Virtual Circuit Routing Research Articles

Hallucination Helps: Energy Efficient Virtual Circuit Routing

We consider virtual circuit routing protocols with an objective of minimizing energy in a network of components that are speed scalable, and that may be shut down when idle. We assume the standard model for component power: the power consumed by a component with load (speed) $s$ is $\sigma+ s^\alpha$, where $\sigma$ is the static power and the exponent $\alpha>1$. We obtain a very simple $O(\log^\alpha k)$-approximation algorithm for multicommodity routing, where $k$ is the number of demand pairs. This improves upon previous results by several logarithmic factors. The key step in our algorithm is a random sampling technique that we call hallucination, which is reminiscent of the sample-augment framework for buy-at-bulk problems, and sampling in cut-sparsification algorithms. We also consider the online setting of the problem, where demand pairs arrive over time. We show that our offline algorithm naturally extends to the online setting, and obtain a randomized competitive ratio of $\tilde{O}( \log^{3\alpha + 1} k)$, which is the first nontrivial bound. The analysis of this algorithm involves the study of priority multicommodity flows, where edges and demand-pairs have priorities and each demand-pair must route its flow only on edges of lower priority. We establish a polylogarithmic flow-cut gap for these priority flows, which we believe is of independent interest. Finally, we show how our technique can be used to achieve a randomized $( O(\log m), O(\log^2 m))$ bicriteria competitive algorithm for the uniform capacitated network design problem, where $m$ is the number of edges. Here, every edge has a cost $c_e$ and uniform capacity $q$, and the goal is to choose the minimum cost subgraph that can support the given multicommodity demand. This is the first online algorithm for this problem. In fact, our approach also improves prior results in the offline setting by several logarithmic factors.

Non-clairvoyant online scheduling of synchronized jobs on virtual clusters

Although virtualization technology is recently applied to next-generation distributed high-performance computing systems, theoretical aspects of scheduling jobs on these virtualized environments are not sufficiently studied, especially in online and non-clairvoyant cases. Virtualization of computing resources results in interference and virtualization overheads that negatively impact the load balancing objectives on commonly used cluster of multi-core physical machines. We present a technique for non-clairvoyant online scheduling of globally synchronized jobs, each of which spawns tasks to execute compute-intensive works. Our technique considers both load balancing of physical cores and per job synchronization cost minimization. We show that in the presence of arbitrary virtualization overheads, interference effects and synchronization cost, the problem can be reduced to an online unrelated parallel machine scheduling, which is solved using routing of virtual circuits. We present a new opportunity cost model to reduce the problem to the routing of virtual circuits and prove the effectiveness of our scheduling technique using mathematical analysis and simulative experiments.

A nonmonotone analysis with the primal–dual approach: Online routing of virtual circuits with unknown durations

We address the question of whether the primal–dual approach for the design and analysis of online algorithms can be applied to nonmonotone problems. We provide a positive answer by presenting a primal–dual analysis to the online algorithm of Awerbuch et al. [3] for routing virtual circuits with unknown durations.

Restart strategies for GRASP with path-relinking heuristics

GRASP with path-relinking is a hybrid metaheuristic, or stochastic local search (Monte Carlo) method, for combinatorial optimization. A restart strategy in GRASP with path-relinking heuristics is a set of iterations {i 1, i 2, …} on which the heuristic is restarted from scratch using a new seed for the random number generator. Restart strategies have been shown to speed up stochastic local search algorithms. In this paper, we propose a new restart strategy for GRASP with path-relinking heuristics. We illustrate the speedup obtained with our restart strategy on GRASP with path-relinking heuristics for the maximum cut problem, the maximum weighted satisfiability problem, and the private virtual circuit routing problem.

Integration of Explicit Effective-Bandwidth-Based QoS Routing With Best-Effort Routing

This paper presents a methodology for protecting low-priority best-effort (BE) traffic in a network domain that provides both virtual-circuit routing with bandwidth reservation for QoS traffic and datagram routing for BE traffic. When a QoS virtual circuit is established, bandwidths amounting to the traffic's effective bandwidths are reserved along the links. We formulate a new QoS-virtual-circuit admission control and routing policy that sustains a minimum level of BE performance. In response to a QoS connection request, the policy executes a two-stage optimization. The first stage seeks a minimum-net-effective-bandwidth reservation path that satisfies a BE protecting constraint; the second stage is a tie-breaking rule, selecting from tied paths one that least disturbs BE traffic. Our novel policy implementation efficiently executes both optimization stages simultaneously by a single run of Dijkstra's algorithm. According to simulation results, within a practical operating range, the consideration that our proposed policy gives to the BE service does not increase the blocking probability of a QoS connection request.

ATM network design for corporate networks

Asynchronous transfer mode (ATM) networks play an important role in support of distributed applications and modern corporate systems. The applications that use these architectures transfer high volumes of data in high-speed bursts and have stringent delay requirements. To address these needs, network managers seek cost efficient network solutions that provide network capacity sufficient to support high-speed applications. In this paper we present a new formulation and solution procedure for designing ATM networks to support corporate applications. Given the locations of the application servers and multiple clients we would like to design a minimum cost ATM network by which the clients can access the servers. Most of the previous work done in this area separates the problem into a routing problem (virtual circuit routing) and an assignment (virtual path assignment) problem. Thus, the solutions tend to be sub-optimal in the combined problem. This research optimizes virtual path (VP) assignment and virtual circuit (VC) routing simultaneously. We formulate the combined problem explicitly and develop an effective solution method. The solution method provides the designer with virtual paths and virtual circuits over which the actual communication takes place. Computational results are provided.

Lower Bounds for On-line Graph Problems with Application to On-line Circuit and Optical Routing

We present lower bounds on the competitive ratio of randomized algorithms for a wide class of on-line graph optimization problems, and we apply such results to on-line virtual circuit and optical routing problems. Lund and Yannakakis [The approximation of maximum subgraph problems, in Proceedings of the 20th International Colloquium on Automata, Languages and Programming, 1993, pp. 40-51] give inapproximability results for the problem of finding the largest vertex induced subgraph satisfying any nontrivial, hereditary property pi--e.g., independent set, planar, acyclic, bipartite. We consider the on-line version of this family of problems, where some graph G is fixed and some subgraph H of G is presented on-line, vertex by vertex. The on-line algorithm must choose a subset of the vertices of H, choosing or rejecting a vertex when it is presented, whose vertex induced subgraph satisfies property pi. Furthermore, we study the on-line version of graph coloring whose off-line version has also been shown to be inapproximable [C. Lund and M. Yannakakis, On the hardness of approximating minimization problems, in Proceedings of the 25th ACM Symposium on Theory of Computing, 1993], on-line max edge-disjoint paths, and on-line path coloring problems. Irrespective of the time complexity, we show an Omega(nepsilon) lower bound on the competitive ratio of randomized on-line algorithms for any of these problems. As a consequence, we obtain an Omega(nepsilon) lower bound on the competitive ratio of randomized on-line algorithms for virtual circuit routing on general networks, in contrast to the known results for some specific networks. Similar lower bounds are obtained for on-line optical routing as well.

Prioritized traffic restoration in connection oriented QoS based networks

Connection oriented quality-of-service (QoS) based networks offer several service classes each designed to handle connections supporting various types of applications. A network failure will typically result in a large number of disrupted connections in each service class, all of which need to be restored simultaneously. In this paper we propose a distributed fault recovery priority scheme for dynamic restoration of connections. The proposed scheme exploits available network resources immediately after a failure together with properties of typical applications carried by the connections in order to give the applications sufficient network performance. The scheme is formulated within the context of switched virtual circuit routing in ATM networks, but it is applicable to ATM virtual path restoration as well and to other class based QoS networks like DiffServ MPLS based networks. The priority based restoration scheme is formulated as a centralized path flow integer programming optimization problem serving as a comparison benchmark for suboptimal distributed schemes. We propose a distributed heuristic scheme and give numerical results illustrating the quality of the proposed distributed scheme in comparison to the centralized optimal approach. Our numerical results show that the proposed distributed scheme can significantly improve utilization of network resources and enhance network performance after a failure.

A GRASP with path‐relinking for private virtual circuit routing

AbstractA frame relay service offers virtual private networks to customers by provisioning a set of long‐term private virtual circuits (PVCs) between customer endpoints on a large backbone network. During the provisioning of a PVC, routing decisions are made without any knowledge of future requests. Over time, these decisions can cause inefficiencies in the network and occasional offline rerouting of the PVCs is needed. In this paper, the offline PVC routing problem is formulated as an integer multicommodity flow problem with additional constraints and with an objective function that minimizes propagation delays and/or network congestion. We propose variants of a GRASP with path‐relinking heuristic for this problem. Experimental results for realistic‐size problems are reported, showing that the proposed heuristics are able to improve the solutions found with standard routing techniques. Moreover, the structure of our objective function provides a useful strategy for setting the appropriate value of its weight parameter, to achieve some quality of service (QoS) level defined by a desired balance between propagation delay and delay due to network congestion. © 2003 Wiley Periodicals, Inc.

Approximating the single source unsplittable min-cost flow problem

In the single source unsplittable min-cost flow problem, commodities must be routed simultaneously from a common source vertex to certain destination vertices in a given graph with edge capacities and costs; the demand of each commodity must be routed along a single path so that the total flow through any edge is at most its capacity. Moreover, the total cost must not exceed a given budget. This problem has been introduced by Kleinberg [7] and generalizes several NP-complete problems from various areas in combinatorial optimization such as packing, partitioning, scheduling, load balancing, and virtual-circuit routing. Kolliopoulos and Stein [9] and Dinitz, Garg, and Goemans [4] developed algorithms improving the first approximation results of Kleinberg for the problem of minimizing the violation of edge capacities and for other variants. However, known techniques do not seem to be capable of providing solutions without also violating the cost constraint. We give the first approximation results with hard cost constraints. Moreover, all our results dominate the best known bicriteria approximations. Finally, we provide results on the hardness of approximation for several variants of the problem.

On-line load balancing of temporary tasks revisited

We study load balancing problems of temporary jobs (i.e., jobs that arrive and depart at unpredictable time) in two different contexts, namely, machines and network paths. Such problems are known as machine load balancing and virtual circuit routing in the literature. We present new on-line algorithms and improved lower bounds.

Competitive Routing of Virtual Circuits with Unknown Duration

In this paper we present a strategy to route unknown duration virtual circuits in a high-speed communication network. Previous work on virtual circuit routing concentrated on the case where the call duration is known in advance. We show that by allowing O(logn) reroutes per call, we can achieve O(logn) competitive ratio with respect to the maximum load (congestion) for the unknown duration case, where n is the number of nodes in the network. This is in contrast to the Ω(n) lower bound on the competitive ratio for this case if no rerouting is allowed (Azar et al., 1992, Proc. 33rd IEEE Annual Symposium of Foundations of Computer Science, pp. 218–225). Our routing algorithm can be also applied in the context of machine load balancing of tasks with unknown duration. We present an algorithm that makes O(logn) reassignments per task and achieves O(logn) competitive ratio with respect to the load, where n is the number of parallel machines. For a special case of unit load tasks we design a constant competitive algorithm. The previously known algorithms that achieve up to polylogarithmic competitive ratio for load balancing of tasks with unknown duration dealt only with special cases of related machines case and unit-load tasks with restricted assignment (Azar et al., 1993, Proc. Workshop on Algorithms and Data Structures, pp. 119–130; Azar et al., 1992, Proc. 3rd ACM-SIAM Symposium on Discrete Algorithms, pp. 203–210).

Load Balancing for Response Time

A centralized scheduler must assign tasks to servers, processing on-line a sequence of task arrivals and departures. Each task runs for an unknown length of time, but comes with a weight that measures resource utilization per unit time. The response time of a server is the sum of the weights of the tasks assigned to it. The goal is to minimize the maximum response time of any server. Previous papers on on-line load balancing have generally concentrated only on keeping the current maximum load bounded by some function of the maximum off-line load ever seen. Our goal is to keep the current maximum load on an on-line server bounded by a function of the current off-line load. Thus the loads are not permanently skewed by transient peaks, and the algorithm takes advantage of reductions in total weight. To achieve this, the scheduler must occasionally reassign tasks, in an attempt to decrease the maximum load. We study several variants of load balancing, including identical machines, related machines, and virtual circuit routing. In each case, only a limited amount of reassignment is used but the load is kept substantially lower than possible without reassignment.

On-Line Resource Management with Application to Routing and Scheduling

We propose a framework to model on-line resource management problems based on an on-line version of positive linear programming. We consider both min cost problems and max benefit problems and propose logarithmic competitive algorithms that are optimal up to a constant factor. The proposed framework provides a general methodology that applies to a wide class of on-line problems: shop scheduling, packet routing, and in general a class of packing and assignment problems. Previously studied problems as on-line multiprocessor scheduling and on-line virtual circuit routing can also be modeled within this framework.

Load Profiling Based Routing for Guaranteed Bandwidth Flows

AbstractTo support the stringent Quality of Service (QoS) requirements of real‐time (e.g. audio/video) applications in integrated services networks, several routing algorithms that allow for the reservation of the needed bandwidth over a Virtual Circuit (VC), established on one of several candidate routes, have been proposed. Traditionally, such routing is done using the least‐loaded concept, and thus results in balancing the load across the set of candidate routes. In this paper, we propose the use of load profiling as an attractive alternative to load balancing for routing guaranteed bandwidth VCs (flows). Load profiling techniques allow the distribution of “available” bandwidth across a set of candidate routes to match the characteristics of incoming VC QoS requests. We thoroughly characterize the performance of VC routing using load profiling and contrast it to routing using load balancing and load packing. We do so both analytically and via extensive simulations of multi‐class traffic routing in Virtual Path (VP) based networks. Our findings show that for routing guaranteed bandwidth flows in VP networks, load profiling is desirable as it reduces VP bandwidth fragmentation, which increases the likelihood of accepting new VC requests. This fragmentation could be particularly harmful when the granularity of VC requests is large. Typically, this occurs when a common VC is established to carry the aggregate traffic flow of many high‐bandwidth real‐time sources. For VP‐based networks, our simulation results show that our load‐profiling VC routing scheme performs better or as well as the traditional load‐balancing VC routing in terms of revenue under both skewed and uniform workloads. Furthermore, load‐profiling routing improves routing fairness by proactively increasing the chances of admitting high‐bandwidth Hows.

Routing virtual circuits with temporal QoS requirements in virtual path-based ATM networks

Real-time communication with performance guarantees is expected to become an important feature of future computer networks used for embedded real-time systems and/or for interactive multimedia services. Given an ATM network topology, its virtual path (VP) layout, and its traffic demands, we consider in this paper the problem of selecting for each virtual circuit (VC) with user-specified end-to-end temporal QoS requirements a route (i.e., a sequence of VPs) along which sufficient resources are available to meet the delay requirements. Our objective is 1) to provide the temporal QoS guarantee for each VC to be established while not jeopardizing the QoS guarantees to other existing VCs and 2) to reduce the call blocking probability for future VCs by using the minimum possible resources. We adopt the real-time channel model to characterize the traffic characteristics and the temporal QoS requirement of a VC. We impose a deterministic guarantee that every message generated at the source node be delivered to the destination node in a time period no longer than the relative deadline. We then propose a VC routing scheme based on the distributed Bellman-Ford algorithm to identify an appropriate route through the network. By appropriate, we mean that the route traverses a minimum number of VPs among all possible routes that have sufficient resources to fulfill the end-to-end temporal QoS requirement of the VG to be established. To ensure that sufficient bandwidth is available over all the VPs along the selected route, we incorporate in our proposed scheme a priority assignment method to calculate the worst-case delay which messages of a VC will experience on a VP along which the VC is routed. We study the performance of, and the message overhead incurred in, the proposed scheme. We also discuss how to extend the proposed routing scheme to accommodate multicast routing.

On-line routing of virtual circuits with applications to load balancing and machine scheduling

In this paper we study the problem of on-line allocation of routes to virtual circuits (both point-to-point and multicast ) where the goal is to route all requests while minimizing the required bandwidth. We concentrate on the case of Permanent virtual circuits (i.e., once a circuit is established it exists forever), and describe an algorithm that achieves on O (log n ) competitive ratio with respect to maximum congestin, where n is the number of nodes in the network. Informally, our results show that instead of knowing all of the future requests, it is sufficient to increase the bandwidth of the communication links by an O (log n ) factor. We also show that this result is tight, that is, for any on-line algorithm there exists a scenario in which Ω(log n ) increase in bandwidth is necessary in directed networks. We view virtual circuit routing as a generalization of an on-line load balancing problem, defined as follows: jobs arrive on line and each job must be assigned to one of the machines immediately upon arrival. Assigning a job to a machine increases the machine's load by an amount that depends both on the job and on the machine. The goal is to minimize the maximum load. For the related machines case, we describe the first algorithm that achieves constant competitive ratio. for the unrelated case (with n machines), we describe a new method that yields O (log n )-competitive algorithm. This stands in contrast to the natural greed approach, whose competitive ratio is exactly n .

On the Value of Coordination in Distributed Decision Making

We discuss settings where several agents combine efforts to solve problems. This is a well-known setting in distributed artificial intelligence. Our work addresses theoretical questions in this model which are motivated by the work of Deng and Papadimitriou [ Proc. 12th IFIPS Congress, Madrid, 1992; Proc. World Economic Congress, Moscow, 1992]. We consider optimization problems, in particular load balancing and virtual circuit routing, in which the input is divided among the agents. An underlying directed graph, whose nodes are the agents, defines the constraints on the information each agent may have about the portion of the input held by other agents. The questions we discuss are as follows: Given a bound on the maximum out-degree in this graph, which is the best graph? What is the quality of the solution obtained as a function of the maximum out-degree?

On-line routing for permanent virtual circuits

This paper considers the problem of routing a set of permanent virtual circuit requests over a backbone network. Several factors make this routing problem complicated. Routing decisions must be made on-line without any knowledge of future request sets. Furthermore, frequent rerouting to correct inefficiencies that can result from the on-line routing decisions is not possible since rerouting creates a service disruption for the customer. Finally, the forward and reverse bandwidth of a virtual circuit must be routed over the same single path. Using an extensive set of simulations, this paper evaluates several different strategies for on-line permanent virtual circuit routing. We find that a strategy based on recent results in competitive analysis and ideas from combinatorial optimization consistently provides the best performance.

Adaptive virtual circuit routing

The paper deals with the adaptive routing problem in virtual circuit communication networks. A newly arriving call at a source node is routed along the minimum length path to its destination node. All packets belonging to this call follow the same path through the network. The superiority of a quadratic state-dependent routing algorithm to the shortest-queue routing algorithm is shown via simulation. The sooner the network state information becomes available to the router and the more often that this information is updated, the smaller the achieved average packet delay. Also, the age of this information at the router should be less or at least comparable to (but not extremely larger than) the mean interarrival time of virtual circuits.