Scheduling a multi class queue with many exponential servers: asymptotic optimality in heavy traffic

We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal. Our cost is an expected cumulative discounted function, linear or nonlinear, of appropriately normalized performance measures. As a special case, the cost per unit time can be a function of the number of customers waiting to be served in each class, the number actually being served, the abandonment rate, the delay experienced by customers, the number of idling servers, as well as certain combinations thereof. We study the system in an asymptotic heavy-traffic regime where the number of servers n and the offered load r are simultaneously scaled up and carefully balanced: n\approx r+\beta \sqrtr for some scalar \beta. This yields an operation that enjoys the benefits of both heavy traffic (high server utilization) and light traffic (high service levels.

Holistic assessment of call centre performance

In modern call centres 60–70% of the operational costs come in the form of the human agents who take the calls. Ensuring that the call centre operates at lowest cost and maximum efficiency involves a trade‐off of the cost of agents against lost revenue and increased customer dissatisfaction due to lost calls. Modelling the performance characteristics of a call centre in terms of the agent queue alone misses key performance influencers, specifically the interaction between channel availability at the media gateway and the time a call is queued. A blocking probability at the media gateway, as low as 0.45%, has a significant impact on the degree of queuing observed and therefore the cost and performance of the call centre. Our analysis also shows how abandonment impacts queuing delay. However, the call centre manager has less control over this than the level of contention at the media gateway. Our commercial assessment provides an evaluation of the balance between abandonment and contention, and shows that the difference in cost between the best and worst strategy is £130K per annum, however this must be balanced against a possible additional £2.98 m exposure in lost calls if abandonment alone is used

Constraining dark matter halo properties using lensed SNLS supernovae

This paper exploits the gravitational magnification of SNe Ia to measure properties of dark matter haloes. The magnification of individual SNe Ia can be computed using observed properties of foreground galaxies and dark matter halo models. We model the dark matter haloes of the galaxies as truncated singular isothermal spheres with velocity dispersion and truncation radius obeying luminosity dependent scaling laws. A homogeneously selected sample of 175 SNe Ia from the first 3-years of the Supernova Legacy Survey (SNLS) in the redshift range 0.2 < z < 1 is used to constrain models of the dark matter haloes associated with foreground galaxies. The best-fitting velocity dispersion scaling law agrees well with galaxy-galaxy lensing measurements. We further find that the normalisation of the velocity dispersion of passive and star forming galaxies are consistent with empirical Faber-Jackson and Tully-Fisher relations, respectively. If we make no assumption on the normalisation of these relations, we find that the data prefer gravitational lensing at the 92 per cent confidence level. Using recent models of dust extinction we deduce that the impact of this effect on our results is very small. We also investigate the brightness scatter of SNe Ia due to gravitational lensing. The gravitational lensing scatter is approximately proportional to the SN Ia redshift. We find the constant of proportionality to be B = 0.055 +0.039 -0.041 mag (B < 0.12 mag at the 95 per cent confidence level). If this model is correct, the contribution from lensing to the intrinsic brightness scatter of SNe Ia is small for the SNLS sample.Comment: 11 pages, 7 figures, accepted for publication in MNRA

The WiggleZ Dark Energy Survey: Direct constraints on blue galaxy intrinsic alignments at intermediate redshifts

Correlations between the intrinsic shapes of galaxy pairs, and between the intrinsic shapes of galaxies and the large-scale density field, may be induced by tidal fields. These correlations, which have been detected at low redshifts (z<0.35) for bright red galaxies in the Sloan Digital Sky Survey (SDSS), and for which upper limits exist for blue galaxies at z~0.1, provide a window into galaxy formation and evolution, and are also an important contaminant for current and future weak lensing surveys. Measurements of these alignments at intermediate redshifts (z~0.6) that are more relevant for cosmic shear observations are very important for understanding the origin and redshift evolution of these alignments, and for minimising their impact on weak lensing measurements. We present the first such intermediate-redshift measurement for blue galaxies, using galaxy shape measurements from SDSS and spectroscopic redshifts from the WiggleZ Dark Energy Survey. Our null detection allows us to place upper limits on the contamination of weak lensing measurements by blue galaxy intrinsic alignments that, for the first time, do not require significant model-dependent extrapolation from the z~0.1 SDSS observations. Also, combining the SDSS and WiggleZ constraints gives us a long redshift baseline with which to constrain intrinsic alignment models and contamination of the cosmic shear power spectrum. Assuming that the alignments can be explained by linear alignment with the smoothed local density field, we find that a measurement of \sigma_8 in a blue-galaxy dominated, CFHTLS-like survey would be contaminated by at most +/-0.02 (95% confidence level, SDSS and WiggleZ) or +/-0.03 (WiggleZ alone) due to intrinsic alignments. [Abridged]Comment: 18 pages, 12 figures, accepted to MNRAS; v2 has correction to one author's name, NO other changes; v3 has minor changes in explanation and calculations, no significant difference in results or conclusions; v4 has an additional footnote about model interpretation, no changes to data/calculations/result

Testing a simple recipe for estimating galaxy masses from minimal observational data

The accuracy and robustness of a simple method to estimate the total mass profile of a galaxy is tested using a sample of 65 cosmological zoom-simulations of individual galaxies. The method only requires information on the optical surface brightness and the projected velocity dispersion profiles and therefore can be applied even in case of poor observational data. In the simulated sample massive galaxies ($\sigma \simeq 200-400$ \kms) at redshift $z=0$ have almost isothermal rotation curves for broad range of radii (RMS $\simeq 5$ for the circular speed deviations from a constant value over $0.5R_{\rm eff} < r < 3R_{\rm eff}$). For such galaxies the method recovers the unbiased value of the circular speed. The sample averaged deviation from the true circular speed is less than $\sim 1$ with the scatter of $\simeq 5-8$ (RMS) up to $R \simeq 5R_{\rm eff}$. Circular speed estimates of massive non-rotating simulated galaxies at higher redshifts ($z=1$ and $z=2$) are also almost unbiased and with the same scatter. For the least massive galaxies in the sample ($\sigma < 150$ \kms) at $z=0$ the RMS deviation is $\simeq 7-9$ and the mean deviation is biased low by about $1-2$. We also derive the circular velocity profile from the hydrostatic equilibrium (HE) equation for hot gas in the simulated galaxies. The accuracy of this estimate is about RMS $\simeq 4-5$ for massive objects ($M > 6.5\times 10^{12} M_\odot$) and the HE estimate is biased low by $\simeq 3-4$, which can be traced to the presence of gas motions. This implies that the simple mass estimate can be used to determine the mass of observed massive elliptical galaxies to an accuracy of $5-8$ and can be very useful for galaxy surveys.Comment: 15 pages, 14 figures, 1 tabl

Probing Orientifold Behavior Near NS Branes

The effect of NS 5 branes on an orientifold is studied. The orientifold is allowed to pass through a pile of k NS branes forming a regularized CHS geometry. Its effect on open strings in its vicinity is used to study the change in the orientifold charge induced by the NS branes.Comment: Important references added, 30 pages, 8 figure

Missing Dark Matter in the Local Universe

A sample of 11 thousand galaxies with radial velocities V_ LG < 3500 km/s is used to study the features of the local distribution of luminous (stellar) and dark matter within a sphere of radius of around 50 Mpc around us. The average density of matter in this volume, Omega_m,loc=0.08+-0.02, turns out to be much lower than the global cosmic density Omega_m,glob=0.28+-0.03. We discuss three possible explanations of this paradox: 1) galaxy groups and clusters are surrounded by extended dark halos, the major part of the mass of which is located outside their virial radii; 2) the considered local volume of the Universe is not representative, being situated inside a giant void; and 3) the bulk of matter in the Universe is not related to clusters and groups, but is rather distributed between them in the form of massive dark clumps. Some arguments in favor of the latter assumption are presented. Besides the two well-known inconsistencies of modern cosmological models with the observational data: the problem of missing satellites of normal galaxies and the problem of missing baryons, there arises another one - the issue of missing dark matter.Comment: 19 pages, 7 figures, 1 table (accepted

Dark energy constraints from cosmic shear power spectra: impact of intrinsic alignments on photometric redshift requirements

Cosmic shear constrains cosmology by exploiting the apparent alignments of pairs of galaxies due to gravitational lensing by intervening mass clumps. However galaxies may become (intrinsically) aligned with each other, and with nearby mass clumps, during their formation. This effect needs to be disentangled from the cosmic shear signal to place constraints on cosmology. We use the linear intrinsic alignment model as a base and compare it to an alternative model and data. If intrinsic alignments are ignored then the dark energy equation of state is biased by ~50 per cent. We examine how the number of tomographic redshift bins affects uncertainties on cosmological parameters and find that when intrinsic alignments are included two or more times as many bins are required to obtain 80 per cent of the available information. We investigate how the degradation in the dark energy figure of merit depends on the photometric redshift scatter. Previous studies have shown that lensing does not place stringent requirements on the photometric redshift uncertainty, so long as the uncertainty is well known. However, if intrinsic alignments are included the requirements become a factor of three tighter. These results are quite insensitive to the fraction of catastrophic outliers, assuming that this fraction is well known. We show the effect of uncertainties in photometric redshift bias and scatter. Finally we quantify how priors on the intrinsic alignment model would improve dark energy constraints.Comment: 14 pages and 9 figures. Replaced with final version accepted in "Gravitational Lensing" Focus Issue of the New Journal of Physics at http://www.iop.org/EJ/abstract/1367-2630/9/12/E0

The Whole is Greater than the Sum of the Parts: Optimizing the Joint Science Return from LSST, Euclid and WFIRST

The focus of this report is on the opportunities enabled by the combination of LSST, Euclid and WFIRST, the optical surveys that will be an essential part of the next decade's astronomy. The sum of these surveys has the potential to be significantly greater than the contributions of the individual parts. As is detailed in this report, the combination of these surveys should give us multi-wavelength high-resolution images of galaxies and broadband data covering much of the stellar energy spectrum. These stellar and galactic data have the potential of yielding new insights into topics ranging from the formation history of the Milky Way to the mass of the neutrino. However, enabling the astronomy community to fully exploit this multi-instrument data set is a challenging technical task: for much of the science, we will need to combine the photometry across multiple wavelengths with varying spectral and spatial resolution. We identify some of the key science enabled by the combined surveys and the key technical challenges in achieving the synergies.Comment: Whitepaper developed at June 2014 U. Penn Workshop; 28 pages, 3 figure

Quadruple-peaked spectral line profiles as a tool to constrain gravitational potential of shell galaxies

Stellar shells observed in many giant elliptical and lenticular as well as a few spiral and dwarf galaxies, presumably result from galaxy mergers. Line-of-sight velocity distributions of the shells could, in principle, if measured with a sufficiently high S/N, constitute one of methods to constrain the gravitational potential of the host galaxy. Merrifield & Kuijken (1998) predicted a double-peaked line profile for stationary shells resulting from a nearly radial minor merger. In this paper, we aim at extending their analysis to a more realistic case of expanding shells, inherent to the merging process, whereas we assume the same type of merger and the same orbital geometry. We use analytical approach as well as test particle simulations to predict the line-of-sight velocity profile across the shell structure. Simulated line profiles are convolved with spectral PSFs to estimate the peak detectability. The resulting line-of-sight velocity distributions are more complex than previously predicted due to non-zero phase velocity of the shells. In principle, each of the Merrifield & Kuijken (1998) peaks splits into two, giving a quadruple-peaked line profile, which allows more precise determination of the potential of the host galaxy and, moreover, contains additional information. We find simple analytical expressions that connect the positions of the four peaks of the line profile and the mass distribution of the galaxy, namely the circular velocity at the given shell radius and the propagation velocity of the shell. The analytical expressions were applied to a test-particle simulation of a radial minor merger and the potential of the simulated host galaxy was successfully recovered. The shell kinematics can thus become an independent tool to determine the content and distribution of the dark matter in shell galaxies, up to ~100 kpc from the center of the host galaxy.Comment: 15 pages, 16 figures | v2: accepted for publication in A&A, minor language correction