A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation

Consider a system performing a continuous-time random walk on the integers, subject to catastrophes occurring at constant rate, and followed by exponentially-distributed repair times. After any repair the system starts anew from state zero. We study both the transient and steady-state probability laws of the stochastic process that describes the state of the system. We then derive a heavy-traffic approximation to the model that yields a jump-diffusion process. The latter is equivalent to a Wiener process subject to randomly occurring jumps, whose probability law is obtained. The goodness of the approximation is finally discussed.Comment: 18 pages, 5 figures, paper accepted by "Methodology and Computing in Applied Probability", the final publication is available at http://www.springerlink.co

Enhanced mechanical and thermal strength in mixed enantiomers based supramolecular gel

Mixing supramolecular gels based on enantiomers leads to re-arrangement of gel fibers at the molecular level, which results in more favorable packing and tuneable properties. Bis(urea) compounds tagged with a phenylalanine methyl ester in racemic and enantiopure forms were syn-thesized. Both enantiopure and racemate compounds formed gels in a wide range of solvents and the racemate (1-rac) formed a stronger gel network compared to the enantiomers. The gel (1R+1S) obtained by mixing equimolar amount of enantiomers (1R and 1S) showed enhanced mechanical and thermal stability compared to enantiomers and racemate gels. The preservation of chirality in these compounds was analyzed by circular dichroism and optical rotation measurements. Analysis of the SEM and AFM images revealed that the network in the mixed gel is a combination of enantiomers and racemate fibers, which was further supported by solid state NMR. The analysis of the packing in xerogels by solid state NMR spectra and the existence of twisted-tape morphology in SEM and AFM images confirmed the presence of both self-sorted and co-assembled fibers in mixed gel. The enhanced thermal and mechanical strength may be attributed to the enhanced intermolecular forces between the racemate and enantiomer and the combination of both self-sorted and co-assembled enantiomers in the mixed gel.We thank University of Iceland Research Fund for financial support. D.G. thanks University of Iceland for the Doctoral Research grant and Z.K. thanks University of Ljubljana for the Erasmus exchange program. We thankfully acknowledge Dr. A. Rawal, The Mark Wainwright Analytical Centre, UNSW for solid state NMR studies and Dr. Sigrídur Jónsdóttir, University of Iceland for solution NMR and Mass spectroscopy. P.T. thanks the Australian Research Council for an ARC Centre of Excellence grant (CE140100036) and A.D.M. thanks the National Health and Medical Research Council for a Dementia Development Research Fellowship (APP1106751). L.F. and A.V. thank the FCT (UID/BIO/04469/2013), COMPETE 2020 (POCI-01-0145-FEDER-006684), and Norte2020 Programa Operacional Regional do Norte (BioTecNorte operation, NORTE-01-0145-FEDER-000004) for rheological studies. The rheological study was supported by a STSM Grant from COST Action CM1402 Crystallize.info:eu-repo/semantics/publishedVersio

Total Idle Time Density Function of M/C<inf>2</inf>/1 Systems under (0,k) Policy

© Published under licence by IOP Publishing Ltd. The aim of this paper is to derive the probability density function (pdf) of the total idle time of busy period of M/C2/1 queues operating under control policies through lattice path combinatorics (LPC) approach. The service distribution is approximated by Coxian two-phase distribution. We focus on deriving the pdf of total idle time of M/C2/1 queues under (0,k) control policy, wherein the server goes on the vacation when the system becomes empty and re-opens for service immediately at the arrival of the kthcostumer. We present an important result which is the theorem of the pdf of total idle time when system is in busy period that ends with a departure