graph. The two solutions are then combined ....

Fratta L, Gerla M, Kleinrock L. The flow deviation method: an approach to store-and-forward communication network design. Networks 1973;3:97--133.

....[4] thus typically the two problems are solved separately [5] If each node is only equipped with a single transceiver port, P = 1, only a single path exists between each pair of nodes, thus there is no routing problem. In the case of multiple transceivers per node, flow deviation methods [6] can be used to find the optimal routing that minimizes the maximum link load for a given topology configuration. For simplicity, however, we focus on minimum hop routing. In addition to simplicity, minimum hop routing is attractive because it minimizes the total network load and is commonly used ....

L. Fratta, M. Gerla, and L. Kleinrock, "The flow deviation method: An approach to store-and-forward communication network design, " Networks, vol. 3, pp. 97--133, 1973.

.... multi commodity flow routing only problem (either for discrete or for continuous variables) using arc path approach in the context of communications networks as well as transportation networks has been addressed by several researchers over the years; see, for example, 5] 9] 10] 17] 18] [19], 20] 23] 33] 34] To our knowledge, the combinatorial optimization problem as presented in model (P) i.e. the multi hour combined routing and capacity design problem (with single route selection case) in a multi service environment has not received much attention in the literature. 3. ....

L. Fratta, M. Gerla and L. Kleinrock, "The Flow Deviation Method: An Approach to Storeand -Forward Computer Communication Network Design," Networks , Vol. 3, pp. 97-133, 1973.

....delay [3] In this work we follow the model in [17] 18] and base our performance criteria is minimization of congestion. The approach in [17] 18] is based on starting with an initial heuristic topology and modifying it with branch exchange operations guided by the flow deviation method [10], 11] The propagation delay in [3, 4] on the other hand is minimized in terms of the pairwise distances between the stations using simulated annealing. Our approach is different. First we note that because of interdependency between routing and logical topology, the problem of finding a good ....

....improvements of 5 to 20 over the previous results reported in [17] 18] on the same traffic models. 2 Their reported results are based on starting with a greedy topology and modifying it with branch exchange operations. The routing problem is solved by using the Flow Deviation method [10]. Our results suggest that the choice of starting topology is one likely of the reasons that our algorithms outperforms the previous results. Other, more significant reasons for the performance difference may include more powerful heuristics for chooising between alternative configurations, the ....

[Article contains additional citation context not shown here]

L.Fratta, M.Gerla, and L.Kleinrock, "The Flow Deviation Method: An Approach to Storeand -Forward Communication Network Design," Networks, Vol. 3, 1973.

....Optimization, University of Waterloo, Canada. 1 Introduction and Definitions Nonlinear cost multicommodity flow problems arise in many practical applications. For example, optimal packet routing and capacity allocation in packet switched telecommuncations networks can be modelled in this way [5, 7]. Previous approaches to these problems have focussed on the application of general convergent techniques such as the Frank Wolfe method [7] or others [5] In this paper, we concentrate on a special class of nonlinear cost multicommodity flow problems in which there are only two commodities. In ....

....applications. For example, optimal packet routing and capacity allocation in packet switched telecommuncations networks can be modelled in this way [5, 7] Previous approaches to these problems have focussed on the application of general convergent techniques such as the Frank Wolfe method [7], or others [5] In this paper, we concentrate on a special class of nonlinear cost multicommodity flow problems in which there are only two commodities. In this situation it is known that the constraints can be decoupled using a simple transformation [10, 14, 9] In the case of linear cost flows, ....

L. Fratta, M. Gerla and L. Kleinrock, "The flow deviation method: an approach to store-and-forward communications network design", Networks 3 (1973) 97-133.

....cuts (columns) are made up of indicator vectors of paths on a network, the problem is sparse. By exploiting sparsity, accpm could solve [32, 40] extremely large instances, with up to 5000 arcs and or 10000 commodities. The survey paper [73] investigates several methods such as the flow deviation [28], a primal dual proximal method [64] and the projection method [8] on large nonlinear multicommodity flow problems. The most striking result is that accpm is not always the fastest, but it is constantly good and is by far the most stable one. 6 At least on problems of medium to large size, but ....

L. Fratta, M. Gerla and L. Kleinrock, "The flow deviation method : an approach to storeand -forward communication network design", Networks, 3 (1973), pp. 97-133.

....transmitted and which is optimal according to some chosen cost criterion. The average message delay is the most frequently performance measure used in the literature for such networks. Under appropriate assumptions, this problem belongs to the class of nonlinear convex multicommodity flow problems [20], 6] Much of the motivation for this work comes from these message routing problems. The present study is concerned only with the nonlinear convex models for which, to our knowledge, no overview has been published. In theory these models can be solved by general nonlinear programming techniques. ....

.... the techniques, early approaches were based on classical mathematical programming algorithms which were adapted to the convex multicommodity flow problem (steepest descent, Newton methods, conjugate gradient methods) In particular the most popular among existing algorithms such as Flow Deviation [20], 38] and Projected Newton [4] fall into the category of feasible direction methods. Linear or piecewise linear Authors Models Type Solution Subproblems Decomposition Applications References techniques Fratta et al. 20] 3 gradient shortest paths by commodity Telecom. LeBlanc [38] method ....

[Article contains additional citation context not shown here]

L. Fratta, M. Gerla and L. Kleinrock, "The flow deviation method : an approach to storeand -forward communication network design", Networks, 3 (1973), pp. 97-133.

....approach, however, is limited to specific types of network topology and a structured layout which cannot be assumed for a general network. Furthermore, deriving the route from the address in general conflicts with alternate routing approach. Flow based techniques, used in many existing networks [7, 8], are also inadequate for our environment. These routing strategies are destination based (typically require a table entry per destination) but more importantly, result in bifurcated routing necessitating intermediate nodes to generate random numbers. Two strategies are considered in this paper ....

L. Fratta, M. Gerla, and L. Kleinrock, "The flow deviation method: An approach to store and forward communication network design," Networks, vol. 3, no. 2, pp. 97--133, 1973.

....performance improvements of 5 to 20 over the previous results reported in [25] 26] on the same traffic models. The reported results are based on starting with a greedy topology and modifying it with branch exchange operations. The routing problem is solved by using the Flow Deviation method [12]. We suspect that the choice of starting topology is one of the reasons that our algorithms outperforms the previous results. Another reason for the performance difference is the step size in the search process. The edge perturbation mode is 2 change operation whereas the branch exchange ....

....step size in the search process. The edge perturbation mode is 2 change operation whereas the branch exchange operations on digraphs are quite tricky. Finally, Linear Programming for solving the Routing Problem may be a better choice (in contrast to the Flow Deviation method which is suggested in [12] for non linear, unconstraint flow problems) In order to study the sensitivity of our heuristics to different starting topologies, we generated random 3 starting points and computed the standard deviation of minimum congestion for each perturbation mode by gathering information from 30 ....

L.Fratta, M.Gerla, and L.Kleinrock, "The Flow Deviation Method: An Approach to Storeand -Forward Communication Network Design," Networks, Vol. 3, 1973.

....with annealing. The probability of acceptance is based on a negative exponential factor and is inversely proportional to the difference between the current solution and the best solution obtained so far. 4. 5 Flow Deviation Algorithm By properly adjusting link flows, the flow deviation algorithm [12] provides an optimal algorithm for minimizing the network wide average packet delay. However, traffic from a given source to a destination may be bifurcated, i.e. different fractions of it may be routed along different paths in order to minimize the packet delay. If the flows are not balanced, ....

L. Fratta, M. Gerla, and L. Kleinrock. The flow deviation method: an approach to store-and-forward communication network design. Networks, 3:97--133, 1973.

....analysis of the previous section, we focus only on the TFR machine model. Routing in computer networks has been investigated extensively in the last three decades. In terms of optimization, bifurcated routing has been shown to achieve optimal performance and several approaches have been developed[10,11]. These approaches treat the routing problem as a multicommodity minimum cost flow problem. It has been shown that under such circumstances optimal routing results only if traffic flows along Minimum First Derivative Length (MFDL) paths i.e. paths in which the sum of the first derivative of the ....

....one, in which a cost function is reduced in each iteration by diverting some flow from expensive routes to less expensive ones. The classical solutions determine inexpensive routes by means of the first derivative of the cost function with respect to the flows. The flow deviation algorithm[11] determines inexpensive routes by searching for shortest paths according to the MFDL metric. Gallager s algorithm [10] exchanges marginal costs among nodes and diverts traffic to those routes where the marginal cost is the smallest. The structure of the optimality conditions (OC1) OC3) or, ....

[Article contains additional citation context not shown here]

L. Fratta, M. Gerla, and L. Kleinrock, "The Flow Deviation Method: An Approach to Store and Forward Communication Network Design," Networks 3(2) pp. 97-133 (1973).

....point) is addressed briefly. We note that the routing problem in a network with a single common (convex) objective can be solved in a fairly standard way using convex programming techniques. Centralized and distributed algorithms of that type have been described in the literature (e.g. [21, 22]) When the objective function is convex but not common to all users the setting becomes that of a convex game. As mentioned above and shown in the sequel, uniqueness of the Nash point cannot be derived directly from available results of convex game theory (such as [19] This leads us to exploit ....

M. G. L. Fratta and L. Kleinrock, "The flow deviation method: An approach to store and forward communication network design," Networks, vol. 3, pp. 97--133, 1973.

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L.Fratta, M.Gerla, and L.Kleinrock. The Flow Deviation Method: An Approach to Storeand -forward Network Design. In Networks 3, pages 97--133, 1973. 11

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Fratta, L., Gerla, M. and Kleinrock, L. [1973] "The flow deviation method: An approach to store-and-forward network design," in Networks 3, pp. 97--133.

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Fratta, L., Gerla, M. and Kleinrock, L. [1973] "The flow deviation method: An approach to store-and-forward network design," in Networks 3, pp. 97--133.

....speculates that the average delay is a convex function in the space over the traffic requirements on al links, on the basis of the ZAP approximation [8] of the throughPut delay curves. Thus, he adapts the flow deviation method, originally developed for wire based store and forward networks in [4], to the multihop packet radio networks. Some other authors [2] 3] 3] create more or less idealistic assumptions (such as zero propagation delay Paper approved by the Editor for Computer Communication of the IEEE Communications Society. Manuscript received February 14, 1983; revised January ....

L. Fratta, M. Gerla, and L. Kleinrock, "The flow deviation method: An approach to store-and-forward communication network design," Networks, vol. 3, pp. 97-133, 1973.

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L. Fratta, M. Gerla and L. Kleinrock. The flow deviation method: an approach to store-andforward communication network design. Networks 3:97-133, 1971.

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M. G. L. Fratta and L. Kleinrock, "The flow deviation method: An approach to store and forward communication network design," Networks, vol. 3, pp. 97--133, 1973.

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L. Fratta, M. Gerla and L. Kleinrock, The flow deviation method: an approach to storeand -forward communication network design, Networks 3 (1971), 97 -- 133.

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L. Fratta, M. Gerla, and L. Kleinrock, "The Flow Deviation Method: An Approach to Store and Forward Communication Network Design," Networks, 3, pp. 97-133 (1973).

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L.Fratta, M.Gerla, and L.Kleinrock, "The flow deviation method: An approach to store-andforward communication network design," Networks, vol. 3, pp. 97--133, 1973.

No context found.

L. Fratta, M. Gerla, and L. Kleinrock. The flow deviation method: An approach to store-andforward communication network design. Networks, 3:97--133, 1973.

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L. Fratta, M. Gerla and L. Kleinrock, "The flow deviation method---an approach to the store-and-forward communication network design," Networks 3, 97--133 (1973).

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Fratta, L., Gerla, M., and Kleinrock, L., "The flow deviation method: an approach to store-and-forward communication network design" Networks, pp. 97--133, 1971.

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L. Fratta, M. Gerla, L. Kleinrock "The flow deviation method: An approach to store-and-forward communication network design," Networks, 3, pp.97133, 1973.

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