Heavy-traffic limits for Polling Models with Exhaustive Service and non-FCFS Service Order Policies

We study cyclic polling models with exhaustive service at each queue under a variety of non-FCFS local service orders, namely Last-Come-First-Served (LCFS) with and without preemption, Random-Order-of-Service (ROS), Processor Sharing (PS), the multi-class priority scheduling with and without preemption, Shortest-Job-First (SJF) and the Shortest Remaining Processing Time (SRPT) policy. For each of these policies, we rst express the waiting-time distributions in terms of intervisit-time distributions. Next, we use these expressions to derive the asymptotic waiting-time distributions under heavy-trac assumptions, i.e., when the system tends to saturate. The results show that in all cases the asymptotic wait

Heavy-traffic limits for Discriminatory Processor Sharing models with joint batch arrivals

We study the performance of Discriminatory Processor Sharing (DPS) systems, with exponential service times and in which batches of customers of different types may arrive simultaneously according to a Poisson process. We show that the stationary joint queue-length distribution exhibits state-space collapse in heavy traffic: as the load ρ tends to 1, the scaled joint queue-length vector (1−ρ)Q converges in distribution to the product of a determin

On the Q-phase of carbonaceous chondrites

One of the unresolved puzzles of meteoritics is the nature of the carrier of the so-called heavy planetary gases. Apparently, these gases reside mainly in a minor fraction, which has been dubbed Q by Lewis et al. in analogy of the naming by Papanastasiou et al. of a minor glassy phase in lunar rocks highly enriched in trace elements such as Pb and U. Q stands for the archaic term quintessence, the fifth or last and highest substance in ancient and medieval philosophy above fire, air, water and earth. In this contribution, an attempt is made to provide evidence that Q is carbonaceous, with carbon in the form of closed structures such as carbon nanotubes which serve as micro bottles for the heavy noble gases. To this end, Q was characterized with micro-PIXE and NRA, whereas HREM was used to search for nanotubes. Q itself was obtained as residue after chemical destruction of samples of Allende, Leoville and Vigarano

Deviations of the Kβ/Kα intensity ratio of Ti upon impact of low velocity ions

Deviations of the branching ratio of the decay of K-vacancies in Ti have been observed during bombardment with low velocity ions of H, He and N. Beams of these ions have been used for various applications in which resonant nuclear reactions were used as the main analytical technique, whereas the X-ray signal could conveniently be used for monitoring the accumulated charge. During the evaluation of this monitoring signal, it was observed that the commonly made assumption that the