We consider the fundamental problem of bandwidth allocation among flows in a packet-switched network. The classical max-min rate allocation has been widely regarded as a fair rate allocation policy. But, for a flow with a minimum rate requirement and a peak rate constraint, the classical max-min policy no longer suffices to determine rate allocation since it is not capable of supporting either the minimum rate or the peak rate constraint from a flow. We generalize the theory of the classical max-min rate allocation with the support of both the minimum rate and peak rate constraints for each flow. Additionally, to achieve generalized max-min rate allocation in a fully distributed packet network, we present a distributed algorithm that uses a feedback-based flow control mechanism. Our design not only offers a fresh perspective on flow marking technique, but also advances the state-of-the-art flow marking technique favored by other researchers. We provide proof that such a distributed algorithm, through asynchronous iterations, will always converge to the generalized max-min rate allocation under any network configuration and any set of link distances. We use simulation results to demonstrate the fast convergence property of the distributed algorithm.

A key functionality in today's widely used interior gateway routing protocols such as OSPF and IS-IS involves the computation of a shortest path tree (SPT). In many existing commercial routers, the computation of an SPT is done from scratch following changes in the link states of the network. As there may coexist multiple SPTs in a network with a set of given link states, such recomputation of an entire SPT not only is inefficient but also causes frequent unnecessary changes in the topology of an existing SPT and creates routing instability. This paper presents a new dynamic SPT algorithm that makes use of the structure of the previously computed SPT. Our algorithm is derived by recasting the SPT problem into an optimization problem in a dual linear programming framework, which can also be interpreted using a ball-and-string model. In this model, the increase (or decrease) of an edge weight in the tree corresponds to the lengthening (or shortening) of a string. By stretching the strings until each node is attached to a tight string, the resulting topology of the model defines an (or multiple) SPT(s). By emulating the dynamics of the ball-and-string model, we can derive an efficient algorithm that propagates changes in distances to all affected nodes in a natural order and in a most economical way. Compared with existing results, our algorithm has the best-known performance in terms of computational complexity as well as minimum changes made to the topology of an SPT. Rigorous proofs for correctness of our algorithm and simulation results illustrating its complexity are also presented.

The open shortest path first (OSPF) and IS-IS routing protocols widely used in today's Internet compute a shortest path tree (SPT) from each router to other routers in a routing area. Many existing commercial routers recompute an SPT from scratch following changes in the link states of the network. Such recomputation of an entire SPT is inefficient and may consume a considerable amount of CPU time. Moreover, as there may coexist multiple SPTs in a network with a set of given link states, recomputation from scratch causes frequent unnecessary changes in the topology of an existing SPT and may lead to routing instability. We present new dynamic SPT algorithms that make use of the structure of the previously computed SPT. Besides efficiency, our algorithm design objective is to achieve routing stability by making minimum changes to the topology of an existing SPT (while maintaining shortest path property) when some link states in the network have changed. We establish an algorithmic framework that allows us to characterize a variety of dynamic SPT algorithms including dynamic versions of the well-known Dijkstra, Bellman-Ford, D'Esopo-Pape algorithms, and to establish proofs of correctness for these algorithms in a unified way. The theoretical asymptotic complexity of our new dynamic algorithms matches the best known results in the literature.

Link-state protocols such as OSPF are the dominant routing technology in today's Internet. Despite their many advantages, these protocols require the flooding of new information across the entire routing area after changes in any link state (e.g., link failures). As the routing area grows or the frequency of link-state changes increases, the overhead (in terms of bandwidth and processing cost) of flooding becomes prohibitive. Furthermore, such flooding over a large area will cause temporary inconsistency of link states among many routers, potentially creating many transient routing loops that can last for a long time. This limits the scalability of the routing protocols to large routing areas. To overcome such problems, we present in this paper a novel algorithm that minimizes the amount of information distributed by link-state routing protocols. Upon a link failure, our algorithm will distribute the link-state changes to the minimum number of routers that are needed to ensure loop-free routing. Moreover, implementing our algorithm requires only a simple extension to any existing link-state protocol.

A key functionality in today's widely used interior gateway routing protocols such as OSPF and IS-IS involves the computation of a shortest path tree (SPT). In many existing commercial routers, the computation of an SPT is done from scratch following changes in the link states of the network. As there may coexist multiple SPTs in a network with a set of given link states, such recomputation of an entire SPT not only is inefficient but also causes frequent unnecessary changes in the topology of an existing SPT and creates routing instability. This paper presents a new dynamic SPT algorithm that makes use of the structure of the previously computed SPT. This algorithm is derived by recasting the SPT problem into an optimization problem in a dual linear programming framework, which can also be interpreted using a ball-and-string model. In this model, the increase (or decrease) of an edge weight in the tree corresponds to the lengthening (or shortening) of a string. By stretching the strings until each node is attached to a tight string, the resulting topology of the model defines an (or multiple) SPT(s). By emulating the dynamics of the ball-and-string model, we can derive an efficient algorithm that propagates changes in distances to all affected nodes in a natural order and in a most economical way. Compared with existing results, our algorithm has the best-known performance in terms of computational complexity as well as minimum changes made to the topology of an SPT. Rigorous proofs for correctness of our algorithm and simulation results illustrating its complexity are also presented.

The growth of the Internet and its acceptance has sparkled keen interest in the research community in respect to many apparent scaling problems for a large infrastructure based on IP technology. A self-contained problem of considerable practical and theoretical interest is the longest-prefix lookup operation, perceived as one of the decisive bottlenecks. Several novel approaches have been proposed to speed up this operation that promise to scale forwarding technology into gigabit speeds. This paper surveys these new lookup algorithms and classifies them based on applied techniques, accompanied by a set of practical requirements that are critical to the design of high-speed routing devices. We also propose several new algorithms to provide lookup capability at gigabit speeds. In particular, we show the theoretical limitations of routing table size and show that one of our new algorithms is almost optimal, while requiring only a small number of memory accesses to perform each address lookup.

This paper presents a novel generic weight-based network bandwidth sharing policy and an available bit rate (ABR) algorithm that achieves this policy. Our policy supports the minimum cell rate (MCR) requirement and peak cell rate (PCR) constraint of each connection and allocates network bandwidth among all connections based on a weight associated with each connection. To achieve this policy for ABR connections, we design an ABR algorithm which employs per virtual connection (VC) accounting to keep track of the state information of each VC. Our ABR algorithm is proven to provide guaranteed convergence to our generic weight-based rate allocation policy under any network configuration and any set of link distances. Simulation results show that our ABR algorithm has a fast convergence property.

We generalize the classical max-min rate allocation policy with the support of the minimum rate requirement and peak rate constraint for each connection. Since a centralized algorithm for the generalized max-min (GMM) rate allocation requires global information, which is difficult to maintain and manage in a large network, we develop a distributed protocol to achieve the GMM policy using the available bit rate (ABR) flow control mechanism. We give a proof that our distributed protocol converges to the GMM rate allocation through distributed and asynchronous iterations under any network configuration and any set of link distances.

A novel concept in available bit rate (ABR) service model as defined by the ATM Forum is the minimum cell rate (MCR) bandwidth guarantee for each connection. In this paper, we present a network bandwidth allocation policy to support each ABR connection's MCR requirement, as well as its peak cell rate (PCR) constraint. Furthermore, we develop two explicit-rate (ER) based ABR algorithms consistent with the ATM Forum ABR traffic management framework to achieve this rate allocation policy. The first ABR implementation is a simple heuristic algorithm which does not require per-VC accounting. It requires minimal implementation complexity and offers satisfactory performance in a LAN environment. The second ABR implementation employs per-VC accounting and is proven to converge to our rate allocation policy for any network topology and any set of link distances.

In the ATM Forum activities, considerable efforts have focused on the congestion control of point-to-point available bit rate (ABR) service. We present a novel approach that extends existing point-to-point (unicast) congestion control protocols to a point-to-multipoint (multicast) environment. In particular, we establish a unified framework to derive a multicast congestion control protocol for an ABR service from a given rate-based unicast protocol. We generalize a known necessary and sufficient condition on the max-min fairness of unicast rate allocation for a multicast service. Using this condition, we show that the resulting multicast protocol derived using our framework preserves the fairness characteristics of the underlying unicast protocol. The practical significance of our approach is illustrated by extending a standard congestion control mechanism for an ABR service to a multicast environment. The performance of the resulting multicast protocol is examined using benchmark network configurations suggested by the traffic management subworking group at the ATM Forum, and simulation results are presented to substantiate our claims.

We present a simulation study of the TCP performance in ATM networks with available bit rate (ABR) service and unspecified bit rate (UBR) service with early packet discard (EPD) schemes. We focus our study in a LAN environment using some benchmark network configurations proposed in the ATM Forum. Our simulation results show the following: (1) with UBR service and EPD schemes, TCP suffers significant performance degradation in terms of fairness and requires relatively large switch buffer even with a small number of active virtual connections over a LAN configuration, and (2) for the same set of network configurations and with ABR service using explicit rate feedback schemes, TCP achieves a good performance in terms of fairness and link utilization, and requires a relatively small switch buffer.

We formalize the notions of latency, effective throughput, fairness, and transient period in a complexity theoretic framework. This new framework allows us to prove the first known complexity results and tight bounds on the latency in a client/server distributed computing system. Using this formal complexity model, we study a general class of fair and maximally efficient control algorithms that maximizes the effective throughput and minimizes the transient period. We show that any fair and maximally efficient algorithm will result in at least cNlogN+O(N) latency, where N is the number of greedy clients in the network and the constant c is a parameter of the chosen algorithm. This lower bound is also shown to be tight.

This paper presents a fundamental study on the message and time complexity of reliable broadcast/multicast protocols in point-to-point networks subject to omission failures. We assume a weakly synchronous model in which there is a known upper bound on the delay in delivering a message from one process to another. A faulty process may omit sending or receiving messages; this characterizes a common faulty behavior in networking applications. We focus our study on the number of messages and the maximum amount of time required of any fault-tolerant protocol in failure-free executions. We present protocols that, in an n-process network subject to at most t faulty processes, guarantee the delivery of a message from any process to all other nonfaulty processes. In particular, when no failure occurs in the network, our protocols require (n+t-1) messages and at most (n-1+upper bound [log/sub 2/(t+1)])/spl middot//spl delta/ units of time, where /spl delta/ is the maximum time required to deliver a message from a process to another. Moreover, we show that our protocols are optimal with respect to message and time complexity. The new insights provided by the lower bound proofs yield a graph-theoretic characterization of all message and time optimal reliable broadcast/multicast protocols in failure-free executions. We further discuss the implications of our results on the support of multicast services in high-speed switching networks such as ATM.>

An essential feature in any fault tolerant design of distributed systems is a mechanism by which a process can reliably broadcast information to other processes in the presence of failures. The paper studies the message complexity of fault tolerant broadcast protocols in weakly synchronous and totally asynchronous distributed systems with point to point communication links, where the system failures are caused by the processes but the communication links are completely reliable. We focus on the number of messages required of any fault tolerant protocol in failure free executions. Our motivation is that one should incur the cost of handling failures only when they actually occur. We present protocols that, in an n-process system subject to at most t crash failures where 1/spl les/t>