Universality of Load Balancing Schemes on Diffusion Scale

We consider a system of $N$ parallel queues with identical exponential service rates and a single dispatcher where tasks arrive as a Poisson process. When a task arrives, the dispatcher always assigns it to an idle server, if there is any, and to a server with the shortest queue among $d$ randomly selected servers otherwise $(1 \leq d \leq N)$. This load balancing scheme subsumes the so-called Join-the-Idle Queue (JIQ) policy $(d = 1)$ and the celebrated Join-the-Shortest Queue (JSQ) policy $(d = N)$ as two crucial special cases. We develop a stochastic coupling construction to obtain the diffusion limit of the queue process in the Halfin-Whitt heavy-traffic regime, and establish that it does not depend on the value of $d$, implying that assigning tasks to idle servers is sufficient for diffusion level optimality

A fourth HI 21-cm absorption system in the sight-line of MG J0414+0534: a record for intervening absorbers

We report the detection of a strong HI 21-cm absorption system at z=0.5344, as well as a candidate system at z=0.3389, in the sight-line towards the z=2.64 quasar MG J0414+0534. This, in addition to the absorption at the host redshift and the other two intervening absorbers, takes the total to four (possibly five). The previous maximum number of 21-cm absorbers detected along a single sight-line is two and so we suspect that this number of gas-rich absorbers is in some way related to the very red colour of the background source. Despite this, no molecular gas (through OH absorption) has yet been detected at any of the 21-cm redshifts, although, from the population of 21-cm absorbers as a whole, there is evidence for a weak correlation between the atomic line strength and the optical--near-infrared colour. In either case, the fact that so many gas-rich galaxies (likely to be damped Lyman-alpha absorption systems) have been found along a single sight-line towards a highly obscured source may have far reaching implications for the population of faint galaxies not detected in optical surveys, a possibility which could be addressed through future wide-field absorption line surveys with the Square Kilometre Array.Comment: Accepted by ApJ Letter

Dynamic and Thermodynamic Stability and Negative Modes in Schwarzschild-Anti-de Sitter

The thermodynamic properties of Schwarzschild-anti-de Sitter black holes confined within finite isothermal cavities are examined. In contrast to the Schwarzschild case, the infinite cavity limit may be taken which, if suitably stated, remains double valued. This allows the correspondence between non-existence of negative modes for classical solutions and local thermodynamic stability of the equilibrium configuration of such solutions to be shown in a well defined manner. This is not possible in the asymptotically flat case. Furthermore, the non-existence of negative modes for the larger black hole solution in Schwarzschild-anti-de Sitter provides strong evidence in favour of the recent positive energy conjecture by Horowitz and Myers.Comment: 21 pages, 5 figures, LaTe