Queuing delays in randomized load balanced networks

Valiant’s concept of Randomized Load Balancing (RLB), also promoted under the name ‘two-phase routing’, has previously been shown to provide a cost-effective way of implementing overlay networks that are robust to dynamically changing demand patterns. RLB is accomplished in two steps; in the first step, traffic is randomly distributed across the network, and in the second step traffic is routed to the final destination. One of the benefits of RLB is that packets experience only a single stage of routing, thus reducing queueing delays associated with multi-hop architectures. In this paper, we study the queuing performance of RLB, both through analytical methods and packet-level simulations using ns2 on three representative carrier networks. We show that purely random traffic splitting in the randomization step of RLB leads to higher queuing delays than pseudo-random splitting using, e.g., a round-robin schedule. Furthermore, we show that, for pseudo-random scheduling, queuing delays depend significantly on the degree of uniformity of the offered demand patterns, with uniform demand matrices representing a provably worst-case scenario. These results are independent of whether RLB employs priority mechanisms between traffic from step one over step two. A comparison with multi-hop shortest-path routing reveals that RLB eliminates the occurrence of demand-specific hot spots in the network

Magnetohydrodynamics of insulating spheres

The effect of electric and magnetic fields on a conducting fluid surrounding an insulating object plays a role in various industrial, biomedical and micro-fluidic applications. Computational simulations of the magnetohydrodynamic flow around an insulating sphere, with crossed magnetic and electric fields perpendicular to the main flow, are performed for Rm << 1 in the ranges 0.1 &#8804; Re &#8804; 100, 1 &#8804; Ha &#8804; 20 and 0.01 &#8804; N &#8804; 1000. Careful examination of this fundamental three-dimensional flow reveals a rich physical structure with surface charge on the sphere neighbouring volume charge of opposite sign. Hartmann layers, circulating current and asymmetric velocity and current profiles appear as a result of the applied magnetic and electric field. A parametric study on the magnetic field’s influence on the drag coefficient is performed computationally. The obtained results bridge a gap between various analytical solutions of limiting cases and show good correspondence to earlier work. Correlations for the drag coefficient are proposed that can be valuable for the description of insulating inclusions in various flow applications with magnetic fields

Computational Simulations of Magnetic Particle Capture in Arterial Flows

The aim of Magnetic Drug Targeting (MDT) is to concentrate drugs, attached to magnetic particles, in a specific part of the human body by applying a magnetic field. Computational simulations are performed of blood flow and magnetic particle motion in a left coronary artery and a carotid artery, using the properties of presently available magnetic carriers and strong superconducting magnets (up to B $\approx$ 2 T). For simple tube geometries it is deduced theoretically that the particle capture efficiency scales as $\eta \sim \sqrt{\textrm{Mn}_p}$ , with $\textrm{Mn}_p$ the characteristic ratio of the particle magnetization force and the drag force. This relation is found to hold quite well for the carotid artery. For the coronary artery, the presence of side branches and domain curvature causes deviations from this scaling rule, viz. $\eta \sim \textrm{Mn}_p ^ {\beta}$, with $\beta>1/2$. The simulations demonstrate that approximately a quarter of the inserted 4 $\mu$m particles can be captured from the bloodstream of the left coronary artery, when the magnet is placed at a distance of 4.25 cm. When the same magnet is placed at a distance of 1 cm from a carotid artery, almost all of the inserted 4 $\mu$m particles are captured. The performed simulations, therefore, reveal significant potential for the application of MDT to the treatment of atherosclerosis

Magnetic particle motion in a Poiseuille flow

The manipulation of magnetic particles in a continuous flow with magnetic fields is central to several biomedical applications, including magnetic cell separation and magnetic drug targeting. A simplified twodimensional 2D equation describing the motion of particles in a planar Poiseuille flow is considered for various magnetic field configurations. Exact analytical solutions are derived for the particle motion under the influence of a constant magnetization force and a force decaying as a power of the source distance, e.g., due to a current carrying wire or a magnetized cylinder. For a source distance much larger than the transversal size of the flow, a general solution is derived and applied to the important case of a magnetic dipole. This solution is used to investigate the dependence of the particle capture efficiency on the dipole orientation. A correction factor to convert the obtained 2D results to a three-dimensional cylindrical geometry is derived and validated against computational simulations. Simulations are also used to investigate parameter ranges beyond the region of applicability of the analytical results and to investigate more complex magnetic field configurations