Static and dynamic routing and wavelength assignment algorithms for future transport networks

In this paper, two static and three dynamic routing algorithms have been proposed and compared to some of the existing algorithms on the basis of blocking probability. The two proposed static routing and wavelength assignment (RWA) algorithms reduce the blocking probability to maximize the utilization of network. For dynamic algorithms, first a model with no weights assignments is presented and then three algorithms are proposed and analysed with weight assignment resulting in reduction of blocking probability. All these algorithms are analysed and compared with four wavelength assignment schemes which are first-fit, random, most used and least used. It is shown that our proposed static algorithms give the best performance for first-fit wavelength assignment and most used wavelength assignment strategies with reduced complexity. For least used wavelength assignment and random wavelength assignment, 1 fixed and 2 alternate routing algorithm gives the lowest blocking probability. For dynamic routing, it has been shown that our proposed algorithm “less weight to maximum empty and nearest” gives the least blocking probability as compared to the other dynamic routing algorithms for random, most used and least used wavelength assignment strategies.     

Blocking in wavelength-routed all-optical WDM network with wavelength conversion

The blocking probability in wavelength-routed all optical networks is very important measure of performance of the network, which can be affected by many factors such as network topology, traffic load, number of links, algorithms employed and whether wavelength conversion is available or not. In this paper, we have proposed a mathematical model to reduce the blocking probability of the WDM optical network for wavelength-convertible networks. The model can be used to evaluate the blocking performance of any network topology also it can be useful to improve its blocking performance of the given network topology. The blocking probability variation of the network for a particular load (per link) has been studied based on the load variation and total number of wavelengths used in the network. This model gives good results for high load (per link).     

Restoration approach in WDM optical networks

Critical applications require proactive-based survivability strategy which provides 100% degree of survivability, low blocking probability and very low restoration time. In this paper, we have proposed an efficient proactive restoration approach for WDM optical network that efficiently utilizes the resources and reduces blocking probability as compared to existing proactive restoration approach. It gives priority to primary lightpath as compared to backup lightpath because primary lightpath should not share resources with other lightpaths in critical applications but backup lightpaths can share the resources, i.e. backup multiplexing.     

Combined Path and Maximum Empty Static Routing Algorithms with Wavelength Assignment for Future Transport Networks

Abstract

In this article, two static routing algorithms have been proposed and compared to some of the existing algorithms on the basis of blocking probability. The two proposed static routing and wavelength assignment algorithms reduce the blocking probability to maximize the utilization of the network. All of these algorithms are analyzed and compared with four wavelength assignment schemes, which are first-fit, random, most used, and least used. It is shown that our proposed static algorithms give the best performance for first-fit wavelength assignment and most used wavelength assignment strategies with reduced complexity. For least used wavelength assignment and random wavelength assignment, 1 fixed and 2 alternate routing algorithm gives the lowest blocking probability.     

A novel burst-outputted model in an OBS core router

In this paper, the performances of a novel burst-outputted model which based on differentiated probability in an optical burst switching (OBS) core router have been proposed and analyzed. Different from the same probability to select output-port model in previous works, proposed model gives a burst-outputted process with different probabilities, which based on the fact that, output-ports may lead to variable distance with the same destination. The burst blocking probability, the system-passed rate, the average output-port occupied value and the efficiency have been given and discussed.     

有业务量疏导能力的WDM网格网阻塞性能分析

提出一个新分析模型来计算有业务量疏导能力的波分复用(WDM)网格网的呼叫阻塞概率,WDM网络中的业务量疏导定义为复用、解复用和交换低速率业务量到高容量光路的行为.该模型首先把原始网络分解为单个子系统,然后再对这些子系统进行独立分析,最后对这些子系统的结果进行适当组合得到整个网络的解.同时,模型考虑了链路负载和链路阻塞事件之间的相关性.仿真结果表明该模型给出的结果较准确.     

Statistical Description of Contact-Interacting Brownian Walkers on the Line

The distribution of interval lengths between Brownian walkers on the line is investigated. The walkers are independent until collision; at collision, the left walker disappears, and the right walker survives with probability p. This problem arises in the context of diffusion-limited reactions and also in the scaling limit of the voter model. A systematic expansion in correlation between neighbor intervals gives a series of approximations of increasing accuracy for the probability density functions of interval lengths. The first approximation beyond mere statistical independence between successive intervals already gives excellent results, as established by comparison with direct numerical simulations.     

Recovery schemes for different distributed connection management in generalized multi-protocol label switching networks

As the wavelength division multiplexing (WDM) technology matures and the demands for bandwidth increase, survivability becomes more and more important in generalized multi-protocol label switching (GMPLS) controlled intelligent optical networks (IONs). There are great interests to study the performance of restorability under one certain connection management strategy. And studies in the problem of providing recovery from link failures under two different resource reservation schemes, forward reservation protocols (FRPs) and backward reservation protocols (BRPs), are presented. They are examined from the point of view of connection blocking probability, restorability and average recovery time. The two different connection management schemes and the survey of different recovery schemes are first presented. The performance of these recovery strategies is analyzed and compared both through theoretical analysis and simulation results. The main stressed idea is that using BRPs gives the best performance in terms of restorability and blocking probability in restorable GMPLS networks.     

Generic routing and wavelength assignment algorithm for a wavelength-routed WDM network

In this paper, we have developed a simple mathematical model which is used for the calculation of blocking probability of network. A generic routing and wavelength assignment algorithm has also been proposed for the optimization and minimization of blocking probability. The implementation of the proposed model has less complexity and the computation used in this model is quite efficient. This paper suggests an optimum path and assigns wavelength to that path, as a solution to routing and wavelength assignment problem to have least blocking probability. This model can be implemented on different network topologies. Further, the model is also used to evaluate the blocking performance of a 6-node simple network topology and hence used to improve its performance on the basis of blocking probability.     

Generic-II routing and wavelength assignment algorithm for a wavelength-routed WDM network

In this paper, we have developed a Generic routing and wavelength assignment algorithm (Generic RWA-II) which is used for the calculation of blocking probability of network. A simple mathematical model has also been proposed for the optimization and minimization of blocking probability. The implementation of the proposed model and algorithm has less complexity and the computation used in this model is quite efficient. This paper suggests an optimum path and assigns wavelength to that path, as a solution to routing and wavelength assignment problem to have least blocking probability. This model can be implemented on different network topologies. Further, the model is also used to evaluate the blocking performance of a 6-node simple network topology and hence used to improve its performance on the basis of blocking probability.     

Blocking probability analysis of survivable routing in WDM optical networks with/without sparse-wavelength conversion

In this paper, a new algorithm for wavelength assignment has been proposed and its performance is evaluated in terms of blocking probability and fairness. It has been shown that the proposed algorithm offers the least blocking probability. The blocking performance of wavelength division multiplexing (WDM) network has been analyzed for the network having 10 nodes and for varying loads. As the load per link (in Erlangs) increases, the blocking probability increases. The result shows that the performance of first-fit algorithm is better than random algorithm whereas the proposed algorithm offers the least blocking.     

Performance optimization of GMPLS networks with finite number of sources

The performance of GMPLS network depends upon the various parameters such as number of channels, number of sources, traffic intensity etc. In this paper we have proposed a call blocking model for mode of operation to determine the type of applications suitable for GMPLS networks. Further we have suggested a switch model for GMPLS network and developed a mathematical model for GMPLS network for call blocking probability and call holding probability. In proposed model blocking probability of the network is reduced and then the call blocking performance of the model is compared with the call holding performance.     

Multiple-electron excitation in X-ray absorption: a simple generic model

The probability of multiple-electron excitation in X-ray absorption is calculated using a simple generic model. The model permits calculations to be made for all atoms with little input data or computing effort. The high-energy limit of this probability, which gives the usual EXAFS amplitude reduction factor, is calculated in the 'sudden approximation' using Slater orbitals. Good agreement with experiment is found. The energy dependence of this probability is also calculated using a simple model form of perturbing potential and found to agree well with experiment for rare gas atoms. The effect on the X-ray absorption coefficient of including multiple-electron excitations is also determined and is found to be small, again in agreement with observation.     

Routing and wavelength assignment in wavelength-routed all-optical WDM networks

In this paper, low-complexity mathematical model has been developed which is used for the calculation of the blocking probability of network and this model does not require any simulation statistics. The implementation of the model proposed has less complexity and the computation used in this model is quite efficient. The routing algorithm has also been proposed in this paper depending upon the proposed model, which is very efficient in calculation and minimization of the blocking probability. This algorithm suggests an optimum path as a solution to routing problem. The wavelength assignment technique has also been suggested in this paper to minimize the blocking probability. The proposed model and algorithms can be implemented on different network topologies. Furthermore, the model, routing algorithm and wavelength assignment technique is also used to evaluate the blocking performance of NSFNet and EUPAN Network topology and hence used to improve its performance on the basis of the blocking probability.     

Blocking in wavelength-routed all-optical WDM network with or without wavelength conversion

The blocking probability in wavelength-routed all-optical networks is a very important measure of performance of the network. This blocking probability can be affected by many factors such as network topology, traffic load, number of links, algorithms employed and whether wavelength conversion is available or not. In this paper we have proposed a mathematical model to reduce the blocking probability of the WDM optical network for both wavelength convertible networks as well as for wavelength non-convertible networks. The model is can be used to evaluate the blocking performance of any network topology also it can be useful to improve its performance of the given network topology.     

The O(n) Model on the Annulus

We use Coulomb gas methods to derive an explicit form for the scaling limit of the partition function of the critical O(n) model on an annulus, with free boundary conditions, as a function of its modulus. This correctly takes into account the magnetic charge asymmetry and the decoupling of the null states. It agrees with an earlier conjecture based on Bethe ansatz and quantum group symmetry, and with all known results for special values of n. It gives new formulae for percolation (the probability that a cluster connects the two opposite boundaries) and for self-avoiding loops (the partition function for a single loop wrapping non-trivially around the annulus.) The limit n→0 also gives explicit examples of partition functions in logarithmic conformal field theory.     

Probability and complex quantum trajectories: Finding the missing links

It is shown that a normalisable probability density can be defined for the entire complex plane in the modified de Broglie-Bohm quantum mechanics, which gives complex quantum trajectories. This work is in continuation of a previous one that defined a conserved probability for most of the regions in the complex space in terms of a trajectory integral, indicating a dynamical origin of quantum probability. There it was also shown that the quantum trajectories obtained are the same characteristic curves that propagate information about the conserved probability density. Though the probability density we now adopt for those regions left out in the previous work is not conserved locally, the net source of probability for such regions is seen to be zero in the example considered, allowing to make the total probability conserved. The new combined probability density agrees with the Born’s probability everywhere on the real line, as required. A major fall out of the present scheme is that it explains why in the classical limit the imaginary parts of trajectories are not observed even indirectly and particles are confined close to the real line.     

Blocking probability analysis model for flexible spectrum optical networks

Compared to the traditional wavelength division multiplexing （WDM） optical networks with rigid and coarse granularities, flexible spectrum optical networks have high spectrum efficiency, which can support the service with various bandwidth requirements, such as sub and super channel. Among all network performance parameters, blocking probability is an important parameter for the performance evaluation and network planning in circuit~based optical networks including flexible spectrum optical networks. We propose an analytical method of blocking probability computation for flexible spectrum optical networks in this letter through mathematical analysis and theoretical derivation. Two blocking probability models are built respectively based on whether considering spectrum consecutiveness or not. Numerical results validate our proposed blocking probability models under different link capacity and traffic loads.     

Mellin Transform of the Limit Lognormal Distribution

The technique of intermittency expansions is applied to derive an exact formal power series representation for the Mellin transform of the probability distribution of the limit lognormal multifractal process. The negative integral moments are computed by a novel product formula of Selberg type. The power series is summed in general by means of its small intermittency asymptotic. The resulting integral formula for the Mellin transform is conjectured to be valid at all levels of intermittency. The conjecture is verified partially by proving that the integral formula reproduces known results for the positive and negative integral moments of the limit lognormal distribution and gives a valid characteristic function of the Lévy-Khinchine type for the logarithm of the distribution. The moment problem for the logarithm of the distribution is shown to be determinate, whereas the moment problems for the distribution and its reciprocal are shown to be indeterminate. The conjecture is used to represent the Mellin transform as an infinite product of gamma factors generalizing Selberg’s finite product. The conjectured probability density functions of the limit lognormal distribution and its logarithm are computed numerically by the inverse Fourier transform.     

Performance analysis of traffic groomed optical network

In this paper we carry out the performance analysis of traffic groomed multilayer optical networks. It is seen that the number of wavelength channels required decreases as the wavelength grooming factor increases. We have evaluated blocking probability for different load and grooming factor. The performance of the network has been evaluated for different conditions; first for fixed number of links with grooming factor set to 3 and subsequently with increase in grooming factor up to 18 in steps. The load on each link is selected as 2, 5, 9, 12, 15 and 20 Erlangs and the blocking probability as function of number of optical channels has been evaluated. In this work the effect of number of wavelength channels, traffic load and grooming factor on network blocking probability has been studied. The investigation reveals that the blocking probability decreases with increase in wavelength channels. Similarly we found that the blocking probability increases with increase in traffic load which is quite evident. Further it is shown that when the grooming factor is increased to significant value (16), the number of wavelengths requirement (8) becomes relatively stable.