Analysis of OBS Networks With Limited Wavelength Conversion

Presented herein is a scalable framework for estimating path blocking probabilities in optical burst switched (OBS) networks where limited wavelength conversion is possible. Although presented under the guise of OBS, it is pertinent to a broader class of optical networks based on the principle of bufferless unacknowledged switching. By applying the framework to the NSFNET topology, it is shown that even the most limited conversion range may reduce path blocking probabilities by several orders of magnitude, compared with no wavelength conversion. Moreover, contrary to previous results derived for all-optical non-OBS networks with acknowledgement, OBS with full wavelength conversion achieves significantly lower blocking probabilities than OBS with limited wavelength conversion when the conversion range is small. Underpinning the framework is a generalization of the classical reduced load approximation. Assuming links evolve independently of each other allows decoupling of the network into its constituent links. A set of fixed-point equations describing the evolution of each conversion range are then solved by successive substitution to estimate link blocking probabilities. Having these link blocking probabilities, path blocking probabilities are evaluated. The complexity of the framework is dominated by the wavelength conversion range and is independent of the number of wavelengths per link under certain symmetry conditions. Both just-in-time (JIT) and just-enough-time (JET) scheduling are considered. Simulations are implemented to corroborate the accuracy of the framework.     

Adaptive wavelength routing in all-optical networks

We consider routing and wavelength assignment in wavelength-routed all-optical networks (WAN) with circuit switching. The conventional approaches to address this issue consider the two aspects of the problem disjointly by first finding a route from a predetermined set of candidate paths and then searching for an appropriate wavelength assignment. We adopt a more general approach in which we consider all paths between a source-destination (s-d) pair and incorporate network state information into the routing decision. This approach performs routing and wavelength assignment jointly and adaptively, and outperforms fixed routing techniques. We present adaptive routing and wavelength assignment algorithms and evaluate their blocking performance. We obtain an analytical technique to compute approximate blocking probabilities for networks employing fixed and alternate routing. The analysis can also accommodate networks with multiple fibers per link. The blocking performance of the proposed adaptive routing algorithms are compared along with their computational complexity     

Performance Evaluations for Dynamic Wavelength Routed All-Optical Multifiber Networks

This paper presents a study on dynamic wavelength routed all-optical networks by simulating traffic on all-optical networks. A performance study is carried out on dynamic all-optical networks for fixed and free routing. It is explained how multiple fibers correspond to limited wavelength conversion, and it is explained why the presence of wavelength converters increase the complexity of optical cross connects. We find that both free routing and wavelength conversion lowers the blocking probability significantly. The new contribution is that we determine the gain in blocking probability as function of the number of fibers per link and the offered load. We find that multiple fibers reduce the effect of wavelength converters significantly.     

On the Algorithm for Allocating Wavelength Converters in All-Optical Networks

In this paper, after presenting the functions of the wavelength converter in all-optical networks, we educe and analyze the blocking probabilities of the network. Based on the above, we propose an algorithm for allocating wavelength converters in all-optical networks and use the computer simulations to evaluate the performance of the proposed allocation algorithm. The simulation results show that the performance of our algorithm is close to that of the optimal ones in terms of blocking probabilities. However, the time complexity of our algorithm is only O(3H+ w2/2).     

Blocking in Wavelength-Routed Optical Networks With Heterogeneous Traffic

In this paper, we present a new analytical model that can give an accurate estimation of the blocking probabilities in wavelength-routed optical networks with heterogeneous traffic. By heterogeneous, we mean that each session offered to the network has its own traffic intensity and burstiness. In such cases, the blocking probability of a session is determined by the busy-wavelength distributions of the links seen at the arrival points of its calls. Thus, we first present two single-link models to estimate the arrival-point busy-wavelength distribution of a link with heterogeneous traffic: the full-population (FP) model and the reduced-population (RP) model. Both models are based on the BPP/M/W/W model, where the first two moments of an arbitrary session are matched by those of a birth–death process whose arrival rate linearly varies with the average number of busy wavelengths occupied by its own calls. We show that different sessions have different arrival-point busy-wavelength distributions depending on the burstiness of their traffic, i.e., a bursty session observes the link more congested than a smooth session. Next, we provide two extensions of the single-link models, the FP-full-load link-correlation model and the RP-reduced-load link-correlation model, to estimate the blocking probabilities of optical networks with heterogeneous traffic and sparse wavelength conversion. Both models employ the existing link-correlation models to take into account the occupied-wavelength-index correlation between two adjacent links. By comparing the results from the models with simulation results, we demonstrate that both models well approximate the blocking probabilities of individual sessions, as well as the network-wide blocking probability, for a wide range of traffic intensity, burstiness, and heterogeneity.     

A computational model for estimating blocking probabilities of multifiber WDM optical networks

In this letter, we propose a computational model for calculating blocking probabilities of multifiber wavelength division multiplexing (WDM) optical networks. We first derive the blocking probability of a fiber based on a Markov chain, from which the blocking probability of a link is derived by means of conditional probabilities. The blocking probability of a lightpath can be computed by a recursive formula. Finally, the network-wide blocking probability can be expressed as the ratio of the total blocked load versus the total offered load. Simulation results for different fiber-wavelength configurations conform closely to the numerical results based on our proposed model, thus demonstrating the feasibility of our proposed model for estimating the blocking performance of multifiber WDM optical networks.     

Link Capacity Sharing between Guaranteed- and Best Effort Services on an ATM Transmission Link under GoS Constraints

While link allocation policies in multi-rate circuit switched loss models have drawn much attention in recent years, it is still an open question how to share the link capacity between service classes in a fair manner. In particular, when an ATM link is offered calls from service classes with/without strict QoS guarantees one is interested in link capacity sharing policies that maximize throughput and keep the per-class blocking probabilities under some GoS constraints. In this paper we propose a model and associated computational technique for an ATM transmission link to which CBR/VBR and ABR classes offer calls. We also propose a simple link allocation rule which takes into account blocking probability constraints for the CBR/VBR calls and a throughput constraint for the ABR calls and attempts to minimize the blocking probability of ABR calls. Numerical examples demonstrate the effectiveness of the policy and of the applied computational technique.     

A path decomposition approach for computing blocking probabilitiesin wavelength-routing networks

We study a class of circuit-switched wavelength-routing networks with fixed or alternate routing and with random wavelength allocation. We present an iterative path decomposition algorithm to evaluate accurately and efficiently the blocking performance of such networks with and without wavelength converters. Our iterative algorithm analyzes the original network by decomposing it into single-path subsystems. These subsystems are analyzed in isolation, and the individual results are appropriately combined to obtain a solution for the overall network. To analyze individual subsystems, we first construct an exact Markov process that captures the behavior of a path in terms of wavelength use. We also obtain an approximate Markov process which has a closed-form solution that can be computed efficiently for short paths. We then develop an iterative algorithm to analyze approximately arbitrarily long paths. The path decomposition approach naturally captures the correlation of both link loads and link blocking events. Our algorithm represents a simple and computationally efficient solution to the difficult problem of computing call-blocking probabilities in wavelength-routing networks. We also demonstrate how our analytical techniques can be applied to gain insight into the problem of converter placement in wavelength-routing networks     

A Virtual Wavelength Translation Scheme for Routing in All-Optical Networks

This paper considers wavelength routed WDM networks where multiple fibers are used for each communication link. For such networks, the effect of wavelength translation can be achieved without explicit use of wavelength translators. We call this as virtual wavelength translation and study the routing issues considering dynamic lightpath allocation. Using multiple (or a bundle of) fibers for each link also allows us to have bundles of varying sizes to accommodate anticipated differences in traffic through different communication links of the network. The paper considers the blocking probabilities of all-optical networks when centralized and distributed lightpath allocation schemes are used.     

Computing approximate blocking probabilities for a class ofall-optical networks

We study a class of all-optical networks using wavelength-division multiplexing (WDM) and wavelength routing, in which a connection between a pair of nodes in the network is assigned a path and a wavelength on that path. Moreover, on the links of that path no other connection can share the assigned wavelength. Using a generalized reduced load approximation scheme we calculate the blocking probabilities for the optical network model for two routing schemes: fixed routing and least loaded routing     

Algorithms for allocating wavelength converters in all-opticalnetworks

In an all-optical wide area network, some network nodes may handle heavier volumes of traffic. It is desirable to allocate more full-range wavelength converters (FWCs) to these nodes, so that the FWCs can be fully utilized to resolve wavelength conflict. We propose a set of algorithms for allocating FWCs in all-optical networks. We adopt the simulation-based optimization approach, in which we collect utilization statistics of FWCs from computer simulations and then perform optimization to allocate the FWCs. Therefore, our algorithms are widely applicable and they are not restricted to any particular model or assumption. We have conducted extensive computer simulations on regular and irregular networks under both uniform and nonuniform traffic. Compared with the best existing allocation, the results show that our algorithms can significantly reduce: (1) the overall blocking probability (i.e., better mean quality of service) and (2) the maximum of the blocking probabilities experienced at all the source nodes (i.e., better fairness). Equivalently, for a given performance requirement on blocking probability, our algorithms can significantly reduce the number of FWCs required     

An analysis of oblivious and adaptive routing in optical networkswith wavelength translation

We present an analysis for both oblivious and adaptive routing in regular, all-optical networks with wavelength translation. Our approach is simple, computationally inexpensive, accurate for both low and high network loads, and the first to analyze adaptive routing with wavelength translation in wavelength division multiplexed (WDM) networks while also providing a simpler formulation of oblivious routing with wavelength translation. Unlike some previous analyses which use the link independence blocking assumption and the call dropping (loss) model (where blocked calls are cleared), we account for the dependence between the acquisition of wavelengths on successive links of a session's path and use a lossless model (where blocked calls are retried at a later time). We show that the throughput per wavelength increases superlinearly (as expected) as we increase the number of wavelengths per link, due both to additional capacity and more efficient use of this capacity; however, the extent of this superlinear increase in throughput saturates rather quickly to a linear increase. We also examine the effect that adaptive routing can have on performance. The analytical methodology that we develop can be applied to any vertex and edge symmetric topology, and with modifications, to any vertex symmetric (but not necessarily edge symmetric) topology. We find that, for the topologies we examine, providing at most one alternate link at every hop gives a per wavelength throughput that is close to that achieved by oblivious routing with twice the number of wavelengths per link. This suggests some interesting possibilities for network provisioning in an all-optical network. We verify the accuracy of our analysis for both oblivious and adaptive routing via simulations for the torus and hypercube networks     

Analyzing Product-Form Stochastic Networks Via Factor Graphs and the Sum-Product Algorithm

A large number of stochastic networks including loss networks and certain queueing networks have product-form steady-state probabilities. However, for most practical networks, evaluating the system performance is a difficult task due to the presence of a normalization constant. We propose a new framework based on probabilistic graphical models to tackle this task. Specifically, we use factor graphs to model the stationary distribution of a network. For networks with arbitrary topology, we can apply efficient message-passing algorithms like the sum-product algorithm to compute the exact or approximate marginal distributions of all state variables and related performance measures such as blocking probabilities. Through extensive numerical experiments, we show that the sum-product algorithm returns very accurate blocking probabilities and greatly outperforms the reduced load approximation for loss networks with a variety of topologies. The factor graph model also provides a promising approach for analyzing product-form queueing networks.     

A Hopfield neural-network-based dynamic channel allocation withhandoff channel reservation control

As channel allocation schemes become more complex and computationally demanding in cellular radio networks, alternative computational models that provide the means for faster processing time are becoming the topic of research interest. These computational models include knowledge-based algorithms, neural networks, and stochastic search techniques. This paper is concerned with the application of a Hopfield (1982) neural network (HNN) to dynamic channel allocation (DCA) and extends previous work that reports the performance of HNN in terms of new call blocking probability. We further model and examine the effect on performance of traffic mobility and the consequent intercell call handoff, which, under increasing load, can force call terminations with an adverse impact on the quality of service (QoS). To maintain the overall QoS, it is important that forced call terminations be kept to a minimum. For an HNN-based DCA, we have therefore modified the underlying model by formulating a new energy function to account for the overall channel allocation optimization, not only for new calls but also for handoff channel allocation resulting from traffic mobility. That is, both new call blocking and handoff call blocking probabilities are applied as a joint performance estimator. We refer to the enhanced model as HNN-DCA++. We have also considered a variation of the original technique based on a simple handoff priority scheme, here referred to as HNN-DCA+. The two neural DCA schemes together with the original model are evaluated under traffic mobility and their performance compared in terms of new-call blocking and handoff-call dropping probabilities. Results show that the HNN-DCA++ model performs favorably due to its embedded control for assisting handoff channel allocation     

Dependency-based analytical model for computing connection blocking rates and its application in the sparse placement of optical converters

In this paper, we present a new analytical model that captures link dependencies in all-optical wavelength-division multiplexing (WDM) networks under uniform traffic and enables the estimation of connection-blocking probabilities more accurately than previously possible. The basic formula of the dependency between two links in this model reflects their degree of adjacency, the degree of connectivity of the nodes composing them, and their carried traffic. Our validation tests have shown that the analytical dependency model gives accurate results and successfully captures the main dependency characteristics observed in the simulation measurements. The usefulness of the model is illustrated by showing how to use it in enhancing a simulation-based algorithm that we recently proposed for the sparse placement of full wavelength converters in WDM networks. To analytically handle the presence of wavelength converters, a lightpath containing converters is divided into smaller subpaths, such that each subpath is a wavelength-continuous path, and the nodes shared between these subpaths are full wavelength-conversion-capable. The blocking probability of the entire path is obtained by computing the probabilities in the individual subpaths. We validate the analytically-based sparse placement algorithm by comparing it with its simulation-based counterpart using a number of network topologies.     

Survivable Load Sharing Protocols: A Simulation Study

The development of robust, survivable wireless access networks requires that the performance of network architectures and protocols be studied under normal as well as faulty conditions where consideration is given to faults occurring within the network as well as within the physical environment. User location, mobility, and usage patterns and the quality of the received radio signal are impacted by terrain, man-made structures, population distribution, and the existing transportation system. The work presented herein has two thrusts. One, we propose the use of overlapping coverage areas and dynamic load balancing as a means to increase network survivability by providing mobiles with multiple access points to the fixed infrastructure. Two, we describe our simulation approach to survivability analysis which combines empirical spatial information, network models, and fault models for more realistic analysis of real service areas. We use our simulation approach to compare the survivability of our load balancing protocols to a reference scheme within two diverse geographic regions. We view survivability as a cost-performance tradeoff using handover activity as a cost metric and blocking probabilities as performance metrics. Our results illustrate this tradeoff for the protocols studied and demonstrate the extent to which the physical environment and faults therein affect the conclusions that are drawn.     

基于关键链路预测的动态路由和波长分配算法

 光网络中的路由和波长分配 （RWA）算法是NP难问题. 目前的解决方案大多是基于启发式算法或图论的,其计算复杂度往往随着网络规模的增加呈指数增长,而且链路阻塞概率建模也十分困难. 本文提出了一种基于“关键链路”预测机制的RWA算法,并综合考虑跳数和空闲波长数的因素,不仅通过链路层面,而且也从网络层面来解决RWA问题. 实验结果表明我们的算法可以实现很好的流量负载均衡和低的阻塞率,具有较小的计算复杂度.     

Design of node configuration for all-optical multi-fiber networks

It is cost-effective to install multiple fibers in each link of an all-optical network, because the cost of fibers is relatively low compared with the installation cost. The resulting network can provide a large capacity for good quality of service, future growth, and fault tolerance. If a node has more incoming/outgoing fibers, it requires larger optical switches. Using the current photonic technology, it is difficult to realize large optical switches. Even if they can be realized, they are expensive. To overcome this problem, we design a node configuration for all-optical networks. We exploit the flexibility that, to establish a lightpath across a node, we can select any one of the available channels in the incoming link and any one of the available channels in the outgoing link. As a result, the proposed node configuration requires significantly smaller optical switches while it can result in nearly the same blocking probability as the existing one. We demonstrate that a good network design is to adopt the proposed node configuration and slightly more fibers in each link, so that the network requires small optical switches while it has a small blocking probability     

Computing approximate blocking probabilities for large lossnetworks with state-dependent routing

A reduced load approximation (also referred to as an Erlang fixed point approximation) for estimating point-to-point blocking probabilities in loss networks (e.g., circuit switched networks) with state-dependent routing is considered. In this approximation scheme, the idle capacity distribution for each link in the network is approximated, assuming that these distributions are independent from link to link. This leads to a set of nonlinear fixed-point equations which can be solved by repeated substitutions. The accuracy and the computational requirements of the approximation procedure for a particular routing scheme, namely least loaded routing, is examined. Numerical results for six-node and 36-node asymmetric networks are given. A novel reduced load approximation for multirate networks with state-dependent routing is also presented     

A Model for Telephone Networks and Its Use for Routing Optimization Purposes

The problem studied here concerns the modeling of call blocking in telephone networks. From the usual assumptions such as exponential arrivals and holding time, lost call cleared, the state of the network is described by a finite Markov chain. From the transition probabilities of this process are derived the differential equations associated with the average occupancy of all trunk groups. These traffic equations are simplified by considering independence of blocking for trunk groups in series. The blocking probabilities are estimated using fictitious offered traffic and the Erlang B formula. Such representation takes into account peaky or smooth traffic characteristics. We develop this one-moment model for routing policies such as load sharing and overflow routing. Performances of the model are given in comparison to the solution of the exact Markov chain model or the results of Monte Carlo simulation. Finally, an application to routing optimization and network dimensioning is treated.