Cyclic networks with general blocking and starvation

We introducegeneral starvation and consider cyclic networks withgeneral blocking and starvation (GBS). The mechanism of general blocking allows the server to process a limited number of jobs when the buffer downstream is full, and that of general starvation allows the server to perform a limited number of services in anticipation of jobs that are yet to arrive. The two main goals of this paper are to investigate how the throughput of cyclic GBS networks is affected by varying (1) the total number of jobsJ, and (2) the buffer allocationk=(k₁..., k_m) subject to a fixed total buffer capacityK=k ₁ +... + k_m. In particular, we obtain sufficient conditions for the throughput to be symmetric inJ and to be maximized whenJ=K/2. We also show that the equal buffer allocation is optimal under the two regimes of light or heavy usage. In order to establish these results, we obtain several intermediate structural properties of the throughput, using duality, reversibility, and concavity, which are of independent interest.Research supported in part by NSF Grant No. ECS-8919818.     

Effect of Pressure on Fluid Damping in MEMS Torsional Resonators with Flow Ranging from Continuum to Molecular Regime

High quality factor of dynamic structures at micro and nano scale is exploited in various applications of micro electro-mechanical systems (MEMS) and nano electro-mechanical system. The quality factor of such devices can be very high in vacuum. However, when vacuum is not desirable or not possible, the tiny structures must vibrate in air or some other gas at pressure levels that may vary from atmospheric to low vacuum. The interaction of the surrounding fluid with the vibrating structure leads to dissipation, thus bringing down the quality factor. Depending on the ambient fluid pressure or the gap between the vibrating and the fixed structure, the fluid motion can range from continuum flow to molecular flow giving a wide range of dissipation. The relevant fluid flow characteristics are determined by the Knudsen number which is the ratio of the mean free path of the gas molecule to the characteristic flow length of the device. This number is very small for continuum flow and reasonably big for molecular flow. In this paper, we study the effect of fluid pressure on the quality factor by carrying out experiments on a MEMS device that consists of a double gimbaled torsional resonator. Such devices are commonly used in optical cross-connects and switches. We only vary fluid pressure to make the Knudsen number go through the entire range of continuum flow, slip flow, transition flow, and molecular flow. We experimentally determine the quality factor of the torsional resonator at different air pressures ranging from 760 Torr to 0.001 Torr. The variation of this pressure over six orders of magnitude ensures required rarefaction to range over all flow conditions. Finally, we get the variation of quality factor with pressure. The result indicates that the quality factor, Q, follows a power law, Q ∝P ^–r , with different values of the exponent r in different flow regimes. In the second part of the paper, we propose the use of effective viscosity for considering velocity slip conditions in solving Navier–Stokes equation numerically. This concept is validated with analytical results for a simple case and then compared with the experimental results presented in this paper. The study shows that the effective viscosity concept can be used effectively even for the molecular regime if the air-gap to length ratio is sufficiently small (h ₀/L<0.01). As this ratio increases, the range of validity decreases.     

Lanthanum(III) and prasedymium(III) complexes with piperazine dithiosemicarbazones

Lanthanum(III) and praseodymium(III) complexes of the type [Ln(L)Cl(H₂O)]₂ (Ln = La(III) or Pr(III); LH₂ = dithiosemicarbazone ligands derived from piperazine dithiosemicarbazide and benzaldehyde, 4-nitrobenzaldehyde, and 2-methoxybenzaldehyde) have been synthesized in methanol in the presence of sodium hydroxide. The complexes have been characterized by elemental analyses, molecular weight, molar conductance, electronic absorption, IR, and ¹H and ¹³C NMR spectral studies. Nephelauxetic ratio, covalency parameter, and bonding parameter for these complexes have also been calculated. Thermal studies of the complexes have been carried out using TG, DTG, and DSC techniques. Kinetic parameters, such as apparent activation energy and order of reaction, were determined by the Coats-Redfern graphical method. The heats of reaction for different reaction steps were calculated from DSC curves. The article was submitted by the authors in English.     

Rescaled mean spherical approximation structure factor for an aqueous suspension of polystyrene spheres

Rescaled mean spherical approximation (RMSA) has been used to calculate the structure factor for the aqueous suspension of polystyrene macroions with the interaction potential taken according to Derjaguin and Landau (1941) and Verwey and Overbeek (1948) (DLVO) model. The effects of charge over the macroion and size on the surface potential and therefore, the structure factor have been studied. The breakdown of the DLVO potential with an excess charge over the macroion (⩾800e) has been reported. The oscillation in the first peak height of structure factor versus wave vector curve with size has been correlated with the Debye length.     

Sample-path optimization of convex stochastic performance functions

In this paper we propose a method for optimizing convex performance functions in stochastic systems. These functions can include expected performance in static systems and steady-state performance in discrete-event dynamic systems; they may be nonsmooth. The method is closely related to retrospective simulation optimization; it appears to overcome some limitations of stochastic approximation, which is often applied to such problems. We explain the method and give computational results for two classes of problems: tandem production lines with up to 50 machines, and stochastic PERT (Program Evaluation and Review Technique) problems with up to 70 nodes and 110 arcs. Sponsored by the National Science Foundation under grant number CCR-9109345, by the Air Force Systems Command, USAF, under grant numbers F49620-93-1-0068 and F49620-95-1-0222, by the U.S. Army Research Office under grant number DAAL03-92-G-0408, and by the U.S. Army Space and Strategic Defense Command under contract number DASG60-91-C-0144. The U.S. Government has certain rights in this material, and is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. Sponsored by a Wisconsin/Hilldale Research Award, by the U.S. Army Space and Strategic Defense Command under contract number DASG60-91-C-0144, and the Air Force Systems Command, USAF, under grant number F49620-93-1-0068. Sponsored by the National Science Foundation under grant number DDM-9201813.