An exact end-to-end blocking probability algorithm for multicast networks

Rapid development of optical communication techniques has made possible large scale wavelength routing optical networks. Nowadays, these networks are deployed worldwide. Large scale networks have natural hierarchies due to either geographical reasons or administrative consideration and are therefore managed in a hierarchical way correspondingly. That is, networks are composed of several subnetworks, which are themselves composed of other even smaller subnetworks. Erlang fixed point approximation (reduced load approximation) has been extensively used in performance evaluation of end to end call blocking probability in traditional circuit switching networks, which are also called loss networks. This method has also been extended for hierarchical loss networks. However, performance evaluation of call blocking probability in hierarchical wavelength routing optical networks has not yet been presented. In this paper, a kind of approximation method is developed for analyzing end to end call blocking probability in hierarchical wavelength routing optical networks. By iteratively running processes combining a top-down load distribution and a bottom-up calculation of node-pair blocking in the network hierarchy, a steady state will be reached and approximate end to end call blocking probability in hierarchical wavelength routing optical network is obtained. Both the link independent model and the link correlation model are used in our analysis. By comparing theoretical results derived from our approximation method and results obtained from discrete event simulation, we illustrate that our method gives reasonable estimate of end to end call blocking probability in hierarchical wavelength routing optical networks, with the correlation model giving much more accurate estimate than the independent model.

Modeling and analyzing the performance of adaptive hierarchical networks

Multicast connections have a bandwidth saving nature. This means that a multicast connection --- in taking the form of a tree with streams merging at the nodes --- requires much less capacity from the network links than a bunch of separate point-to-point connections providing the same connectivity. In this paper, we consider dynamic multicast connections that can be used to model, for example, TV or radio delivery on a telecommunications network, such as an ATM network with virtual circuits. We show how to calculate the blocking probabilities of requests to join such a tree. First, we consider the blocking probabilities occurring in a single link. The resulting model is able to capture heterogeneous capacity requirements for different multicast channels. Then we extend the results to a whole network using the reduced load approximation. The accuracy of the approximation method is studied by simulations.

To reduce the transmission cost in 5G multicast networks that have separate control and data planes, we focus on the minimum-power-cost network-coding subgraph problem for the coexistence of two multicasts in wireless networks. We propose two suboptimal algorithms as extensions of the Steiner tree multicast. The critical 1-cut path eliminating (C1CPE) algorithm attempts to find the minimum-cost solution for the coexistence of two multicast trees with the same throughput by reusing the links in the topology, and keeps the solution decodable by a coloring process. For the special case in which the two multicast trees share the same source and destinations, we propose the extended selective closest terminal first (E-SCTF) algorithm out of the C1CPE algorithm. Theoretically the complexity of the E-SCTF algorithm is lower than that of the C1CPE algorithm. Simulation results show that both algorithms have superior performance in terms of power cost and that the advantage is more evident in networks with ultra-densification.

This paper studies the blocking performance of optical burst switching (OBS) networks using a sequential office control (SOC) state-independent deflection routing policy. We show that unprotected deflection routing may destabilize OBS resulting in higher blocking probabilities than if bursts were not deflected but simply blocked. This study was motivated by the well-known destabilizing effect that alternative routing has on circuit switching in classical telephony networks. We propose two forms of protection to guard against destabilization: 1) wavelength reservation, which is analogous to trunk reservation in circuit switching; and, 2) preemptive priority, which is a new form of protection where bursts that have not been deflected are given preemptive priority over bursts that have been deflected. Our main contribution is a one-moment reduced-load approximation to evaluate the blocking performance of OBS networks using deflection routing protected by either wavelength reservation or preemptive priority. Our reduced-load approximation relies on the usual assumptions of link independence and Poisson distributed link arrivals. We quantify the error admitted in making these two assumptions via simulation. Using our reduced-load approximation, we evaluate the blocking performance of protected and unprotected deflection routing in several randomly generated networks. The chief conclusion of our study is that deflection routing in OBS should be given some form of protection to avoid destabilization resulting from upward load variations, and in terms of blocking performance, preemptive priority is the best form of protection for OBS. We use simulation to verify that our conclusions remain valid for a realistic traffic scenario.

The next generation multimedia applications such as video conferencing and HDTV have raised tremendous challenges on the network design, both in bandwidth and service. As wavelength-division-multiplexing (WDM) networks have emerged as a promising candidate for future networks with large bandwidth, supporting efficient multicast in WDM networks becomes eminent. Different from the IP layer, the cost of multicast at the WDM layer involves not only bandwidth (wavelength) cost, but also wavelength conversion cost and light splitting cost. It is well known that the optimal multicast problem in WDM networks is NP-hard. In this paper, we develop an efficient approximation algorithm consisting of two separate but integrated steps: multicast routing and wavelength assignment. We prove that the problem of optimal wavelength assignment on a multicast tree is not NP-hard; in fact, an optimal wavelength assignment algorithm with complexity of O(NW) is presented. Simulation results have revealed that the optimal wavelength assignment beats greedy algorithms by a large margin in networks using many wavelengths on each link such as dense wavelength-division-multiplexing (DWDM) networks. Our proposed heuristic multicast routing algorithm takes into account both the cost of using wavelength on links and the cost of wavelength conversion. The resulting multicast tree is derived from the optimal lightpaths used for unicast.

This paper presents a new heuristic algorithm called DDBMB (dynamic delay bounded multicast algorithm) to construct a minimum cost multicast tree. The heuristic depends on: (A) bounded delay along paths from source node to each destination node; (B) minimum cost of the multicast tree where the algorithm starts with the minimum delay tree and monotonically decreases the cost iteratively to construct a delay bounded minimum cost tree; and (C) dynamic multicast tree status which is maintained by updating the existing multicast tree when nodes in the network request join or leave. The construction of such constrained multicast tree is known as an NP-complete problem. Compared with other existing relative algorithms, the heuristic demonstrates a better average case behavior and can be very close to having a minimum cost depending on the delay bounds imposed.

A delay-constrained and priority-aware channel assignment algorithm for efficient multicast in wireless mesh networks

Wireless mesh networks (WMN) are believed to be a highly promising technology and will play an increasingly important role in future generation wireless mobile networks. Routing in WMN is a challenging problem as a result of highly dynamic topology as well as bandwidth and energy constraints. The swarm intelligence paradigm, such as ant colony optimization (ACO), has recently been demonstrated as an active approach for routing in both wired and wireless networks. We designed a novel ACO-based multicasting routing algorithm. In the proposed algorithm, a source-based approach is adapted to build a multicast tree among all the multicast members, and an evolutional scheme for the original multicast tree is designed to find a more optimal multicast tree. In addition the evolutional scheme also acts as a local recovery technique when some intermediate nodes move away. Compared with ODMRP and MAODV, the proposed algorithm performs better in terms of average delay, success ratio and efficiency.

This paper is concerned with a restricted version of minimum cost delay-constrained multicast in a network where each link has a delay and a cost. Given a source vertex $s$ and $p$ destination vertices $t_1, t_2, \ldots, t_p$ together with $p$ corresponding nonnegative delay constraints $d_1, d_2, \ldots, d_p$, many QoS multicast problems seek a minimum cost multicast tree in which the delay along the unique $s$--$t_i$ path is no more than $d_i$ for $1 \le i \le p$. This problem is NP-hard even when the topology of the multicast tree is fixed. In this paper we show that every multicast tree has an underlying Steiner topology and that every minimum cost delay-constrained multicast tree corresponds to a minimum cost delay-constrained realization of a corresponding Steiner topology. We present a fully polynomial time approximation scheme for computing a minimum cost delay-constrained multicast tree under a Steiner topology. We also present computational results of a preliminary implementation to illustrate the effectiveness of our algorithm and discuss its applications.

Minimum-energy broadcast and multicast in wireless networks: An integer programming approach and improved heuristic algorithms

We address the multicast issue in a wide area WDM network in which a source broadcasts its message to some sites in the network. This problem can be formalized as the following optimal multicast tree problem. Given a directed graph G = (V, E) with a source s and a set S of nodes, assume that every node in S (⊂ V) is reachable from s. Associated with every link e ∈ E, there is a set Λ(e) of available wavelengths on it, |V| = n and |E| = m, find a multicast tree rooted at s including all the nodes in S with minimizing the cost of the tree, in terms of the sum of the cost of wavelength conversion at nodes and the cost of using wavelengths on links in the tree. That is, not only do we need to find a directed tree rooted at s, but also do we need to assign a specific wavelength Λ ∈ Λ(e) to every tree edge e and to set the switches at every node in the tree. Since this problem is NP-complete, it is unlikely that there is a polynomial algorithm to find an exact solution for it. Instead, we first present an approximation algorithm for the problem which runs in time O(k2n + km +kn log(kn) + (kn)1/e|S|), and delivers a solution within O(|S|e) of the optimal, for any fixed 0 > e ≤ 1. We then present a distributed version of the proposed algorithm. The communication and time complexities of the distributed algorithm are O(km) and O(kn) respectively, and the solution delivered is |S| times of the optimal, where k is the number of wavelengths in the network. Finally, we conduct some experiments to verify the applicability of the proposed algorithms. The experimental results matches our algorithmic claims.

Cored-Based Tree with Forwarding Regions (CBT-FR); A Protocol for Reliable Multicasting in Mobile Ad Hoc Networks

This paper proposes a tabu search (TS) based optimization approach to search a minimum-interference multicast tree which satisfies the end-to-end delay constraint and optimizes the usage of the scarce radio network resource in wireless mesh networks. The path-oriented encoding method is adopted and each candidate solution is represented by a tree data structure (i.e., a set of paths). Since we expect the multicast trees on which the minimum-interference channel assignment can be produced, a fitness function that returns the total channel conflict is devised. The techniques for controlling the tabu search procedure are well developed. A simple yet effective channel assignment algorithm is proposed to reduce the channel conflict. Simulation results show that the proposed TS multicast algorithm can produce the multicast trees which have better performance in terms of both the total channel conflict and the tree cost than that of a well known multicast algorithm in wireless mesh networks.

It is anticipated that a large amount of multicast traffic needs to be supported in future communication networks. The network coding technique proposed recently is promising for establishing multicast connections with a significantly lower bandwidth requirement than that of traditional Steiner-tree-based multicast connections. How to design multicast network topologies with the consideration of efficiently supporting multicast by the network coding technique becomes an important issue now. It is notable, however, that the conventional algorithms for network topology design are mainly unicast-oriented, and they cannot be adopted directly for the efficient topology design of network-coding-based multicast networks by simply treating each multicast as multiple unicasts. In this paper, we consider for the first time the novel topology design problem of network-coding-based multicast networks. Based on the characteristics of multicast and network coding, we first formulate this problem as a mixed-integer nonlinear programming problem, which is NP-hard, and then propose two heuristic algorithms for it. The effectiveness of our heuristics is verified through simulation and comparison with the exhaustive search method. We demonstrate in this paper that, in the topology design of multicast networks, adopting the network coding technique to support multicast transmissions can significantly reduce the overall topology cost as compared to conventional unicast-oriented design and the Steiner-tree-based design.