Routing and wavelength assignment for hypercube in array-based WDM optical networks

Hypercube is one of the most versatile and efficient communication patterns shared by a large number of computational problems. As the number of edges in hypercube grows logarithmically with the size of networks, the complexity of network topologies can be significantly reduced to realize hypercube in optical networks by taking advantage of the parallel transmission characteristic of optical fibers. In this paper, we study the routing and wavelength assignment for realizing hypercube on WDM optical networks including linear arrays and rings with the consideration of communication directions. Specifically, we analyze this problem for both bidirectional and unidirectional hypercubes. For each case, we identify a lower bound on the number of wavelengths required, and design the embedding scheme and wavelength assignment algorithm that uses a provably near-optimal number of wavelengths. In addition, we extend the results to meshes and tori. By our embedding schemes, many algorithms, originally designed based on hypercubes, can be applied to optical networks, and the wavelength requirements can be easily derived using our obtained results.     

Efficient elections in chordal ring networks

We study the message complexity of the problem of distributively electing a leader in chordal rings. Such networks consist of a basic ring with additional links, the extreme cases being the oriented ring and the complete graph with a full sense of direction. We present a general election algorithm for these networks, and prove its optimality. As a corollary, we show thatO(logn) chords at each processor suffice to obtain an algorithm that uses at mostO(n) messages; this improves and extends a previous work, where an algorithm, also usingO(n) messages, was suggested for the case where alln-1 chords exist (the oriented complete network).The work of this author was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant No. A2415.The work of this author was supported in part by Technion Research Grant No. 120-0641.     

A channel assignment problem for optical networks modelled by Cayley graphs

A problem arising from a recent study of scalability of optical networks seeks to assign channels to the vertices of a network so that vertices distance 2 apart receive distinct channels. In this paper we introduce a general channel assignment scheme for Cayley graphs on abelian groups, and derive upper bounds for the minimum number of channels needed for such graphs. As application we give a systematic way of producing near-optimal channel assignments for connected graphs admitting a vertex-transitive abelian group of automorphisms. Hypercubes are examples of such graphs, and for them our near-optimal upper bound gives rise to the one obtained recently by Wan.     

Routing and wavelength assignment for 3-ary n-cube communication patterns in linear array optical networks for n communication rounds

k-ary n-cubes are a class of communication patterns that are employed by a number of typical parallel algorithms. This paper addresses the implementation of parallel algorithms with bidirectional 3-ary n-cube communication patterns on a bidirectional linear array WDM optical networks when the information is transmitted one dimension after another. By giving an embedding scheme ?, we prove the optimal number of wavelengths under ? and design a routing and wavelength assignment strategy of it.     

Routing and wavelength assignment with power considerations in optical networks

Previous studies have solved many variations of the routing and wavelength assignment (RWA) problem in optical networks under the assumption of perfect conditions regarding the power of a signal. In this paper, we investigate the RWA problem while allowing for degradation of routed signals by optical components. The problem is formulated as a mixed-integer non-linear program. We propose a two-phase approach. In the first phase, we solve the pure RWA problem using fixed routes for every connection. In the second phase, power assignment is accomplished by either using a heuristic or using a genetic algorithm. This paper demonstrates that: (i) connections do interact affecting the power of each other, and (ii) global search meta-heuristics provide better solutions.     

DWDM光网络中RWA问题的遗传求解方法

针对密集波分复用(dense wavelength-division multiplexing,DWDM)光网络通信中的动态路由与波长分配(routing and wavelength assignment,RWA)问题,提出了一种基于遗传算法的动态RWA方法.将遗传算法与分层图模型相结合,实现了RWA的方便计算.通过扩展适应值函数,能够有效地处理带时延约束的通信量请求.实验结果表明,与已有最短路径算法(Dijks-tra)相比,该算法能够提供多条候选路由方案,更适应较差环境下的网络通信.     

Traffic grooming, routing, and wavelength assignment in WDM transport networks with sparse grooming resources

While a single fiber strand in wavelength division multiplexing (WDM) has over a terabit-per-second bandwidth and a wavelength channel has over a gigabit-per-second transmission speed, the network may still be required to support traffic requests at rates that are lower than the full wavelength capacity. To avoid assigning an entire lightpath to a small request, many researchers have looked at adding traffic grooming to the routing and wavelength assignment (RWA) problem. In this work, we consider the RWA problem with traffic grooming (GRWA) for mesh networks under static and dynamic lightpath connection requests. The GRWA problem is NP-Complete since it is a generalization of the RWA problem which is known to be NP-Complete. We propose an integer linear programming (ILP) model that accurately depicts the GRWA problem. Because it is very hard to find a solution for large networks using ILP, we solve the GRWA problem by proposing two novel heuristics. The strength of the proposed heuristics stems from their simplicity, efficiency, and applicability to large-scale networks. Our simulation results demonstrate that deploying traffic grooming resources on the edge of optical networks is more cost effective and results in a similar blocking performance to that obtained when distributing the grooming resources throughout the optical network domain.     

Design,performance and wavelength assignment of a wavelength division multiaccess protocol for optical fibre ring networks

This paper presents a multiaccess strategy for use over optical fibre ring networks employing two counter rotating rings, and using wavelength division multiplexing. Transmitters employ tunable lasers, while receivers employ one or more fixed wavelength filters. The paper introduces an algorithm for the optimal assignment of the receivers to the channels, such that the possibility of finding an unused channel leading to a certain receiver is maximized. The paper contains a performance study of the network protocol.     

HARD: A hypercube embedding algorithm for state assignment of finite state machines

To minimize the area of the combinational circuit, required to realize a finite state machine (FSM), an efficient assignment of states of the FSM to a set of binary codes is required. As to find an optimal state assignment is NP-hard, therefore heuristic approaches have been taken. One approach generates an adjacency graph from the FSM model and then tries to embed the adjacency graph onto a hypercube with an objective to minimize the cost of mapping. However, hypercube embedding itself is an NP-complete problem. In this paper we present a solution to the hypercube embedding problem by designing a new technique, designated as HARD, that is a hybrid combination of non-linear programming method and a local search. We have transformed our problem from discrete space to continuous space and have applied logarithmic barrier function method, that in turn uses gradient projection approach to minimize the objective function. Each iteration of the gradient projection method produces a valid solution. Local search is performed around solution to improve its quality by using a Kernighan-Lin style algorithm. Two distributed algorithms for the HARD, have also been designed and implemented on network of workstations under message passing interface, to speed up the search. We have carried out a large number of experiments to determine the efficiency of the HARD in terms of solution quality over many other techniques, and have obtained very promising results.     

Ant colony optimization for dynamic routing and wavelength assignment in WDM networks with sparse wavelength conversion

Since optical WDM networks are becoming one of the alternatives for building up backbones, dynamic routing, and wavelength assignment with delay constraints (DRWA-DC) in WDM networks with sparse wavelength conversions is important for a communication model to route requests subject to delay bounds. Since the NP-hard minimum Steiner tree problem can be reduced to the DRWA-DC problem, it is very unlikely to derive optimal solutions in a reasonable time for the DRWA-DC problem. In this paper, we circumvent to apply a meta-heuristic based upon the ant colony optimization (ACO) approach to produce approximate solutions in a timely manner. In the literature, the ACO approach has been successfully applied to several well-known combinatorial optimization problems whose solutions might be in the form of paths on the associated graphs. The ACO algorithm proposed in this paper incorporates several new features so as to select wavelength links for which the communication cost and the transmission delay of routing the request can be minimized as much as possible subject to the specified delay bound. Computational experiments are designed and conducted to study the performance of the proposed algorithm. Comparing with the optimal solutions found by an ILP formulation, numerical results evince that the ACO algorithm is effective and robust in providing quality approximate solutions to the DRWA-DC problem.     

On isomorphisms and similarities between generalized Petersen networks and periodically regular chordal rings

Generalized Petersen (GP) networks and periodically regular chordal (PRC) rings have been proposed independently to ameliorate the high latency and extreme fragility of simple ring networks. In this paper, we note that certain GP networks are isomorphic to suitably constructed PRC rings, while other varieties correspond to PRC rings that closely approximate their topological and performance attributes. In the absence of equivalence and similarity proofs in the opposite direction, our results indicate that PRC rings may be preferable to GP networks in the sense of covering a broader family of networks and offering greater flexibility in cost-performance tradeoffs.     

Improved upper and lower bounds on the optimization of mixed chordal ring networks

Recently, Chen, Hwang and Liu [S.K. Chen, F.K. Hwang, Y.C. Liu, Some combinatorial properties of mixed chordal rings, J. Interconnection Networks 1 (2003) 3-16] introduced the mixed chordal ring network as a topology for interconnection networks. In particular, they showed that the amount of hardware and the network structure of the mixed chordal ring network are very comparable to the (directed) double-loop network, yet the mixed chordal ring network can achieve a better diameter than the double-loop network. More precisely, the mixed chordal ring network can achieve diameter about as compared to for the (directed) double-loop network, where N is the number of nodes in the network. One of the most important questions in interconnection networks is, for a given number of nodes, how to find an optimal network (a network with the smallest diameter) and give the construction of such a network. Chen et al. [S.K. Chen, F.K. Hwang, Y.C. Liu, Some combinatorial properties of mixed chordal rings, J. Interconnection Networks 1 (2003) 3-16] gave upper and lower bounds for such an optimization problem on the mixed chordal ring network. In this paper, we improve the upper and lower bounds as and , respectively. In addition, we correct some deficient contexts in [S.K. Chen, F.K. Hwang, Y.C. Liu, Some combinatorial properties of mixed chordal rings, J. Interconnection Networks 1 (2003) 3-16].     

Routing wavelength and time-slot reassignment algorithms for TDM based optical WDM networks

In this paper, we consider the problem of maximizing the time of first lightpath request rejection, T in the circuit-switched time division multiplexed (TDM) wavelength-routed (WR) optical WDM networks. TDM is incorporated into WDM, to increase the channel utilization when the carried traffic does not require the entire channel bandwidth. In TDM–WDM network, multiple sessions are multiplexed on each wavelength by assigning a sub-set of the TDM slots to each session. Thus, given a session request with a specified bandwidth, a lightpath has to be established by using the routing, wavelength and time-slot assignment (RWTA) algorithms. If the lightpath cannot be established, lightpath request rejection or call blocking occurs. As each lightpath is substantial revenue and long-lived, lightpath request rejection is highly unfavourable in the optical backbone networks. In this paper, we are proposing an intelligent routing, wavelength and time-slot reassignment algorithm for multi-rate traffic demands, where, when a call gets blocked, the already established calls in the network are rerouted, wavelength and time-slot reassigned so as to accommodate the blocked call. Since we are talking of slow arrivals and long holding times for the lightpaths, it is possible to do this reassignment while provisioning a new call. Simulation based analyses are used to study the performance of the proposed reassignment algorithm. The results show that the proposed reassignment algorithm can be used to maximize the time of first call blocking, thereby accommodating more calls in the network before upgrading the network capacity.     

On the joint link dimensioning and routing metric assignment problem for reliable WDM networks

In this paper, we tackle the joint link dimensioning and routing metric assignment problem for reliable wavelength division multiplexing (WDM) networks. This design problem consists to find the number of wavelength channels on each link and the routing metrics (considering shortest-path routing) that ensure the routing of all virtual wavelength paths (VWPs) and the successful rerouting of the reliable VWPs for all failure scenarios of interest to the network planner. A mixed integer mathematical programming model is proposed for the problem. The model is adapted for the single link failure scenarios. Since the problem is NP-hard, we propose a tabu search algorithm to obtain good approximate solutions for real-size instances of the problem. Finally, a lower bound is proposed and numerical results are presented and analyzed.     

Applying MOEAs to solve the static Routing and Wavelength Assignment problem in optical WDM networks

Wavelength-Division Multiplexing (WDM) in optical networks has revolutionized the Telecommunication field. This technology is able to exploit the enormous bandwidth capability of this kind of networks, allowing communication between end users via all-optical WDM channels (lightpath). Given a set of demands, the problem of setting up lightpaths by routing and assigning a wavelength to each connection is known as Routing and Wavelength Assignment (RWA) problem. There are two types of connection demands: static (demands are given in advance) and dynamic (demands are given in real-time). In this paper we present two different Multiobjective Evolutionary Algorithms (MOEA) with the aim of solving the static RWA problem. The first one is a population-based algorithm, the Differential Evolution (DE), but incorporating the Pareto Tournament concept (DEPT). The second one is a multiobjective version of the Variable Neighborhood Search (VNS), MO-VNS. In order to prove the goodness of our metaheuristics, we have compared them with the standard Fast Non-Dominated Sorting Genetic Algorithm (NSGA-II), typical heuristics in the Telecommunication field, and different varieties of Multiobjective Ant Colony Optimization Algorithms. On the whole, we conclude that our approaches have obtained very promising results.     

Wavelength decomposition approach for computing blocking probabilities in WDM optical networks without wavelength conversions

We present an approximate analytical method to evaluate the blocking probabilities in Wavelength Division Multiplexing (WDM) networks without wavelength converters. Our approach assumes fixed routing with Random or First-Fit wavelength assignment. The new approach views the WDM network as a set of different layers (colors) in which, blocked traffic in one layer is overflowed to another layer. Analyzing blocking probabilities in each layer of the network is derived from an exact approach. A moment matching method is then used to characterize the overflow traffic from one layer to another. The results indicate that our approach is more accurate than previous works.     

A novel ring-tree-based routing and wavelength assignment algorithm for multicasting in DWDM optical mesh networks

Multicast session communications, such as video-conferencing and video-broadcasting, in DWDM mesh networks require the efficient multipoint-to-multipoint multicast algorithms. Several heuristics have approximate solutions using lightpath or light-tree for one-to-multipoint multicast communications, but few papers have discussed the multipoint-to-multipoint multicast problems in DWDM mesh networks. This paper proposes a ring-tree-based routing and wavelength assignment (RTRWA) solution in DWDM mesh networks. It proceeds to multipoint-to-multipoint multicast transmission by reserving links and wavelengths assigned by the Least Converter Count algorithm. The RTRWA algorithm tries to find an optimal ring path that connects all multicast session members with unidirectional links and connects the remaining nodes to the ring path with the light-tree. The RTRWA algorithm outperforms the Steiner minimal tree (SMT) algorithm in terms of the call blocking probability, difference in user capacity and the mean maximum transmission time.     

Selfish routing and wavelength assignment strategies with advance reservation in inter-domain optical networks

The main challenge in developing large data network in the wide area is in dealing with the scalability of the underlying routing system. Accordingly, in this work we focus on the design of an effective and scalable routing and wavelength assignment (RWA) framework supporting advance reservation services in wavelength-routed WDM networks crossing multiple administrative domains. Our approach is motivated by the observation that traffic in large optical networks spanning several domains is not controlled by a central authority but rather by a large number of independent entities interacting in a distributed manner and aiming at maximizing their own welfare. Due to the selfish strategic behavior of the involved entities, non-cooperative game theory plays an important role in driving our approach. Here the dominant solution concept is the notion of Nash equilibria, which are states of a system in which no participant can gain by deviating unilaterally its strategy. On this concept, we developed a selfish adaptive RWA model supporting advance reservation in large-scale optical wavelength-routed networks and developed a distributed algorithm to compute approximate equilibria in computationally feasible times. We showed how and under which conditions such approach can give rise to a stable state with satisfactory solutions and analyzed its performance and convergence features.