Routing Algorithms for Supporting Resource Reservation

Transcription

1 - Routing Algorithms for Supporting Resource Reservation Zheng Wang Jon Crowcroft Department of Computer Science, University College London London WC1 6BT, United Kingdom In this paper, we propose two new routing algorithms for supporting resource reservation. In our algorithms, a path in a network is represented by its bottleneck bandwidth (width) and propagation delay (length). The algorithms find the shortestwidest paths from a given source to all other nodes, using delay aided bandwidth search. The algorithms are scalable and loop-free in distributed hop-by-hop routing. 1. Introduction In recent years, we have seen a drastic increase in the processing power of personal workstations and in the capacity of computer networks. As a result, we are now able to process and transmit real-time digital audio and video with these systems. The experiments over the MBONE, an Internet-wide experimental multicast testbed [2], have demonstrated the enormous potential of this emerging technology. Multimedia applications such as digital audio and video, however, have much more stringent QoS requirements than traditional data applications. For a network to deliver QoS guarantees, it must make appropriate resource reservation and excise necessary resource control. In the past several years, there has been much discussion and research in the area of resource management [3-5, 7-9, 13-21, 24-28]. Most of the work, however, focused on the problem of resource setup and resource enforcement at routers along an established path. Routing for supporting resource reservation is still an open research problem that has not been fully explored. Routing should be an integrated part of any resource reservation system. When a host initiates a request for reserving network resources to another host or a router, the routing protocol has to first chooses a path then the negotiation between the hosts and routers can take place. Therefore, the success or failure of a reservation request, to some large extent, depends on whether the routing protocol can choose the right path. The process of resource reservation can be viewed as a two-step resource search. To find a path in a network that satisfies a set of requirements, the routing protocol first makes a high-level decision as to which path is more likely to have the necessary resources. The resource setup protocol then starts hop-by-hop low-level negotiation with each router on the path to sort out the fine details. To some extent, the decision making in routing is inherently more difficult due to its distributed nature. Resource reservation has raised many new issues for routing. We believe that, in order to support resource reservation, major modifications are required in current routing protocols. In traditional data networks, the primary concern of routing has been the network connectivity. To support resource reservation, routing must however move towards a more resourceoriented system. The key problem in supporting resource reservation is the complexity of such routing algorithms. Current routing protocols are already reaching the limit of feasible complexity. Adding the resource reservation support will inevitably further increase their burden. Our task is therefore to tackle the complexity problem by making sensible tradeoffs between optimality and complexity. In this paper, we propose two new routing algorithms for supporting resource reservation. In our algorithms, a path in a network is represented by its bottleneck bandwidth (width) and propagation delay (length). The algorithms find the shortestwidest paths from a given sources to all other nodes, using delay aided bandwidth search. The algorithms are scalable and loop-free in distributed hop-by-hop routing.

2 2. Problem Definition In this section, we define the problem we try to solve, and outline the essential requirements to any solutions. Resource reservation, to some extent, is a process of translating abstract application QoS requirements into physical network resources. Various reservation schemes differ in styles and details but the basic functions are similar. To make a reservation, an application usually prepares a flow specification, in which it describes the characteristics of the traffic, and specifies the QoS requirements for the flow [22]. The flow specification is then mapped onto constraints on network resources such as bandwidth, cost, buffer size etc. The exact form of mapping depends on the resource enforcement scheme used. The task for routing protocol is to select a path to the destination (either a host or a router) that is most likely to satisfy the resource requirements. After that, hop-by-hop negotiation and resource setup can be carried out. The basic problem for routing in supporting resource reservation therefore can be summarised as finding a path in a network for a given set of constraints. Any routing algorithm for solving this problem must however meet the following essential requirements: The algorithm must be efficient and be able to scale to large networks such as the Internet. Ideally, the complexity of the algorithm should be comparable to current routing algorithms. The algorithm must be able to provide sufficient information to make quantitative assessment on resource availability. The algorithm must be suitable for current routing architectures, such as distributed hop-by-hop routing. 3. Basic Approach The problem of finding a path in a graph subject to two or more constraints is inherently hard. Some solutions do exist [23], but the problem is known to be NP-Complete [11]. Therefore, we are not interested here in any exact solutions. Our approach is to look at possible tradeoffs between optimality and complexity, and try to find algorithms that are scalable and also provide acceptable support for resource reservation. In this section, we discuss the principles and tradeoffs behind our approach, and outline the framework for the routing algorithms we describe in the next two sections Routing Metric Structure In traditional data networks, routing decisions are usually based on simple single-valued metrics such as delay or hop count. Such metrics are clearly inadequate for supporting resource reservation. Multi-valued metrics, such as an array of bandwidth, delay, loss rate etc certainly contain more information but the computation is likely to be substantially more complex. An interesting question is whether we can support resource reservation with a single-valued metric. One possible approach is to use a combination of metrics. The idea is to compress various pieces of information into a single measure that forms the basis for routing decisions. A combination metric is produced with various network parameters such as bandwidth, delay and queue length etc, with a pre-defined formula. Thus, the information contained in a combination metric is "cooked" in the sense it has been processed and mixed. As such, it is not possible to derive the original "raw" information from a combination metric. Combination metrics can only be used as an indicator of network conditions, and making quantitative assessment of the availability of resources is often very difficult. For example, delay is widely used as a routing metric. It can in fact be viewed as a combination metric, consisting of two components of very different nature: queuing delay and propagation delay. A delay metric indicates the delay currently being experienced by packets but it does not reveal any quantitative information about the resource availability. Note that, without knowing the queuing delay or propagation delay, it is not possible even to determine, from a given delay value, whether a path is idle or busy. Another problem with combination metrics is that it may not be possible to combine network parameters of different nature together. For example, suppose that a path consists two segments p 1 p 2. If metric M is delay, M (p 1 p 2 ) = M (p 1 ) + M (p 2 ). If metric M is bandwidth, M (p 1 p 2 ) = min [M (p 1 ),M (p 2 )]. However, if metric M is a combination of delay and bandwidth, neither above are valid, which can cause difficulties in route computation. Although using a combination metric is an interesting approach for reducing complexity, we believe that it does not provide sufficient support for resource reservation. In order to make quantitative assessment on resource availability, we must base routing decisions on explicit information Style of Routing There are two basic styles of routing: source routing and distributed hop-by-hop routing. They have different implications for routing algorithms.

3 In source routing, the source node specifies the entire path that a packet should follow, and each node on path just forwards the packet accordingly. As the forwarding decision is made centrally at the source, it is fairly easy to ensure that path is loop-free. For each flow, the routing algorithm only needs to search once for a suitable path from the source to the destination (one-to-one computation). Also, the computation may be done on demand. There is no need for coordination between different nodes; the source may also choose any algorithm different from ones used by other nodes, and may even use different algorithms at different times. In contrast, in distributed hop-by-hop routing, any packet is forwarded hop-by-hop based on its destination address. At each hop, the node finds the next-hop towards the destination, and forwards accordingly. Therefore, the forwarding of a packet from the source to the destination involves decision making by each individual node on the path. The task of ensuring loop-freeness in such a distributed environment is far more difficult than in source routing. The routing algorithm must be constructed in a way that forwarding decisions at each individual hop are consistent. As we show in the later section, a centralized algorithm suitable for source routing may not necessarily work in distributed hop-by-hop routing. Also, the forwarding decisions are made at each hop, it is not feasible to generate paths on demand. All nodes have to pre-compute paths to every destination (one-to-all computation). Distributed hop-by-hop routing may substantially complicate the design of routing algorithms but it is by far the most widely used and flexible style of routing. It is essential that any algorithm for supporting resource reservation should be looked at both as a centralized algorithm and as a distributed algorithm. There are two basic types of distributed routing: link-state and distance-vector. In link-state routing, the state of each link is broadcasted to all nodes in the network, and each node then computes the forwarding paths independently. In distancevector routing, each node is only informed of the forwarding paths of its neighbor nodes. Our proposed routing algorithms can be used in both types of distributed routing Network Representation The parameters used to represented the network in routing are of fundamental importance. They form the basis for routing decisions, and also determine the the service interface between the routing algorithm and the applications. Any application requirements have to be mapped onto constraints on those parameters for path selection. It is desirable to include as many as possible parameters to describe the network but we have to consider the implications on complexity. As the problem of finding a path subject to two or more constraints is known to be hard, we can only choose parameters that are absolutely essential. The parameters we choose must reflect the most fundamental characteristics of a network that an application needs to know. The parameters must be orthogonal of each other, i.e. free of any redundant information. As the application requirements have to be mapped onto constraints on the network parameters, we start our consideration from the applications viewpoint. When a packet traverse a network, the only visible measure that the applications see is the delay incurred in the network. Thus, any application requirements may be expressed as the constraint on the time of delivery. From the networks viewpoint, the overall delay incurred in the network has two basic components of different nature: propagation delay and queuing delay 1. Propagation delay is caused by the propagation of the eletromagnetic signal, thus is proportional to the distance of the path. Queuing delay is the time a packet waits in a queue, and it largely depends on the application s traffic characteristics and the bottleneck bandwidth of the path. Therefore, the overall delay experienced by a packet is largely determined by bottleneck bandwidth and propagation delay of the path. Based on these considerations, we select the bottleneck bandwidth and propagation delay as the most fundamental parameters in a network; they represent the width and the length of a path in the network. In our proposed routing algorithms, each node maintains two parameters for each outgoing link: residual bandwidth and propagation delay. The residual bandwidth is the unreserved capacity, which is updated each time when a reservation is added or deleted. The propagation delay is changed each time when a link is added or deleted. All application requirements are mapped onto the constraints on the bottleneck bandwidth (width) and propagation delay (length). We believe that our choice of the parameters strikes a sensible balance in the division of work between routing and resource setup protocols. Routing makes a coarse decision based on the bandwidth and propagation delay requirements. Other finer details such as buffer size, CUP load may also affect the application s QoS, but they are only considered in the 1 The overall delay is sometimes divided into three components: propagation delay, queuing delay and transmission delay. Transmission delay is the time for a whole packet to be transmitted. In some sense, it can be viewed as a special kind of queuing delay. In this paper, we include transmission delay in queuing delay.

4 hop-by-hop negotiation by source setup protocols Ordering of Application Requirements Although we have chosen bottleneck bandwidth and propagation delay as our basic parameters for routing decisions, we still have to deal with the difficult problem of finding a path subject to two constraints. The approach we take here is to order the two parameters, i.e. one parameter has higher priority than the other one during the search for a suitable path. Such ordering can achieve substantial reduction in the complexity of search although at the expense of optimality. The search space for the second parameter is limited to the output of the first search. The order of the two parameters is somehow application-dependent. Since the queuing delay is more dynamic, bandwidth is probably considered as the more important one more often. If the bandwidth requirement can not be met, the chance is that queuing delay, and probably also loss rate will be high. On the other hand, if the propagation delay can not be met, the overall delay will be higher but the increase will be predictable and stable. Thus, failing to meet either of the two constraints will result in higher overall delay but the increase of queuing delay can have more severe consequences than that of propagation delay. However, propagation delay is still an important parameter for applications as it affects the overall delay. The performance of some highly interactive applications may deteriorate rapidly when the round trip delay exceeds some thresholds. Long delay makes feedback control less effective and may also force protocols that use pipelining to have large buffer size in the end systems. Therefore, it is desirable to choose paths with shorter delay if the bandwidth requirement can still be met. In our proposed routing algorithms, we give the bandwidth requirement the higher priority. When the bandwidth requirement is met, we always try to choose the path with minimum delay Selection of Path Given a set of requirements, there may be more than one path suitable. An optimal selection would be to choose the smallest fit so that the large one can be left for others. For example, suppose that an application has requested 90 kbps and there are two paths available with 100 kbps and 200 kbps respectively. Ideally, we should choose the path with 100 kbps so that the 200 kbps path is left for future requests. If we choose the 200 kbps path, future requests over 110 kbps have to be rejected. If we have several flows and several suitable paths, optimal selection becomes more difficult. The problem is similar to the Bin-Packing one [11]. Generally speaking, such global optimization requires a search and examination of every possible paths and does not scale well. In our routing algorithms, we use the selfish optimization approach, i.e. the algorithms always choose the best path. For example, if an application requests a path with a bandwidth requirement, the algorithms simply find the path with maximum bandwidth so only one search is needed. The shortest path algorithms widely used in current routing protocols are typical examples of such selfish optimization. 4. Widest Path Algorithms In this section, we first consider the problem of finding a path between two nodes with maximum bandwidth. We refer it the widest path problem. Consider a directed graph G = (N, A) with number of nodes N and number of arcs A, in which each arc (i, j) is assigned two real numbers, b ij as the residual bandwidth and d ij as the propagation delay. To simplify the notation, let b ij = 0 and d ij = if (i, j) is not an arc of the graph. Given any directed path p = (i, j,k,...,l,m), the width of the path width (p) is defined as the bottleneck bandwidth of the path, i.e. width (p) = min [b ij,b jk,..., b lm ], and the length of the path length (p) is defined as the sum of propagation delay, i.e. length (p) = d ij + d jk d lm. Given any two nodes i and m of the graph, the widest path problem is to find a path from node i to node m with maximum width. This problem is, in many respects, remarkably similar to the shortest path problem. The only difference lies in the calculation of the width and the length of a path. Therefore, it appears to be a reasonable approach to apply the techniques used in shortest path algorithms to the widest path problem. There are two basic distributed shortest path routing algorithms: the link-state algorithm based on the Dijkstra algorithm [6], and the distance-vector algorithm based on the Bellman-Ford algorithm [10]. Correspondingly, we have two versions of widest path algorithms. The widest path algorithm suitable for distance-vector routing is shown below 2 : 2 For the sake of simplicity, the algorithm shown here is in a slightly different form from the one required by distancevector routing. The algorithm shown here finds the widest paths from a given node 1 to all other nodes while distancevector routing requires an algorithm that finds the widest path to a given node 1 from all other nodes. However, any one

5 Widest Path Algorithm (distance-vector version) Suppose that node 1 is the source node and h is the number of arcs away from the source node. Let B i (h) be the width of the widest path from node 1 to node i within h hops. By convention, B 1 (h) =. Step 1: Initially, h = 0 and B i (0) = 0, for all i 1 Step 2: Step 3: Find k so that width (1,...,k,i) = max[min [B (h) j, b ji ]], i 1 1 j N B i (h +1) = width (1,...,k,i) Step 4: If h A, the algorithm is complete. Otherwise, h = h + 1 and go to Step 2. The widest path algorithm suitable for link-state routing is shown below: Widest Path Algorithm (link-state version) Suppose that node 1 is the source node Let B i be the width the widest path from node 1 to node i. By convention, B 1 =. Step 1: Initially, L ={1}, B i = b 1i for all i 1 Step 2: Find k / L so that B k = maxb i. i / L L := L {k}. If L contains all nodes, the algorithm is completed Step 3: For all i / L, set B i := max [B i, min [B k, b ki ]] Step 4: Go to Step 2. As centralized algorithms, it is easy to see that both algorithms can find the widest paths from a given source to all other nodes, and the time complexity is equal to that of the corresponding shortest path algorithms. However, there are two problems which make them unsuitable for distributed routing, which we now describe Arbitrary Path Problem Under some circumstances, the above two algorithms suffer from what we call Arbitrary Path Problem. To illustrate the problem, we look at the case where all links in a network have the same amount of bandwidth. In this case, bandwidth no longer imposes any constraints on path selection since any path has the same width (equals to the link bandwidth). To some extent, this is equivalent to the case where all links have zero delay so that any path is a shortest path. However, since the link length in network is always positive, the problem never arises in shortest path algorithms. This problem lies in the fact that a widest path is only constrained by the bottleneck link and other links have little impacts on the selection of paths. Let us look at a more general example (Figure 1). The source node S is connected to a cluster of nodes via link L. Suppose that all links in the cluster have bandwidth equal or larger than link L. So link L is the bottleneck link from node S to all nodes in the cluster. In this case, any possible paths from the source node S to any node in the cluster have a width equal to the bottleneck bandwidth, no matter which paths are chosen. The arbitrary path problem has no impacts on the primary goal of finding the widest paths, since the paths chosen are indeed widest paths. However, it does have some undesirable side-effects. Since under some circumstances any path to the destination is a widest path, a node may choose an unnecessary long path when a shorter path with equal width exists. The arbitrariness in path selection when there are multiple widest paths with equal width also points to potential looping problems. form of the algorithm can be obtained from the another form by reversing the direction of each link while keeping the width unchanged. A similar situation in shortest path algorithms is discussed in [1].

6 Source S Link L 4.2. Looping Problem Destination Cluster Figure 1: Arbitrary Path Problem in Widest Path Algorithms Looping in distributed hop-by-hop routing is a far more serious problem that both widest path algorithms have. Before we describe the details of the problem, we want to distinguish the looping problem here from other types of looping problems. First, the looping problem here only occurs in a distributed routing environment. Both widest path algorithms can produce a loop-free widest path tree used as centralized algorithms. For example, there is no looping problem if the two widest path algorithms are used for source routing. Second, the looping problem here is different from the looping problem in distributed shortest path routing that has been extensively discussed in the literature (see [12] for a comprehensive reference list). The loops in the distributed shortest path algorithms only exist during the convergence, and can be avoided by inter-nodal coordination [12]. The loops we discuss here exist after the convergence, thus are permanent. As we show later, shortest path algorithms do not have any looping problem after convergence. A D B Figure 2: Looping Problem in Widest Path Algorithms Let us consider the network shown in Figure 2 where all links have the same amount of bandwidth. Since all paths have the same width, any path can be a widest path. If the link-state version of the widest path algorithms is used, node A and node C may independently produce their forwarding trees as shown in Figure 3 and Figure 4 respectively. It is easy to see that, for destination D, a loop is formed A B C A. If the distance-vector version of the widest path algorithms is used, node A may receive updates from neighbor node B, C and D that they all can reach node D with equal width, and node A may choose node B as its next-hop to node D. However, node C may choose node A as its next hop to node D. A D C B Figure 3: Forwarding Tree Produced by Node A From the discussion above, it appears that the looping problem is caused by the arbitrariness in path selection when there are multiple widest paths with equal width. However, shortest path algorithms do not have such looping problems although multiple shortest paths with equal length do exist. It turns out that shortest paths have a natural ability of avoiding loops while widest paths do not. We now present a formal proof. C

7 A B D C Figure 4: Forwarding Tree Produced by Node C A p 2 * p 1 * p 1 C p 2 Figure 5: A Loop Involving Node A and Node B Theorem 1: Shortest paths are always loop-free in distributed hop-by-hop routing. B Proof: By contradiction. Suppose that node A and node B are involved in a loop for destination D (Figure 5). Path p 1 p 2 is the shortest path from node A to node D and path p 1 * p 2 * is the shortest path from node B to node D. There are two possibilities: 1) p 2 * = p 1 p 2, and 2) p 2 * p 1 p 2. If p 2 * = p 1 p 2, i.e. path p 1 p 2 is used by node B as part of the shortest path to node D, we have length (p 1 * p 2 * ) < length (p 2 * ) = length (p 1 p 2 ) < length (p 2 ) This contradicts the assumption that path p 1 * p 2 * is the shortest path from node B to node D. If p 2 * p 1 p 2, we have length(p 2 ) < length (p 1 p 2 ) length(p 2 * ) < length(p 1 * p 2 * ) This also contradicts the assumption that path p 1 * p 2 * is the shortest path from node B to node D. The proof is completed. Note that the above Theorem is a property of shortest paths and is independent of any particular algorithms. Intuitively, since all network links have positive length, the path without the loop must be shorter than the one with the loop. A widest path, however, does not have such a property. Note that the width of a path is decided by the bottleneck link. If a loop is not the bottleneck, it has no impacts on the width of the path. So, a path with a loop and a path without a loop have the same width. 5. Shortest-Widest Path Algorithms The examination of the looping problem in widest path algorithms also leads us to the solution. The looping problem in widest path algorithms is caused by the fact that a non-bottleneck path has no impacts on the path selection, thus loops can not be eliminated. It indicates that a second criteria is needed when selecting a path from multiple equal widest paths. Propagation delay is an ideal candidate for the second criteria in the bandwidth search. The basic idea behind what we call Delay Aided Bandwidth Search (DABS) is to use bandwidth as the first criteria for path selection, and use propagation delay as the second criteria when there are multiple suitable paths with equal bandwidth. Therefore, DABS finds a shortest path among the widest paths. We refer the shortest path among the widest paths as the shortest-widest path. It turns out that DABS solves both of the problems in widest path algorithms. DABS guarantees that only the shortest path among the widest paths is selected hence solves the arbitrary path problem. More importantly, the propagation delay criteria in DABS also eliminates any loops in widest paths. We now present a formal proof on the loop-free property of the shortest-widest paths.

8 Theorem 2:Shortest-widest paths are always loop-free in distributed hop-by-hop routing. Proof: By contradiction. Suppose that node A and node B are involved in a loop for destination D (Figure 5). Path p 1 p 2 is the shortest-widest path from node A to node D and path p 1 * p 2 * is the shortest-widest path from node B to node D. By the definition of shortest-widest paths, we have Note that Similarly, From (3) and (4), we have Combining (5) with (2), we have Similarly, we have width (p 2 * ) width (p 1 p 2 ) (1) width (p 2 ) width (p 1 * p 2 * ) (2) width (p 1 * p 2 * ) = min [width (p 1 * ), width (p 2 * )] width (p 2 * ) (3) width (p 1 p 2 ) width (p 2 ) (4) width (p 1 * p 2 * ) width (p 2 ) (5) width (p 1 * p 2 * ) = width (p 2 ) (6) width (p 1 p 2 ) = width (p 2 * ) (7) Equation (6) shows that path p 1 * p 2 * and path p 2 are equal widest paths. Since path p 1 * p 2 * is the shortest-widest path, we have length (p 2 ) length (p 1 * p 2 * ) > length (p 2 * ) (8) Similarly, Equation (7) shows that path p 1 p 2 and path p 2 * are equal widest paths. Since path p 1 p 2 is the shortest-widest path, we have Equation (8) and (9) contradict each other. The proof completes. length (p 2 * ) length (p 1 p 2 ) > length (p 2 ) (9) Note that the above Theorem is also a property of the shortest-wdiest paths and is independent of any particular algorithms. The shortest-widest path algorithms can be produced by adding the length checking when there are multiple equal widest paths. The link-state version and the distance-vector version of the shortest-widest path algorithms are described below: Shortest-Widest Path Algorithm (distance-vector version) Suppose that node 1 is the source node and h is the number of arcs away from the source node. Let B i (h) and D i (h) be the width and length of the chosen shortest-widest path from node 1 to node i within h hops. By convention, B 1 (h) = and D 1 (h) = 0 for all h. Step 1: Initially, h = 0 and B i (0) = 0, for all i 1 Step 2: Step 3: Find set K so that width (1,...,K,i) = max[min [B (h) j, b ji ]], i 1 1 j N If K has more than one element, find k K so that length (1,...,k,i) = min [D (h) j + d ji ], i 1 1 j N Step 4: B i (h +1) = width (1,...,k,i) and D i (h +1) = length (1,...,k,i) Step 6: If h A, the algorithm is complete. Otherwise, h = h + 1 and go to Step 2. Step 2 finds all widest path from node 1 to each node i. If there are more than one widest path found, Step 3 chooses the one with minimum length. Step 4 updates the width and length for the shortest-widest path from node 1 to each node i.

9 Shortest-Widest Path Algorithm (link-state version) Suppose that node 1 is the source node Let B i and D i be the width and length of the chosen shortest-widest path from node 1 to node i. By convention, B 1 = and D 1 = 0. Step 1: Initially, L = {1}, B i = b 1i and D i = d 1i for all i 1 Step 2: Find set K / L so that B K = maxb i. i / L Step 3: If K has more than one element, find k K so that length (1,...,k,i) = min[d (1,..., j,i) ]. j K L := L {k}. If L contains all nodes, the algorithm is completed Step 4: For all i / L, set B i := max [B i, min [B k, b ki ]] Step 5: Go to Step 2. Step 2 finds the nodes with maximum width among the tentatively labeled nodes. If there are more than one node found, Step 3 chooses one with minimum length and permanently labels it. Step 4 updates the tentatively labeled nodes around the newly permanently labeled node. Under some circumstances, such as the case where all links have the same amount of bandwidth, shortest-widest path algorithms are effectively reduced to shortest path algorithms. In this sense, we can view shortest path algorithms as a special case of shortest-widest path algorithms. So we can also use shortest-widest algorithms to compute shortest paths by simply setting the bandwidth of all links to the same amount. In this case, the constraint on the bandwidth requirement is simply ignored. The two shortest-widest path algorithms are scalable. Note that, in the two versions of shortest-widest algorithms, the number of operation required in each iteration is proportional to that in the corresponding versions of shortest path algorithms. Therefore, the time complexity of the two shortest-widest algorithms is equal to that of the shortest path algorithms. 6. Summary and Future Work In this paper, we presented two new routing algorithms for supporting resource reservation. The routing decisions are based on the bandwidth and propagation delay requirements. The algorithms find the shortest-widest paths from a given node to all other nodes. We shown that the algorithms are scalable and loop-free. There are a number of issues that require further research: Design and implement a routing protocol based on the algorithms presented in this paper, and experiment with real networks. Investigate the interaction between routing protocols and resource setup protocols in term of the frequency of route updating and the rate of flow setup. Investigate the implications of our routing algorithms on multicast routing protocols. 7. References [1] D. Bertsekas, R. Gallager, "Data Networks", Prentice-Hall, [2] S. Casner, S. Deering, "First IETF Internet Audiocast", ACM Computer Communication Review, Vol. 22, No. 3, July [3] D. Clark and V. Jacobson. "Flexible and Efficient Resource management for Datagram Networks", presentation slides, [4] D. Clark, S. Shenker, and L. Zhang. "Supporting Real-Time Applications in an Integrated Services Packet Network: Architecture and Mechanism", in Proceedings of SIGCOMM 92, pp 14-26, [5] A. Demers, S. Keshav, and S. Shenker. "Analysis and Simulation of a Fair Queueing Algorithm", In Journal of Internetworking: Research and Experience, 1, pp. 3-26, [6] E. Dijkstra, "A Note on Two Problems in Connection with Graphs", in Numerical Mathematics, Vol. 1, 1959.

10 [7] D. Ferrari. "Distributed Delay Jitter Control in Packet-Switching Internetworks", In Journal of Internetworking: Research and Experience, 4, pp. 1-20, [8] D. Ferrari and D. Verma. "A Scheme for Real-Time Channel Establishment in Wide-Area Networks", In IEEE JSAC, Vol. 8, No. 3, pp , April [9] S. Floyd. "Link-sharing and Resource Management Models for Packet Networks", preprint, [10] L. Ford, D. Fulkerson, "Flows in networks", Princeton University Press, New Jersey, USA, [11] M. R. Garey, D. S. Johnson, "Computers and Intractability - A Guide to the Theory of NP-Completeness", Freeman, California, USA, [12] J. Garcia-Luna-Aceves, "A unified Approach to Loop-Free routing Using Distance Vectors or Link States", in Proc. Sigcomm 89, Texas, USA, Sept [13] S. J. Golestani. "A Stop and Go Queueing Framework for Congestion Management", In Proceedings of SIGCOMM 90, pp 8-18, [14] S. J. Golestani. "Duration-Limited Statistical Multiplexing of Delay Sensitive Traffic in Packet Networks", In Proceedings of INFOCOM 91, [15] R. Guerin and L. Gun. "A Unified Approach to Bandwidth Allocation and Access Control in Fast Packet-Switched Networks", In Proceedings of INFOCOM 92, [16] J. Kurose. "Open Issues and Challenges in Providing Quality of Service Guarantees in High-Speed Networks", In Computer Communication Review, 23(1), pp 6-15, [17] J. Hyman and A. Lazar. "MARS: The Magnet II Real-Time Scheduling Algorithm", In Proceedings of SIGCOMM 91, pp , [18] J. Hyman, A. Lazar, and G. Pacifici. "Real-Time Scheduling with Quality of Service Constraints", In IEEE JSAC, Vol. 9, No. 9, pp , September [19] J. Hyman, A. Lazar, and G. Pacifici. "Joint Scheduling and Admission Control for ATS-based Switching Nodes", In Proceedings of SIGCOMM 92, [20] C. Kalmanek, H. Kanakia, and S. Keshav. "Rate Controlled Servers for Very High-Speed Networks", In Proceedings of GlobeCom 90, pp , [21] R. Nagarajan and J. Kurose. "On Defining, Computing, and Guaranteeing Quality-of-Service in High-Speed Networks", In Proceedings of INFOCOM 92, [22] Partridge, C., "A Proposed Flow Specification", RFC-1363, July [23] C. Partridge, I. Castineyra, "Routing Flows in an internet", Preprint, April [24] A. Parekh. "A Generalized Processor Sharing Approach to Flow Control in Integrated Services Networks", PhD Thesis, Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, [25] H. Schulzrinne, J. Kurose, and D. Towsley. "Congestion Control for Real-Time Traffic", In Proceedings of INFOCOM 90, [26] S. Shenker, D. Clark, L. Zhang, "A Service Model for an Integrated Services Internet", Internet draft, Available for anonymous ftp at ds.internic.net::internet-drafts/draft-shenker-realtime-model-00.txt, October [27] D. Yates, J. Kurose, D. Towsley, and M. Hluchyj. "On Per-Session End-to-End Delay Distribution and the Call Admission Problem for Real Time Applications with QOS Requirements", In Proceedings of SIGCOMM 93, [28] L. Zhang, S. Deering, D. Estrin, S. Shenker, and D. Zappala, "RSVP: A New Resource ReSerVation Protocol", IEEE Network, Sept, 1993.