Call Control in Rings

The call control problem is an important optimization problem encountered in the design and operation of communication networks. The goal of the call control problem in rings is to compute, for a given ring network with edge capacities and a set of paths in the ring, a maximum cardinality subset of the paths such that no edge capacity is violated. We give a polynomial-time algorithm to solve the problem optimally. The algorithm is based on a decision procedure that checks whether a solution with at least k paths exists, which is in turn implemented by an iterative greedy approach operating in rounds. We show that the algorithm can be implemented efficiently and, as a by-product, obtain a linear-time algorithm to solve the problem in chains optimally. For the weighted version of call control in rings, where each path is associated with a weight and the goal is to maximize the total weight of the paths in the solution, we present a simple 2-approximation algorithm and a polynomial-time approximation scheme. While the complexity of the weighted version remains open, we show that it is at least as hard as the bipartite exact matching problem, which has not been resolved to be in P or NP-hard. This latter result follows from recent work by Hochbaum and Levi

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Design And Analysis Of Effective Routing And Channel Scheduling For Wavelength Division Multiplexing Optical Networks

Optical networking, employing wavelength division multiplexing (WDM), is seen as the technology of the future for the Internet. This dissertation investigates several important problems affecting optical circuit switching (OCS) and optical burst switching (OBS) networks. Novel algorithms and new approaches to improve the performance of these networks through effective routing and channel scheduling are presented. Extensive simulations and analytical modeling have both been used to evaluate the effectiveness of the proposed algorithms in achieving lower blocking probability, better fairness as well as faster switching. The simulation tests were performed over a variety of optical network topologies including the ring and mesh topologies, the U.S. Long-Haul topology, the Abilene high-speed optical network used in Internet 2, the Toronto Metropolitan topology and the European Optical topology. Optical routing protocols previously published in the literature have largely ignored the noise and timing jitter accumulation caused by cascading several wavelength conversions along the lightpath of the data burst. This dissertation has identified and evaluated a new constraint, called the wavelength conversion cascading constraint. According to this constraint, the deployment of wavelength converters in future optical networks will be constrained by a bound on the number of wavelength conversions that a signal can go through when it is switched all-optically from the source to the destination. Extensive simulation results have conclusively demonstrated that the presence of this constraint causes significant performance deterioration in existing routing and wavelength assignment (RWA) algorithms. Higher blocking probability and/or worse fairness have been observed for existing RWA algorithms when the cascading constraint is not ignored. To counteract the negative side effect of the cascading constraint, two constraint-aware routing algorithms are proposed for OCS networks: the desirable greedy algorithm and the weighted adaptive algorithm. The two algorithms perform source routing using link connectivity and the global state information of each wavelength. Extensive comparative simulation results have illustrated that by limiting the negative cascading impact to the minimum extent practicable, the proposed approaches can dramatically decrease the blocking probability for a variety of optical network topologies. The dissertation has developed a suite of three fairness-improving adaptive routing algorithms in OBS networks. The adaptive routing schemes consider the transient link congestion at the moment when bursts arrive and use this information to reduce the overall burst loss probability. The proposed schemes also resolve the intrinsic unfairness defect of existing popular signaling protocols. The extensive simulation results have shown that the proposed schemes generally outperform the popular shortest path routing algorithm and the improvement could be substantial. A two-dimensional Markov chain analytical model has also been developed and used to analyze the burst loss probabilities for symmetrical ring networks. The accuracy of the model has been validated by simulation. Effective proactive routing and preemptive channel scheduling have also been proposed to address the conversion cascading constraint in OBS environments. The proactive routing adapts the fairness-improving adaptive routing mentioned earlier to the environment of cascaded wavelength conversions. On the other hand, the preemptive channel scheduling approach uses a dynamic priority for each burst based on the constraint threshold and the current number of performed wavelength conversions. Empirical results have proved that when the cascading constraint is present, both approaches would not only decrease the burst loss rates greatly, but also improve the transmission fairness among bursts with different hop counts to a large extent