D. Lorenz and A. Orla, Optimal partition of QoS requirements on unicast paths and multicast trees, IEEE/ACM Transactions on Networking, Vol. 10, pp. 102--114, Feb. 2002.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....in real time OS has much similarity with the problem of resource allocation in multi hop networks. Specifically, the problem explored by networking research community is how to partition the end to end delay requirement of a real time flow over a multi hop path to achieve an optimization criteria [6, 10]. Here resources in an operating system are analogous to network links in a multi hop path. These analytical models and prototype systems notwithstanding, most state of the art operating systems such as [3, 7, 11] are yet to embrace the concept of multi resource coordination mechanism. The ....

D.H. Lorenz and A. Orda. Optimal partition of QoS requirements on unicast paths and multicast trees. In Proc. of INFOCOM '99, pages 246--253, March 1999.

....of main research results. 5.1 Related Work Several works have addressed the problem of partitioning end to end QoS requirements of flows into perhop QoS requirements. However, none of them do so with the explicit goal of maximizing the number of admissible virtual connections. Lorenz and Orda [29] have proposed a # optimal algorithm to partition the end to end QoS requirements of a flow into per link QoS requirements, the optimization criteria being to minimize the global cost which is defined as the sum of local link costs. The link level cost function is assumed to be weakly convex and ....

....links of the path. As we will demonstrate later, the best cost function that we could devise to capture the load balancing optimization criteria does not yield as high resource usage efficiency as the explicit loadbalancing heuristic that we propose. Another aspect is that the algorithm in [29] considers cost functions that depend upon only single QoS dimension, such as delay. In contrast, our algorithm considers multiple QoS dimensions, such as both delay and delay violation probability requirements. Nagarajan, Kurose and Towsley [31] have proposed Equal Allocation that divides the ....

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D.H. Lorenz and A. Orda. Optimal partition of QoS requirements on unicast paths and multicast trees. In Proc. of INFOCOM'99, pages 246--253, March 1999.

....allocation. Many papers have reported work on QoS mapping problems in which the end to end QoS requirements are mapped into local requirements. Since the problem investigated in this paper falls under this category, it is important to compare and contrast our work against the related work. 3] [4], 5] 6] 7] report work on QoS partitioning where the problem is to optimally partition an end to end QoS requirement into local QoS requirements. However, these works consider the class of additive QoS parameters such as delay and jitter. Thus the problem is to obtain an optimal local delay ....

D. Lorenz and A. Orda, "Optimal Partition of QoS Requirements on Unicast Paths and Multicast Trees", Proceedings of the IEEE INFOCOM, 1999.

....requirements. Since the problem investigated in this paper falls under this category, it is important to compare and contrast our work against the related work. The initial work on the QoS partition problem for unicast paths was reported in [5] However, its focus was on loss rate guarantees. [6] reports work on the general QoS partition problem for weakly convex cost functions. It presents polynomial algorithms for both unicast paths and multicast trees. 7] and [8] address the QoS partitioning and routing problem in networks with uncertain parameters. 9] considers the QoS partitioning ....

....cost functions and obtain efficient solutions. The QoS mapping problem that we consider does not fit in the frameworks above because in our case, the end to end delay bound is not determined by the local delay bounds, but by the rates allocated on the links of the path of a connection. Note that [6] has recognized the fact that this is not a QoS partitioning problem. It was not pursued probably because of the identical rate approach that is applied in such delay to rate mapping problems which will be discussed at length in this paper later. The identical rate approach converts our problem ....

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D. Lorenz and A. Orda, "Optimal Partition of QoS Requirements on Unicast Paths and Multicast Trees", IEEE/ACM Transactions on Networking, October 1998.

....delay requirement in a network of rate based schedulers. A similar problem was investigated in [10] Their focus was on loss rate guarantees. A major contribution of [10] was the development of a nodal metric that predicts the relative performance of QoS allocation policies in a network setting. [9] investigated the problem of optimal resource allocation for end toend QoS requirements. It associated with each link a convex cost function and established a polynomial solution to partition an end to end QoS requirement into nodal requirements such that the overall cost function is minimized. ....

D. H. Lorenz and A.Orda, "Optimal partition of QoS requirements on unicast paths and multicast trees," in Proceedings of IEEE INFOCOM '99, pp. 246-253, March 1999.

....Firoiu and Towsley [71] proposed to decompose the problem into three sub problems: 1) partitioning of end to end QoS requirements into local QoS requirements; 2) mapping of local QoS requirements into resource requirements; and (3) reclaiming of resources allocated in excess. Lorenz et al. [72] generalized Firoiu and Towsley s work [71] and studied the problem of how to partition an end to end QoS requirement into local requirements, such that the overall cost of the multicast tree is minimized. Instead of distributing QoS requirement along a path evenly or proportionally as did in ....

D. H. Lorenz and A. Orda. Optimal partition of QoS requirements on unicast paths and multicast trees. Proceedings of IEEE INFOCOM'99, New York, March 1999.

....on the delay guarantee requested. In particular, to traverse each network link an application pays a fee that reflects the desired delay guarantee on the link. Note that the price delay relationship can be different on each link. This model has been studied by several other researchers. See [10] and the references therein. Such a cost structure can model a setting in which the service provider provides multiple service classes with a different price and QoS guarantees for each link for each class. This model is also equivalent to a network with uncertain parameters where the delay on ....

....be solved optimally in polynomial time. The solution is then rounded back to the original delay values with some bounded error. Our approximation algorithms also use the rounding and scaling technique. Several studies on frameworks related to PARTITION have been conducted, e.g. see [20] 6] [10] and the references therein. Lorenz and Orda [11] and Guerin and Orda [12] investigated both PATH and PARTITION in the context of networks with uncertain parameters. In their studies, the delay on each link is given as a probability distribution p e (d) and their goal is to maximize the product ....

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D. Lorenz and A. Orda, "Optimal partition of QoS requirements on unicast paths and multicast trees," in IEEE Infocom, 1999.

....represents several paths that support different QoS requirements at different cost values. Accordingly, we consider a network model, in which each link is associated with a performancedependent cost function. The problem of optimal partition of QoS requirements was formulated by Lorenz and Orda [6] and has been the subject of several studies [2] 3] 5] 7] 11] Efficient optimal solutions for the special case of convex cost functions for both unicast and multicast were established in [6] However, the convexity assumption is not valid in many cases of practical interest. Since in the ....

....function. The problem of optimal partition of QoS requirements was formulated by Lorenz and Orda [6] and has been the subject of several studies [2] 3] 5] 7] 11] Efficient optimal solutions for the special case of convex cost functions for both unicast and multicast were established in [6]. However, the convexity assumption is not valid in many cases of practical interest. Since in the general case the problem of optimal partition is intractable (i.e. NP hard [6] suitable approximation schemes were presented in [2] 7] 11] While the computational complexity of those proposed ....

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D. H. Lorenz and A. Orda. Optimal Partition of QoS Requirements on Unicast Paths and Multicast Trees. In Proceedings of IEEE INFOCOM '99, New York, NY, March 1999.

.... pose several QoS requirements, it turns out that these often translate mainly into a bandwidth requirement [2] 3] Bandwidth, in turn, belongs to the class of bottleneck path requirements, which are much easier to handle than additive requirements, such as delay, loss and jitter [10] 13] [14]. As for global network optimization, often it turns out that much can be achieved by employing the simple criterion of hop minimization [2] 4] indeed, a consequence of the need to reserve resources such as bandwidth on each link of the connection s path is that, with fewer hops one consumes ....

D. H. Lorenz and A. Orda. Optimal Partition of QoS Requirements on Unicast Paths and Multicast Trees. In Proceedings of IEEE INFOCOM'99, New York, NY, March 1999.

....and resource allocation optimization problem. We use integer cost functions, which better fit practical purposes (see [15] and references therein) We also focus on additive (e.g. delay) QoS requirements, which are typically harder to solve for than bottleneck (e. g, rate) requirements (see [13] for a more detailed discussion) This model and related problems were recently addressed by several works. Some studies assumed that the route (i.e. unicast path or multicast tree) is given and only the resource allocation part of the problem is solved. Heuristics for loss rate guarantees on ....

....solutions for convex cost functions, from an operations research point of view, are discussed in [9] under the broader scope of a general resource allocation problem. 1 An optimal solution for (weakly) convex cost functions and improved results for specific cost functions are shown in [12] [13], and [15] Heuristics for the resource allocation problem for multicast connections are given in [4] and the problem is optimally solved in [13] A variant of this problem for rate guarantees is studied in [10] and a more efficient solution is given in [8] 2 Distributed optimal solutions are ....

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D. H. Lorenz and A. Orda. Optimal partition of QoS requirements on unicast paths and multicast trees. In Proceedings of the IEEE INFOCOM'99, pages 246--253, New York, NY, March 1999.

....of the issues at stake. We feel that the latter is an important first step in exploring this complex problem. One that can then help better assess possible trade offs between performance and complexity, and provide a useful guide for future investigations, both at the conceptual (e.g. 14] [15]) as well as the applied level (e.g. 5] 6] 12] This is even more true given the lack of previous work on the specific topic of this paper. The most relevant body of work to our problem of QoS routing in the presence of inaccurate information, is a set of papers aimed at exploring state ....

....is the aggregation process that occurs in hierarchically interconnected networks. A summary of the paper s results is shown in Figure 2, and we hope that they will foster additional works in what we feel is an important area. Some follow on studies are reported in [5] 6] 12] 13] 14] [15]. Several aspects clearly require further investigation, and we proceed to name a few major ones. One aspect is identifying probability distributions that can realistically capture the inaccuracy in state information. The exponential distribution is an attractive candidate because it is an ....

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D. H. Lorenz and A. Orda, "Optimal Partition of QoS Requirements on Unicast Paths and Multicast Trees," in Proceedings of INFOCOM, New York, NY, March 1999.

....of Industry and Commerce. turns out that these often translate mainly into a bandwidth requirement [2] 3] Bandwidth, in turn, belongs to the class of bottleneck path requirements, which are much easier to handle than additive requirements, such as delay, loss and jitter [11] 14] [15]. As for global network optimization, often it turns out that much can be achieved by employing the simple criterion of hop minimization [2] 4] indeed, a consequence of the need to reserve resources such as bandwidth on each link of the connection s path is that, with fewer hops one consumes ....

D. H. Lorenz and A. Orda. Optimal Partition of QoS Requirements on Unicast Paths and Multicast Trees, In Proceedings of IEEE INFOCOM'99, New York, NY, March 1999.

....analysis and solution structure turn out to be much more complex. Section V relates these findings to unicast and multicast QoS routing. Finally, concluding remarks are presented in Section VI. Due to space limits, some technical details and proofs are omitted from this version and can be found in [15]. 4 II. MODEL AND PROBLEMS In this section we present our framework and introduce the QoS partition problem. We assume that the connection topology is given, i.e. a path p for unicast, or a tree T for multicast. The problem of finding such topologies, namely QoS routing, is briefly discussed in ....

....employs greedy moves until it reaches a ffi optimal partition. This bound is the same for all iterations, since it is a bound on the distance between a 2ffi optimal partition and a ffi optimal partition. Lemma 2: Let x GREEDY MOVE(x; 2; c( Delta) p) Then (x) jpj. The above lemma, proven in [15], resembles the proximity theorem presented in [11] Theorem 2: Algorithm BINARY OPQ solves Problem OPQ in O (jpj log jpj log(D=jpj) Proof: The final call to GREEDY MOVE is with ffi = 1, which produces an optimal allocation. By Lemma 2 and Theorem 1, each call to GREEDY MOVE requires O(jpj log ....

D. H. Lorenz and A. Orda. Optimal partition of QoS requirements on unicast paths and multicast trees. Research Report EE Pub. No. 1167, Department of Electrical Engineering, Technion, Haifa, Israel, July 1998. Available ftp: ftp://ftp.technion.ac.il/pub/supported/ee/Network/lor.mopq98.ps.

....analysis and solution structure turn out to be much more complex. Section V applies these findings to unicast and multicast QoS routing. Finally, concluding remarks are presented in Section VI. Due to space limits, many technical details and proofs are omitted from this version and can be found in [15]. II. MODEL AND PROBLEMS In this section we present our framework and introduce the QoS partition problem. We assume that the connection topology is given, i.e. a path p for unicast, or a tree T for multicast. The problem of finding such topologies, namely QoS routing, is briefly discussed in ....

....and employs greedy moves until it reaches a ffi optimal partition. This bound is the same for all iterations, since it is a bound on the distance between a 2ffi optimal partition and a ffi optimal partition. Lemma 2: Let x GREEDY MOVE(x; 2; c( Delta) p) Then (x) jpj. This lemma, proven in [15], resembles the proximity theorem presented in [11] Theorem 2: Algorithm BINARY OPQ solves Problem OPQ in O (jpj log jpj log(D=jpj) Proof: By Lemma 2 and Theorem 1, each call to GREEDY MOVE requires O(jpj log jpj) Since there are O(D=jpj) such calls, the result follows. E. Faster ....

D. H. Lorenz and A. Orda. Optimal partition of QoS requirements on unicast paths and multicast trees. Research Report EE Pub. No. 1167, Department of Electrical Engineering, Technion, Haifa, Israel, July 1998. Available ftp: ftp://ftp.technion.ac.il/pub/supported/ee/Network/lor.mopq98.ps.

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D. Lorenz and A. Orla, Optimal partition of QoS requirements on unicast paths and multicast trees, IEEE/ACM Transactions on Networking, Vol. 10, pp. 102--114, Feb. 2002.

No context found.

D.H. Lorenz and A. Orda. Optimal partition of QoS requirements on unicast paths and multicast trees. In Proc. of INFOCOM'99, pages 246--253, March 1999.

No context found.

D.H. Lorenz and A. Orda. Optimal partition of QoS requirements on unicast paths and multicast trees. IEEE/ACM Transactions on Networking, 10(1):102--114, February 2002.

No context found.

D. H. Lorenz and A. Orda. (1998, July) Optimal partition of QoS requirements on unicast paths and multicast trees. Dept. Elect. Eng., Technion. Haifa, Israel. [Online]. Available: ftp://ftp.technion.ac.il/pub/ supported/ee/Network/lor.mopq98.ps

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D. H. Lorenz and A. Orda. "Optimal partition of QoS requirements on unicast paths and multicast trees", INFOCOM'2002.

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Dean H. Lorenz, Ariel Orda, "Optimal Partition of QoS Requirements on Unicast Paths and Multicast Trees", Department of Electrical Engineering, Technion, Haifa, Israel, July 1998, Research Report EE Pub. No. 1167.

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