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This paper considers the online routing, modulation, spectrum, and core allocation problem in elastic optical networks. Three algorithms are proposed to minimize the bandwidth blocking probability while taking into account the impact of interference from established lightpaths. These algorithms are based on a sequence of alternative paths, ordered in terms of increasing lengths, determined by Yen's algorithm. Each of the algorithms for the selected single or dual lightpath enforces the constraints of spectrum continuity, contiguity of the slots, and non-overlapping of the spectra with the established lightpaths, maximizes the number of bits per symbol, and selects a specific core on each link of the path. Simulation studies performed for two sample networks showed that the crosstalk has a significant impact on the bandwidth blocking probability. The best results were obtained by iterating over all paths and all slots, selecting the lightpath with the lowest average crosstalk per slot, consisting of the most loaded cores.

In a real solid there are different types of defects. During sudden cooling, near cracks, there can appear high thermal stresses. In this paper, the time-fractional heat conduction equation is studied in an infinite space with an external circular crack with the interior radius R in the case of axial symmetry. The surfaces of a crack are exposed to the constant heat flux loading in a circular ring R

We present a novel algorithm for dynamic routing with dedicated path protection which, as the presented simulation results suggest, can be efficient and exact. We present the algorithm in the setting of optical networks, but it should be applicable to other networks, where services have to be protected, and where the network resources are finite and discrete, e.g., wireless radio or networks capable of advance resource reservation. To the best of our knowledge, we are the first to propose an algorithm for this long-standing fundamental problem, which can be efficient and exact, as suggested by simulation results. The algorithm can be efficient because it can solve large problems, and it can be exact because its results are optimal, as demonstrated and corroborated by simulations. We offer a worst-case analysis to argue that the search space is polynomially upper bounded. Network operations, management, and control require efficient and exact algorithms, especially now, when greater emphasis is placed on network performance, reliability, softwarization, agility, and return on investment. The proposed algorithm uses our generic Dijkstra algorithm on a search graph generated "on-the-fly" based on the input graph. We corroborated the optimality of the results of the proposed algorithm with brute-force enumeration for networks up to 15 nodes large. We present the extensive simulation results of dedicated-path protection with signal modulation constraints for elastic optical networks of 25, 50, and 100 nodes, and with 160, 320, and 640 spectrum units. We also compare the bandwidth blocking probability with the commonly-used edge-exclusion algorithm. We had 48,600 simulation runs with about 41 million searches.