Routing and Admission Control in General Topology Networks with Poisson Arrivals

Emerging high-speed networks will carry traffic for services such as video-on-demand and video teleconferencing that require resource reservation along the path on which the traffic is sent. High bandwidth-delay product of these networks prevents circuit rerouting, i.e., once a circuit is routed on a certain path, the bandwidth taken by this circuit remains unavailable for the duration (holding time) of this circuit. As a result, such networks will need effectiveroutingandadmission controlstrategies. Recently developed on-line routing and admission control strategies have logarithmic competitive ratios with respect to theadmission ratio(the fraction of admitted circuits). Such guarantees on performance are rather weak in the most interesting case where the rejection ratio of the optimum algorithm is very small or even 0. Unfortunately, these guarantees cannot be improved in the context of the considered models, making it impossible to use these models to identify algorithms that are going to perform well in practice. In this paper we develop routing and admission control strategies for a probabilistic model, where the requests for virtual circuits between any two points arrive according to a Poisson process and where the circuit holding times are exponentially distributed. Our model is close to the one that was developed to analyze and tune the (currently used) strategies for managing traffic in long-distance telephone networks. We strengthen this model by assuming that the rates of the Poisson processes (the “traffic matrix”) are unknown to the algorithm and are chosen by the adversary. Our strategy is competitive with respect to the expectedrejection ratio. More precisely, it achieves an expected rejection ratio of at mostR* + ?, whereR* is the optimum expected rejection ratio. The expectations are taken over the distribution of the request sequences, and, whereris the maximum fraction of an edge bandwidth that can be requested by a single circuit. Our result should be viewed in the context of the previous competitive routing and admission control strategies that requirer ≤ 1/log n, but are not able to formally analyze the (intuitively clear) relation betweenrand the performance achievable in realistic situations.     

Subexponential decay of correlations

We describe a method for proving subexponential lower bounds for correlations functions, and apply it to study decay of correlations for maps with countable Markov partitions. One result is that LS Young’s upper estimates [Y2] are optimal in many situations. Our method is based on a general result concerning the asymptotics of renewal sequences of bounded operators acting on Banach spaces, which we apply to the iterates of the transfer operator. Oblatum 14-VII-2001 & 5-VI-2002?Published online: 6 August 2002 Dedicated to B. Weiss on the occasion of his 60th birthday RID="*" ID="*"This research was supported by the Nuffield Foundation, NUF-NAL 00.     

Invariant measures and asymptotics for some skew products

For certain group extensions of uniquely ergodic transformations, we identify all locally finite, ergodic, invariant measures. These are Maharam type measures. We also establish the asymptotic behaviour for these group extensions proving logarithmic ergodic theorems, and bounded rational ergodicity.     

The isotopic composition of evaporating waters - review of the historical evolution leading up to the Craig-Gordon model

Attempts to explain the variations in the abundance of heavy isotopic species of water throughout the hydrologic cycle solely by means of the classical equilibrium-fractionation processes could not be reconciled with measured abundances of the isotopic species in residues of "evaporation systems". Focusing on the evaporation of surface waters, the paper follows the evolution of the concepts during the 1950-ties and early 1960-ties leading up to the formulation of the Craig-Gordan Evaporation Model in 1965.     

Thermodynamic formalism for null recurrent potentials

We extend Ruelle’s Perron-Frobenius theorem to the case of Hölder continuous functions on a topologically mixing topological Markov shift with a countable number of states. LetP(?) denote the Gurevic pressure of ? and letL _? be the corresponding Ruelle operator. We present a necessary and sufficient condition for the existence of a conservative measure ν and a continuous functionh such thatL _? ^* ν=e ^P(?)ν,L _? h=e ^P(?) h and characterize the case when ∝hdν<∞. In the case whendm=hdν is infinite, we discuss the asymptotic behaviour ofL _? ^k , and show how to interpretdm as an equilibrium measure. We show how the above properties reflect in the behaviour of a suitable dynamical zeta function. These resutls extend the results of [18] where the case ∝hdν<∞ was studied.     

Invariant Radon measures for horocycle flows on Abelian covers

We classify the ergodic invariant Radon measures for horocycle flows on ^d–covers of compact Riemannian surfaces of negative curvature, thus proving a conjecture of M. Babillot and F. Ledrappier. An important tool is a result in the ergodic theory of equivalence relations concerning the reduction of the range of a cocycle by the addition of a coboundary. Dedicated to the memory of M. Babillot     

Probing the molecular interaction of chymotrypsin with organophosphorus compounds by 31P diffusion NMR in aqueous solutions

In the present study, we applied for the first time (31)P diffusion NMR to resolve different species obtained by the addition of organophosphorus compounds (OP) such as diisopropyl phosphorofluoridate (DFP) or 1-pyrenebutyl phosphorodichloridate (PBPDC) to alpha-chymotrypsin (Cht). (31)P diffusion NMR was used since the products of these reactions constitute a mixture of OP-covalent conjugates of the enzyme and OP-containing hydrolysis products that have noninformative (1)H NMR spectra. It was shown that the peak, attributed to the covalent native diisopropylphosphoryl-Cht (DIP-Cht) conjugate by chemical shift considerations, has a greater diffusion coefficient (D = (0.65 +/- 0.01) x 10(-5) cm(2) s(-1)) than expected from its molecular mass (approximately 25 kDa). This peak was therefore suggested to consist of at least two superimposed signals of diisopropyl phosphoryl (DIP) pools of high and low molecular weights that happen to have the same chemical shift. This conclusion was substantiated by the use of DMSO-d(6) that separated the overlapping signals. Diffusion measurements performed on the extensively dialyzed and unfolded DIP-Cht conjugate still resulted in a high diffusion coefficient ((0.30 +/- 0.05) x 10(-5) cm(2) s(-1)) relative to the assumed molecular mass. This observation was attributed to a dynamic dealkylation at the OP moiety (i.e., aging) that occurred during the relatively long diffusion measurements, where DIP-Cht was converted to the corresponding monoisopropyl phosphoryl Cht (MIP-Cht) conjugate. Homogeneous aged forms of OP-Cht were obtained by use of DFP and heat-induced dealkylation of DIP-Cht, and by PBPDC that provided the aged form via the hydrolysis of a P-Cl bond (PBP-Cht). The thermally stable aged conjugates enabled a reliable determination of the diffusion coefficients over several days of data acquisition, and the values found were (0.052 +/- 0.002) x 10(-5) cm(2) s(-1) and (0.054 +/-0.004) x 10(-5) cm(2) s(-1) for the MIP-Cht and the PBP-Cht adducts, respectively, values in the range expected for a species with a molecular weight of 25 kDa. The advantages and limitations of (31)P diffusion NMR in corroborating the type of species that prevail in such systems are briefly discussed.