Simple and explicit bounds for multi-server queues with 1/(1−ρ)1/(1 - \rho) (and sometimes better) scaling

We consider the FCFS $GI/GI/n$ queue, and prove the first simple and explicit bounds that scale as $\frac{1}{1-\rho}$ (and sometimes better). Here $\rho$ denotes the corresponding traffic intensity. Conceptually, our results can be viewed as a multi-server analogue of Kingman's bound. Our main results are bounds for the tail of the steady-state queue length and the steady-state probability of delay. The strength of our bounds (e.g. in the form of tail decay rate) is a function of how many moments of the inter-arrival and service distributions are assumed finite. More formally, suppose that the inter-arrival and service times (distributed as random variables $A$ and $S$ respectively) have finite $r$th moment for some $r > 2.$ Let $\mu_A$ (respectively $\mu_S$) denote $\frac{1}{\mathbb{E}[A]}$ (respectively $\frac{1}{\mathbb{E}[S]}$). Then our bounds (also for higher moments) are simple and explicit functions of $\mathbb{E}\big[(A \mu_A)^r\big], \mathbb{E}\big[(S \mu_S)^r\big], r$, and $\frac{1}{1-\rho}$ only. Our bounds scale gracefully even when the number of servers grows large and the traffic intensity converges to unity simultaneously, as in the Halfin-Whitt scaling regime. Some of our bounds scale better than $\frac{1}{1-\rho}$ in certain asymptotic regimes. More precisely, they scale as $\frac{1}{1-\rho}$ multiplied by an inverse polynomial in $n(1 - \rho)^2.$ These results formalize the intuition that bounds should be tighter in light traffic as well as certain heavy-traffic regimes (e.g. with $\rho$ fixed and $n$ large). In these same asymptotic regimes we also prove bounds for the tail of the steady-state number in service. Our main proofs proceed by explicitly analyzing the bounding process which arises in the stochastic comparison bounds of amarnik and Goldberg for multi-server queues. Along the way we derive several novel results for suprema of random walks and pooled renewal processes which may be of independent interest. We also prove several additional bounds using drift arguments (which have much smaller pre-factors), and make several conjectures which would imply further related bounds and generalizations

"Precious Metals-Exchange Rate Volatility Transmissions and Hedging Strategies"

This study examines the conditional volatility and correlation dependency and interdependency for the four major precious metals (that is, gold, silver, platinum and palladium), while accounting for geopolitics within a multivariate system. The implications of the estimated results for portfolio designs and hedging strategies are also analyzed. The results for the four metals system show significant short-run and long-run dependencies and interdependencies to news and past volatility. These results have become more pervasive when the exchange rate and FFR are included. Monetary policy also has a differential impact on the precious metals and the exchange rate volatilities. Finally, the applications of the results show the optimal weights in a two-asset portfolio and the hedging ratios for long positions.

Comment on 'Secure Communication using mesoscopic coherent states', Barbosa et al, Phys Rev Lett 90, 227901 (2003)

In a recent letter, Barbosa et al [PRL 90, 227901(2003)] claim that secure communication is possible with bright coherent pulses, by using quantum noise to hide the data from an eavesdropper. We show here that the secrecy in the scheme of Barbosa et al is unrelated to quantum noise, but rather derives from the secret key that sender and receiver share beforehand

Probing Form Factors in Top Quark Pair Production at e−e+e^-e^+ Colliders

We describe how to probe new physics through large CP violation effects and non--standard Z-t-t couplings via the scattering process e^-e^+ -> t tbar. [Talk presented at the Workshop on Physics and Experiments with Linear $e^+e^-$ Colliders, Waikoloa, Hawaii, 26-30 April 1993.]Comment: 4 pages, TeXsis, MSUTH 93/0

Precious Metals-Exchange Rate Volatility Transmissions and Hedging Strategies

This study examines the conditional volatility and correlation dependency and interdependency for the four major precious metals (that is, gold, silver, platinum and palladium), while accounting for geopolitics within a multivariate system. The implications of the estimated results for portfolio designs and hedging strategies are also analyzed. The results for the four metals system show significant short-run and long-run dependencies and interdependencies to news and past volatility. These results have become more pervasive when the exchange rate and FFR are included. Monetary policy also has a differential impact on the precious metals and the exchange rate volatilities. Finally, the applications of the results show the optimal weights in a two-asset portfolio and the hedging ratios for long positions.

Constraints on Flavored 2d CFT Partition Functions

We study the implications of modular invariance on 2d CFT partition functions with abelian or non-abelian currents when chemical potentials for the charges are turned on, i.e. when the partition functions are "flavored". We begin with a new proof of the transformation law for the modular transformation of such partition functions. Then we proceed to apply modular bootstrap techniques to constrain the spectrum of charged states in the theory. We improve previous upper bounds on the state with the greatest "mass-to-charge" ratio in such theories, as well as upper bounds on the weight of the lightest charged state and the charge of the weakest charged state in the theory. We apply the extremal functional method to theories that saturate such bounds, and in several cases we find the resulting prediction for the occupation numbers are precisely integers. Because such theories sometimes do not saturate a bound on the full space of states but do saturate a bound in the neutral sector of states, we find that adding flavor allows the extremal functional method to solve for some partition functions that would not be accessible to it otherwise.Comment: 45 pages, 16 Figures v3: typos corrected, expanded appendix on numeric implementatio