Delay Constrained Least Cost Research Articles

Bootstrapped LARAC algorithm for fast delay‐sensitive QoS provisioning in SDN networks

SummaryIn today's networks, QoS provisioning becomes a major concern for service providers due to the massive increase in connected devices (e.g., mobile devices, servers, and Things), traffic in between, and the diverse service requirements (e.g., delay and bandwidth). Software‐Defined Networking (SDN) promises solution for such issues with its central network control flexibility compared to traditional networking; nonetheless, a design of a fast and QoS guaranteeing routing algorithm is still needed. Delay Constrained Least Cost (DCLC) is a well‐known NP‐hard problem. LAgrange Relaxation‐based Aggregated Cost (LARAC) algorithm is a Dijkstra‐based QoS‐aware algorithm and one of many heuristic algorithms proposed in the literature to solve the DCLC problem. Despite its outstanding performance over other algorithms in SDN, it still needs improvement. In this article, we present a modified version of LARAC, called MODLARAC, to improve the solution feasibility search state by exploiting LARAC's lower‐bound paths before the approximation process start. Also, we modify its stop condition to avoid extra non‐useful Dijkstra calls. We implement and evaluate MODLARAC using a realistic ISP network topology using Mininet and controlled by Floodlight SDN controller. We then compare MODLARAC against the original LARAC and BiLAD algorithms. The obtained results showed improvement up to 20% reduction in Dijkstra calls count compared to original LARAC and BiLAD algorithms without a significant increase in path's cost or delay metrics. It reached only 3% increase in path cost and 7% in path delay in its worst case with a safe distance of 11% lower than the delay demand.

Holu: Power-Aware and Delay-Constrained VNF Placement and Chaining

Service function chains (SFCs) are an ordered set of virtual network functions (VNFs) which can realize a specific network service. Enabled by virtualization technologies, these VNFs are hosted on physical machines (PMs), and interconnected by network switches. In today networks, these resources are usually under-utilized and/or over-provisioned, resulting in power-inefficient deployments. To improve power-efficiency, SFCs should be deployed utilizing the minimum number of PMs and network equipment, which are not concomitant. Considering the existing PM and switch power consumption models and their resource constraints, we formulate the power-aware and delay-constrained joint VNF placement and routing (PD-VPR) problem as an Integer Linear Program (ILP). Due to the NP-completeness of the problem, we propose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Holu</i> , a fast heuristic framework that efficiently solves the PD-VPR problem in an online manner. Specifically, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Holu</i> decomposes the PD-VPR into two sub-problems and solve them sequentially: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i)</i> a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">VNF placement</i> problem that consists of mapping the VNFs to PMs using a centrality-based ranking method, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii)</i> a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">routing</i> problem that efficiently splits the delay budget between consecutive VNFs of the SFC, and finds a Delay-Constrained Least-Cost (DCLC) shortest-path through the selected PMs (hosting VNFs) using the Lagrange Relaxation based Aggregated Cost (LARAC) algorithm. Our simulation results indicate that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Holu</i> outperforms the state-of-the-art algorithms in terms of total power consumption and acceptance rate by 24.7% and 31%, respectively.

Solving the Delay-Constrained Least-Cost routing problem using Tabu Search with Edge Betweenness

Multicast routing consists of concurrently sending the same information from a source to a subset of all possible destinations in a computer network thus becomes an important technology communication. To solve the problem, a current approach for efficiently supporting a multicast session in a network consists of establishing a multicast tree that covers the source and all terminal nodes. This problem can be reduced to a minimal Steiner tree problem (MST) which aims to look for a tree that covers a set of nodes with a minimum total cost, the problem is NP-hard. In this paper, we investigate metaheuristics approaches for the Delay-Constrained Least-Cost (DCLC) problem, we propose a novel algorithm based on Tabu Search procedure with the Edge Betweenness (EB). The EB heuristic used first to improve KMB heuristic, able to measure the edge value to being included in a given path. The obtained solution improved using the tabu search method. The performance of the proposed algorithm is evaluated by experiments on a number of benchmark instances from the Steiner library. Experimental results show that the proposed metaheuristic gives competitive results in terms of cost and delay compared to the optimal results in Steiner library and other existing algorithms in the literature.

Unicast QoS Routing Algorithms for SDN: A Comprehensive Survey and Performance Evaluation

A variety of communication networks, such as industrial communication systems, have to provide strict delay guarantees to the carried flows. Fast and close to optimal quality of service (QoS) routing algorithms, e.g., delay-constrained leastcost (DCLC) routing algorithms, are required for routing flows in such networks with strict delay requirements. The emerging software-defined networking (SDN) paradigm centralizes the network control in SDN controllers that can centrally execute QoS routing algorithms. A wide range of QoS routing algorithms have been proposed in the literature and examined in individual studies. However, a comprehensive evaluation framework and quantitative comparison of QoS routing algorithms that can serve as a basis for selecting and further advancing QoS routing in SDN networks is missing in the literature. This makes it difficult to select the most appropriate QoS routing algorithm for a particular use case, e.g., for SDN controlled industrial communications. We close this gap in the literature by conducting a comprehensive up-to-date survey of centralized QoS routing algorithms. We introduce a novel four-dimensional (4D) evaluation framework for QoS routing algorithms, whereby the 4D correspond to the type of topology, two forms of scalability of a topology, and the tightness of the delay constraint. We implemented 26 selected DCLC algorithms and compared their runtime and cost inefficiency within the 4D evaluation framework. While the main conclusion of this evaluation is that the best algorithm depends on the specific sub-space of the 4D space that is targeted, we identify two algorithms, namely Lagrange relaxation-based aggregated cost (LARAC) and search space reduction delay-cost-constrained routing (SSR+DCCR), that perform very well in most of the 4D evaluation space.

A New Hybrid GRASP with the Pilot Method Forthe Delay-Constrained Multicast Routing Problem

Multicast routing problem is a well know optimization problem for transmitting real-time multimedia applications in telecommunication networks. As the underpinning mathematical model, the constrained minimum Steiner tree problem in graphs is a well-known NP-complete problem. In this paper we investigate a new hybrid GRASP (Greedy Randomized Adaptive Search Procedure) approach where a pilot method is applied to further enhance the search for the Delay-Constrained Least-Cost (DCLC) multicast routing problem. Experimental results demonstrate the efficiency of the hybrid GRASP algorithm and the contributions of the post-processing pilot method to better solutions in most cases. The proposed GRASP approach is a competitive approach in solving the DCLC multicast routing problem.

A Fast Hybrid ε-Approximation Algorithm for Computing Constrained Shortest Paths

Considerable efforts have been dedicated to develop both heuristic and approximation algorithms for the NP-complete delay-constrained least-cost (DCLC) routing problem, but to the best of our knowledge, no prior work has been done to mingle the two tracks of research. In this letter we introduce a novel idea to show how a heuristic method can be used to boost the average performance of an approximation algorithm. Simulations on networks of up to 8192 nodes demonstrate that our new hybrid e-approximation algorithm is faster than the best known approximation algorithm by one or two orders of magnitude (depending on the network size and e).

A scalable method for DCLC problem using hierarchical MDP model

It is well known that the delay-constrained least-cost (DCLC) routing problem is NP-complete, hence various heuristic methods have been proposed for this problem. However, these heuristic methods have poor scalability as the network scale increases. In this paper we propose a new method based on the Markov Decision Process (MDP) theory and the hierarchical routing scheme to address the scalability issue of the DCLC routing problem. We construct a new two-level hierarchy MDP model and apply an infinite-horizon discounted cost model to the upper level for the end-to-end inter-domain link selection. Since the infinite-horizon discounted cost model is independent of network scale, the scalability problem is resolved. With the proposed model, we further give the algorithm of solving the optimal policy to obtain the DCLC routing. Simulation results show that the proposed method improves the scalability significantly.

A hybrid scatter search meta-heuristic for delay-constrained multicast routing problems

This paper investigates the first hybrid scatter search and path relinking meta-heuristic for the Delay-Constrained Least-Cost (DCLC) multicast routing problem. The underpinning mathematic model of the DCLC multicast routing problem is the constrained Steiner tree problem in graphs, a well known NP-complete problem. After combining a path relinking method as the solution combination method in scatter search, we further explore two improvement strategies: tabu search and variable neighborhood search, to intensify the search in the hybrid scatter search algorithm. A large number of simulations on some benchmark instances from the OR-library and a group of random graphs of different characteristics demonstrate that the improvement strategy greatly affects the performance of the proposed scatter search algorithm. The hybrid scatter search algorithm intensified by a variable neighborhood descent search is highly efficient in solving the DCLC multicast routing problem in comparison with other algorithms and heuristics in the literature.

Hybrid co-evolutionary particle swarm optimization and noising metaheuristics for the delay constrained least cost path problem

This paper presents a co-evolutionary particle swarm optimization (PSO) algorithm, hybridized with noising metaheuristics, for solving the delay constrained least cost (DCLC) path problem, i.e., shortest-path problem with a delay constraint on the total "cost" of the optimal path. The proposed algorithm uses the principle of Lagrange relaxation based aggregated cost. It essentially consists of two concurrent PSOs for solving the resulting minimization-maximization problem. The main PSO is designed as a hybrid PSO-noising metaheuristics algorithm for efficient global search to solve the minimization part of the DCLC-Lagrangian relaxation by finding multiple shortest paths between a source-destination pair. The auxiliary/second PSO is a co-evolutionary PSO to obtain the optimal Lagrangian multiplier for solving the maximization part of the Lagrangian relaxation problem. For the main PSO, a novel heuristics-based path encoding/decoding scheme has been devised for representation of network paths as particles. The simulation results on several networks with random topologies illustrate the efficiency of the proposed hybrid algorithm for the constrained shortest path computation problems.

Heuristic Methods for Delay Constrained Least Cost Routing Using&lt;tex&gt;$k$&lt;/tex&gt;-Shortest-Paths

The delay constrained least cost (DCLC) problem is to find the least cost path in a graph subject to a delay constraint. First formulated in the context of routing in computer networks, the DCLC model also applies to problems of path planning and other decision problems. DCLC is NP-complete. Many heuristic methods have been proposed for it. This note presents two new methods based on the /spl kappa/-shortest-path (/spl kappa/SP) approach. These heuristic methods-one centralized, the other distributed-are both polynomial. In numerical experiments the proposed algorithms almost always find the optimal paths.

Tightest constraint first: An efficient delay sensitive multicast routing algorithm

As a key issue in multicast routing with quality of service (QoS) support, constrained minimum Steiner tree (CMST) problem has been a research focus for more than a decade, and tens of heuristics have been developed to solve this NP-complete problem. Among all the previously proposed algorithms, the bounded shortest path algorithm (BSMA) (IEEE INFOCOM'95 1995; 1:377–385) have been proved to be capable of producing a multicast tree that has on average the lowest cost. However, such an excellent cost performance is accompanied with an extremely high time complexity. Recently, Feng et al. presented an alternative implementation of BSMA, which makes use of the latest research results on the delay-constrained least cost (DCLC) routing problem. Simulations indicate that, in comparison with the original implementation, the alternative implementation has a much lower time complexity with virtually identical cost performance, and it also runs much faster than many renowned heuristics such as KPP (IEEE/ACM Trans. Networking 1993; 1(3):286–292) and CAO (The design and evaluation of routing algorithms for real-time channels. Technical Report ICSI TR-94-024, International Computer Science Institute, University of California at Berkeley, June 1994). In this paper, we propose a brand new heuristic TCF, which is based on an idea called ‘tightest constraint first.’ TCF runs a DCLC heuristic only once for each destination and therefore has a provably low time complexity. We further propose an iterative heuristic ITCF, which uses TCF to obtain an initial tree and then gradually refines it. Extensive simulations demonstrate that, in the average sense, TCF can achieve a cost performance comparable to or better than that of BSMA, the cost performance of ITCF is even better than that of TCF, TCF runs approximately twice as fast as ITCF, and ITCF runs 2–4 times as fast as the best implementation of BSMA. Copyright © 2005 John Wiley & Sons, Ltd.

An efficient quality of service routing algorithm for delay-sensitive applications

It is well known that the Delay-Constrained Least-Cost (DCLC) unicast routing problem is NP-complete, hence various heuristic algorithms have been developed for this problem. In this paper, we propose a more efficient distributed algorithm, namely, Selection-Function-based DCLC (SF-DCLC), based on a novel selection function for the DCLC problem. The proposed SF-DCLC algorithm requires limited network state information at each node and is always able to find a loop-free path satisfying the delay bound if such paths exist. Simulation study shows that SF-DCLC is not as sensitive to the delay bound and the size of networks as some other DCLC routing algorithms, and has very low cost-inefficiency compared to the optimal one in various network scenarios we have studied. A noteworthy feature of SF-DCLC is that SF-DCLC has very high probability of finding the optimal solution in polynomial time with low computational complexity and message complexity.

A distributed algorithm for delay-constrained unicast routing

We study the NP-hard delay-constrained least cost (DCLC) path problem. A solution to this problem is needed to provide real-time communication service to connection-oriented applications, such as video and voice. We propose a simple, distributed heuristic solution, called the delay-constrained unicast routing (DCUR) algorithm, DCUR requires limited network state information to be kept at each node: a cost vector and a delay vector. We prove DCUR's correctness by showing that it is always capable of constructing a loop-free delay-constrained path within finite time, if such a path exists. The worst case message complexity of DCUR is O(|V|/sup 2/) messages, where |V| is the number of nodes. However, simulation results show that, on the average, DCUR requires much fewer messages. Therefore, DCUR scales well to large networks. We also use simulation to compare DCUR to the optimal algorithm, and to the least delay path algorithm. Our results show that DCUR's path costs are within 10% of those of the optimal solution.