An all geometric discrete-time multiserver queueing system

In this work we look at a discrete-time multiserver queueing system where the number of available servers is distributed according to one of two geometrics. The arrival process is assumed to be general independent, the service times deterministically equal to one slot and the buffer capacity infinite. The queueing system resides in one of two states and the number of available servers follows a geometric distribution with parameter determined by the system state. At the end of a slot there is a fixed probability that the system evolves from one state to the other, with this probability depending on the current system state only, resulting in geometrically distributed sojourn times. We obtain the probability generating function (pgf) of the system content of an arbitrary slot in steady-state, as well as the pgf of the system content at the beginning of an arbitrary slot with a given state. Furthermore we obtain an approximation of the distribution of the delay a customer experiences in the proposed queueing system. This approximation is validated by simulation and the results are illustrated with a numerical example

A discrete-time HOL priority queue with multiple traffic classes.

A

Estimating internal pelvic sizes using external body measurements in the double-muscled Belgian Bleu beef breed

In the double-muscled (DM) Belgian Blue beef (BBB) breed, caesarean section (CS) is being applied systematically as a management tool to prevent dystocia. As a matter of fact, CS is the only possible way of calving in the breed. High birth weight and a relatively small pelvic area are the main causes of dystocia and, in the DM-BBB breed, the reasons for the systematically applied CS. Selection for lower birth weight and larger pelvic sizes might reduce dystocia and routine CS. Few data on inner pelvic sizes of pedigree animals are available. Using external measurements to estimate the inner pelvic sizes might be an option to resolve this problem. In this study, animals of the DM-BBB breed were measured and weighed on farms and in abattoirs. External and internal pelvic sizes increased with live weight and age of the animals. Gender had a significant influence on inner pelvic traits. Increased muscular conformation was associated with decreased inner pelvic dimensions. Models with weight, gender, age, withers height and outer pelvic width (TcTc) can be used to estimate inner pelvic sizes (R-2 between 0.35 and 0.77). The estimated inner pelvic sizes can then be used to genetically evaluate pelvic traits in the DM-BBB breed. Improving weight, withers height and TcTc width in combination with lowering muscular conformation may help to decrease the high rate of caesarean section in the DM-BBB

AN ULTRA-FAINT GALAXY CANDIDATE DISCOVERED in EARLY DATA from the MAGELLANIC SATELLITES SURVEY

We report a new ultra-faint stellar system found in Dark Energy Camera data from the first observing run of the Magellanic Satellites Survey (MagLiteS). MagLiteS J0644-5953 (Pictor II or Pic II) is a low surface brightness (μ = 28.5+1 -1 mag arcsec-2 within its half-light radius) resolved overdensity of old and metal-poor stars located at a heliocentric distance of 45+5 -4 kpc. The physical size (r1/2 = 46+15 -11) and low luminosity (Mv = -3.2+0.4 -0.5 mag) of this satellite are consistent with the locus of spectroscopically confirmed ultra-faint galaxies. MagLiteS J0644-5953 (Pic II) is located 11.3+3.1 -0.9 kpc from the Large Magellanic Cloud (LMC), and comparisons with simulation results in the literature suggest that this satellite was likely accreted with the LMC. The close proximity of MagLiteS J0644-5953 (Pic II) to the LMC also makes it the most likely ultra-faint galaxy candidate to still be gravitationally bound to the LMC.Peer reviewe

Transform-domain analysis of packet delay in network nodes with QoS-aware scheduling

In order to differentiate the perceived QoS between traffic classes in heterogeneous packet networks, equipment discriminates incoming packets based on their class, particularly in the way queued packets are scheduled for further transmission. We review a common stochastic modelling framework in which scheduling mechanisms can be evaluated, especially with regard to the resulting per-class delay distribution. For this, a discrete-time single-server queue is considered with two classes of packet arrivals, either delay-sensitive (1) or delay-tolerant (2). The steady-state analysis relies on the use of well-chosen supplementary variables and is mainly done in the transform domain. Secondly, we propose and analyse a new type of scheduling mechanism that allows precise control over the amount of delay differentiation between the classes. The idea is to introduce N reserved places in the queue, intended for future arrivals of class 1

Performance analysis of priority queueing systems in discrete time

The integration of different types of traffic in packet-based networks spawns the need for traffic differentiation. In this tutorial paper, we present some analytical techniques to tackle discrete-time queueing systems with priority scheduling. We investigate both preemptive (resume and repeat) and non-preemptive priority scheduling disciplines. Two classes of traffic are considered, high-priority and low-priority traffic, which both generate variable-length packets. A probability generating functions approach leads to performance measures such as moments of system contents and packet delays of both classes

Analysis of a Two-Class FCFS Queueing System with Interclass Correlation

This paper considers a discrete-time queueing system with one server and two classes of customers. All arriving customers are accommodated in one queue, and are served in a First-Come-First-Served order, regardless of their classes. The total numbers of arrivals during consecutive time slots are i.i.d. random variables with arbitrary distribution. The classes of consecutively arriving customers, however, are correlated in a Markovian way, i.e., the probability that a customer belongs to a class depends on the class of the previously arrived customer. Service-time distributions are assumed to be general but class-dependent. We use probability generating functions to study the system analytically. The major aim of the paper is to estimate the impact of the interclass correlation in the arrival stream on the queueing performance of the system, in terms of the (average) number of customers in the system and the (average) customer delay and customer waiting time

Magellan/M2FS Spectroscopy of Tucana 2 and Grus 1

We present results from spectroscopic observations with the Michigan/Magellan Fiber System (M2FS) of $147$ stellar targets along the line of sight to the newly-discovered `ultrafaint' stellar systems Tucana 2 (Tuc 2) and Grus 1 (Gru 1). Based on simultaneous estimates of line-of-sight velocity and stellar-atmospheric parameters, we identify 8 and 7 stars as probable members of Tuc 2 and and Gru 1, respectively. Our sample for Tuc 2 is sufficient to resolve an internal velocity dispersion of $8.6_{-2.7}^{+4.4}$ km s$^{-1}$ about a mean of $-129.1_{-3.5}^{+3.5}$ km s$^{-1}$ (solar rest frame), and to estimate a mean metallicity of [Fe/H]= $-2.23_{-0.12}^{+0.18}$. These results place Tuc 2 on chemodynamical scaling relations followed by dwarf galaxies, suggesting a dominant dark matter component with dynamical mass $2.7_{-1.3}^{+3.1}\times 10^6$ $\mathrm{M}_{\odot}$ enclosed within the central $\sim 160$ pc, and dynamical mass-to-light ratio $1900_{-900}^{+2200}$ $\mathrm{M}_{\odot}/L_{V,\odot}$. For Gru 1 we estimate a mean velocity of $-140.5_{-1.6}^{+2.4}$ km s$^{-1}$ and a mean metallicity of [Fe/H]=$-1.42_{-0.42}^{+0.55}$, but our sample does not resolve Gru 1's velocity dispersion. The radial coordinates of Tuc 2 and Gru 1 in Galactic phase space suggest that their orbits are among the most energetic within distance $\leq 300$ kpc. Moreover, their proximity to each other in this space arises naturally if both objects are trailing the Large Magellanic Cloud.Comment: replaced with ApJ-accepted version, all spectra and data products (including samples from posterior PDFs) are available at http://www.andrew.cmu.edu/user/mgwalker/tuc2gru1_dataproducts.tar.g