Performance of distributed mechanisms for flow admission in wireless adhoc networks

Given a wireless network where some pairs of communication links interfere with each other, we study sufficient conditions for determining whether a given set of minimum bandwidth quality-of-service (QoS) requirements can be satisfied. We are especially interested in algorithms which have low communication overhead and low processing complexity. The interference in the network is modeled using a conflict graph whose vertices correspond to the communication links in the network. Two links are adjacent in this graph if and only if they interfere with each other due to being in the same vicinity and hence cannot be simultaneously active. The problem of scheduling the transmission of the various links is then essentially a fractional, weighted vertex coloring problem, for which upper bounds on the fractional chromatic number are sought using only localized information. We recall some distributed algorithms for this problem, and then assess their worst-case performance. Our results on this fundamental problem imply that for some well known classes of networks and interference models, the performance of these distributed algorithms is within a bounded factor away from that of an optimal, centralized algorithm. The performance bounds are simple expressions in terms of graph invariants. It is seen that the induced star number of a network plays an important role in the design and performance of such networks.Comment: 21 pages, submitted. Journal version of arXiv:0906.378

A computer simulation study of tilted smetic mesophases.

Results are presented from a series of simulations undertaken to determine the effect of a novel form of molecular biaxiality upon the phase behaviour of the well established Gay-Berne (GB) liquid crystal model. Firstly, the simulation of a bulk system interacting via the Internally-Rotated Gay-Berne (IRGB) potential, which offers a single-site representation of a molecule rigidly constrained into a zig-zag conformation, is presented. The results of simulations performed for systems of IRGB particles with an aspect ratio of 3:1 confirm that the introduction of biaxiality into the model results in the destabilisation of the orientationally ordered phases. For particles with a sufficiently pronounced zig-zag conformation, this results in the complete destabilisation of the smectic A phase and the smectic B phase being replaced by the tilted smectic J phase. Following these observations, the effect upon the phase behaviour of increasing molecular elongation is also considered, with an increase in the aspect ratio from 3:1 to 4:1 resulting in the nematic and smectic J phases being replaced by smectic A and smectic G phases respectively. Secondly, a version of the IRGB potential modified to include a degree of molecular flexibility is considered. Results obtained from bulk systems interacting via the flexible IRGB for 3:1 and 4:1 molecules show that the introduction of flexibility results in the destabilisation of the smectic A phase and the stabilisation of the nematic and tilted hexatic phases. Finally, the effect upon the phase behaviour of the rigid IRGB model of the inclusion of a longitudinal linear quadrupole is examined. These results show that increasing quadrupole moment results in the destabilisation of the tilted hexatic phase, although the biaxial order parameter is increased with increasing quadrupole moment. There is no clear correlation between quadrupole magnitude and the other observed phase transitions, with the nematic and smectic A phases being variously stabilised and destabilised with increasing quadrupole magnitude. For the 4:1 molecules with large quadrupole moments, buckled smectic layers are observed where some molecules are tilted with respect to a local layer normal. Of all the systems considered here, this buckled structure is the one which most closely resembles the elusive smectic C phase

Resource allocation in a multicast tree

muralik @ lucent.com Abstract- We consider how to allocate bandwidth in a multicast tree so as to optimize some global measure of per-formance. In our model each receiver has a budget to be used for bandwidth reservation on links along its path from the source, and each link has a cost function depending on the amount of total bandwidth resewed at the link by all re-ceivers using that link We formulate and solve a problem of allocating bandwidth in the multicast tree such that the sum of link costs is minimized