/pdf/reversibility-and-stochastic-networks-17kl9p5ino.pdf

Reversibility and Stochastic Networks

We present an analytical technique of very low complexity, using the inclusion-exclusion principle of combinatorics, for the performance evaluation of all-optical, wavelength-division multiplexed networks with no wavelength conversion. The technique is a generalized reduced-load approximation scheme which is applicable to arbitrary topologies and traffic patterns. One of the main issues in computing blocking probabilities in all-optical networks is the significant link load correlation introduced by the wavelength continuity constraint. One of the models we propose takes this into account and gives good results even under conditions with high link load correlation. Through numerous experiments we show that our models can be used to obtain fast and accurate estimates of blocking probabilities in all-optical networks and scale well with the path length and capacity of the network. We also extend one of our models to take into account alternate routing, ina the form of Fixed Alternate Routing and Least Loaded Routing.

/pdf/blocking-in-all-optical-networks-2gb2rwpxbm.pdf

Blocking in all-optical networks

Dynamic routing and spectrum (re)allocation in future flexgrid optical networks

Blocking probability has been one of the key performance indexes in the design of wavelength-routed all-optical WDM networks. Existing research has demonstrated that an effective Routing and Wavelength Assignment (RWA) algorithm and wavelength conversion are two primary vehicles for improving the blocking performance. However, these two issues have largely been investigated separately; in particular the existing RWA algorithms have seldom considered the presence of wavelength conversion. In this paper, we firstly demonstrate that the existing dynamic RWA algorithms do not work well in the presence of wavelength conversion as they usually only take into account the current traffic, and do not explicitly consider the route lengths. We then propose a weighted least-congestion routing and first-fit wavelength assignment (WLCR-FF) algorithm that considers both the current traffic load and the route lengths jointly. We further introduce an analytical model that can evaluate the blocking performance for WLCR algorithm. We carry out extensive numerical studies over typical topologies including ring, mesh-torus, and the 14-node NSFNET; and compare the performance of WLCR-FF with a wide variety of existing routing algorithms including static routing, fixed-alternate routing and least-loaded routing. The results conclusively demonstrate that the proposed WLCR-FF algorithm can achieve much better blocking performance in the presence of sparse or/and full wavelength conversion.

Dynamic routing and wavelength assignment in the presence of wavelength conversion for all-optical networks

In this paper, we analyze the blocking probability of distributed lightpath establishment in wavelength-routed WDM networks by studying the two basic methods: destination-initiated reservation (DIR) and source-initiated reservation (SIR). We discuss three basic types of connection blocking: 1) blocking due to insufficient network capacity; 2) blocking due to outdated information; and 3) blocking due to over-reservation. It is shown that the proposed models are highly accurate for both the DIR and the SIR methods, in both the regular and irregular network topologies, under the whole range of traffic loads.

Analysis of blocking probability for distributed lightpath establishment in WDM optical 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.

/pdf/a-path-decomposition-approach-for-computing-blocking-31zdv0u330.pdf

A path decomposition approach for computing blocking probabilities in wavelength-routing networks

We consider wavelength routing networks with and without wavelength converters, and several wavelength allocation policies Through numerical and simulation results we obtain upper and lower bounds on the blocking probabilities for two wavelength allocation policies that are most likely to be used in practice, namely, most-used and first-fit allocation These bounds are the blocking probabilities obtained by the random wavelength allocation policy with either no converters or with converters at all nodes of the network Furthermore, we demonstrate that using the most-used or first-fit policies gives an improvement on call blocking probabilities that is equivalent to employing converters at a number of nodes in a network with the random allocation policy These results have been obtained for a wide range of loads for both single-path and general mesh topology networks The main conclusion of our work is that the gains obtained by employing specialized and expensive hardware (namely, wavelength converters) can be realized cost-effectively by making more intelligent choices in software (namely, the wavelength allocation policy)

A Comparison of Allocation Policies in Wavelength Routing Networks

We study a class of circuit-switched wavelength routing networks with and without wavelength converters, and we present the first part of a new analytical framework to accurately and efficiently evaluate the blocking performance of such networks. The model allows non-uniform traffic, it accounts for the correlation among the loads at all links in a path, and it can be used when the location of converters is fixed but arbitrary. We first construct an exact Markov process that captures the behaviour of a path in terms of wavelength use. We also obtain an approximate Markov process which has a closed-form solution that can be efficiently computed for short paths. We then develop an iterative algorithm to analyze approximately arbitrarily long paths. The algorithm decomposes a path into shorter segments which are then studied in isolation using the corresponding approximate Markov process. The individual solutions are appropriately combined to obtain a solution for the original path. Finally, we demonstrate how the analytical techniques can be used to gain insight into the problem of converter placement in wavelength routing networks.

Blocking in wavelength routing networks .I. The single path case

We consider wavelength routing networks with and without wavelength converters, and several wavelength allocation policies. Through numerical and simulation results we obtain upper and lower bounds on the blocking probabilities for two wavelength allocation policies that are most likely to be used in practice, namely, most-used and first-fit allocation. These bounds are the blocking probabilities obtained by the random wavelength allocation policy with either no converters or with converters at all nodes of the network. Furthermore, we demonstrate that using the most-used or first-fit policies gives an improvement on call blocking probabilities that is equivalent to employing converters at a number of nodes in a network with the random allocation policy. These results have been obtained for a wide range of loads for both single-path and general mesh topology networks. The main conclusion of our work is that the gains obtained by employing specialized and expensive hardware (namely, wavelength converters) can be realized cost-effectively by making more intelligent choices in software (namely, the wavelength allocation policy).

/pdf/comparison-of-allocation-policies-in-wavelength-routing-26dyo6f8p3.pdf

Comparison of allocation policies in 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 accurately and efficiently evaluate the blocking performance of such networks with and without wavelength converters. Our iterative algorithm analyzes the original network by decomposing it into single path sub-systems. These sub-systems are analyzed in isolation by using our previous algorithms for a single path of a wavelength routing network, and the individual results are appropriately combined to obtain a solution for the overall network. The path decomposition approach can naturally capture the correlation of both link loads and link blocking events, giving accurate results for a wide range of loads and network topologies. Our model also allows non-uniform traffic, i.e., call request arrival rates that can vary with the source-destination pair, and it can be used when the location of converters is fixed but arbitrary. Our algorithm represents a simple and computationally efficient solution to the difficult problem of computing call blocking probabilities in wavelength routing networks. We validate our algorithm by applying it to both regular and irregular topologies of realistic size and comparing to simulation results. We also demonstrate how our analytical techniques can be applied to gain insight into the problem of converter placement in wavelength routing networks.

Yuhong Zhu

Papers

A path decomposition approach for computing blocking probabilities in wavelength-routing networks

A Comparison of Allocation Policies in Wavelength Routing Networks

Blocking in wavelength routing networks .I. The single path case

Comparison of allocation policies in wavelength routing networks

Blocking in Wavelength Routing Networks, Part II: Mesh Topologies