Queue-length balance equations in multiclass multiserver queues and their generalizations

A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: the distribution of the queue length just before an arrival epoch equals the distribution of the queue length just after a departure epoch. The constraint for this result to be valid is that arrivals, and also service completions, with probability one occur individually, i.e., not in batches. We show that it is easy to write down somewhat similar balance equations for {\em multidimensional} queue-length processes for a quite general network of multiclass multiserver queues. We formally derive those balance equations under a general framework. They are called distributional relationships, and are obtained for any external arrival process and state dependent routing as long as certain stationarity conditions are satisfied and external arrivals and service completions do not simultaneously occur. We demonstrate the use of these balance equations, in combination with PASTA, by (i) providing very simple derivations of some known results for polling systems, and (ii) obtaining new results for some queueing systems with priorities. We also extend the distributional relationships for a non-stationary framework

Origin of Native Driving Force in Protein Folding

We derive an expression with four adjustable parameters that reproduces well the 20x20 Miyazawa-Jernigan potential matrix extracted from known protein structures. The numerical values of the parameters can be approximately computed from the surface tension of water, water-screened dipole interactions between residues and water and among residues, and average exposures of residues in folded proteins.Comment: LaTeX file, Postscript file; 4 pages, 1 figure (mij.eps), 2 table

Multipair contributions to the spin response of nuclear matter

We analyse the effect of non-central forces on the magnetic susceptibility of degenerate Fermi systems. These include the presence of contributions from transitions to states containing more than one quasiparticle-quasihole pair, which cannot be calculated within the framework of Landau Fermi-liquid theory, and renormalization of the quasiparticle magnetic moment, as well as explicit non-central contributions to the quasiparticle interaction. Consequently, the relationship between the Landau parameters and the magnetic susceptibility for Fermi systems with non-central forces is considerably more complicated than for systems with central forces. We use sum-rule arguments to place a lower bound on the contribution to the static susceptibility coming from transitions to multipair states