Exponential penalty function control of loss networks

We introduce penalty-function-based admission control policies to approximately maximize the expected reward rate in a loss network. These control policies are easy to implement and perform well both in the transient period as well as in steady state. A major advantage of the penalty approach is that it avoids solving the associated dynamic program. However, a disadvantage of this approach is that it requires the capacity requested by individual requests to be sufficiently small compared to total available capacity. We first solve a related deterministic linear program (LP) and then translate an optimal solution of the LP into an admission control policy for the loss network via an exponential penalty function. We show that the penalty policy is a target-tracking policy--it performs well because the optimal solution of the LP is a good target. We demonstrate that the penalty approach can be extended to track arbitrarily defined target sets. Results from preliminary simulation studies are included.Comment: Published at http://dx.doi.org/10.1214/105051604000000936 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Analysis of join-the-shortest-queue routing for web server farms

Join the Shortest Queue (JSQ) is a popular routing policy for server farms. However, until now all analysis of JSQ has been limited to First-Come-First-Serve (FCFS) server farms, whereas it is known that web server farms are better modeled as Processor Sharing (PS) server farms. We provide the first approximate analysis of JSQ in the PS server farm model for general job-size distributions, obtaining the distribution of queue length at each queue. To do this, we approximate the queue length of each queue in the server farm by a one-dimensional Markov chain, in a novel fashion. We also discover some interesting insensitivity properties of PS server farms with JSQ routing, and discuss the near-optimality of JSQ

Closed-form approximations for optimal (r, q) and (S, T) policies in a parallel processing environment

Ministry of Education, Singapore under its Academic Research Funding Tier

Simulating the global distribution of nitrogen isotopes in the ocean

We present a new nitrogen isotope model incorporated into the three-dimensional ocean component of a global Earth system climate model designed for millennial timescale simulations. The model includes prognostic tracers for the two stable nitrogen isotopes, 14N and 15N, in the nitrate (NO3−), phytoplankton, zooplankton, and detritus variables of the marine ecosystem model. The isotope effects of algal NO3− uptake, nitrogen fixation, water column denitrification, and zooplankton excretion are considered as well as the removal of NO3− by sedimentary denitrification. A global database of δ15NO3− observations is compiled from previous studies and compared to the model results on a regional basis where sufficient observations exist. The model is able to qualitatively and quantitatively reproduce many of the observed patterns such as high subsurface values in water column denitrification zones and the meridional and vertical gradients in the Southern Ocean. The observed pronounced subsurface minimum in the Atlantic is underestimated by the model presumably owing to too little simulated nitrogen fixation there. Sensitivity experiments reveal that algal NO3− uptake, nitrogen fixation, and water column denitrification have the strongest effects on the simulated distribution of nitrogen isotopes, whereas the effect from zooplankton excretion is weaker. Both water column and sedimentary denitrification also have important indirect effects on the nitrogen isotope distribution by reducing the fixed nitrogen inventory, which creates an ecological niche for nitrogen fixers and, thus, stimulates additional N2 fixation in the model. Important model deficiencies are identified, and strategies for future improvement and possibilities for model application are outlined

Glacial-interglacial modulation of the marine nitrogen cycle by high-latitude O2 supply to the global thermocline

Author Posting. © American Geophysical Union, 2004. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Paleoceanography 19 (2004): PA4007, doi:10.1029/2003PA001000.An analysis of sedimentary nitrogen isotope records compiled from widely distributed marine environments emphasizes the global synchrony of denitrification changes and provides evidence for a strong temporal coupling of these variations to changes in nitrogen fixation as previously inferred. We explain the global coherence of these records by a simple physical control on the flux of dissolved oxygen to suboxic zones and the coupling to fixation via the supply of phosphorus to diazotrophs in suitable environments. According to our hypothesis, lower glacial-stage sea surface temperature increased oxygen solubility, while stronger winds in high-latitude regions enhanced the rate of thermocline ventilation. The resultant colder, rapidly flushed thermocline lessened the spatial extent of denitrification and, consequently, N fixation. During warm periods, sluggish circulation of warmer, less oxygen rich thermocline waters caused expansion of denitrification zones and a concomitant increase in N fixation. Local fluctuations in export productivity would have modulated this global signal.Financial support for this work was provided by the Natural Sciences and Engineering Research Council of Canada and by a WHOI postdoctoral fellowship to MK

A review of nitrogen isotopic alteration in marine sediments

Key Points: Use of sedimentary nitrogen isotopes is examined; On average, sediment 15N/14N increases approx. 2 per mil during early burial; Isotopic alteration scales with water depth Abstract: Nitrogen isotopes are an important tool for evaluating past biogeochemical cycling from the paleoceanographic record. However, bulk sedimentary nitrogen isotope ratios, which can be determined routinely and at minimal cost, may be altered during burial and early sedimentary diagenesis, particularly outside of continental margin settings. The causes and detailed mechanisms of isotopic alteration are still under investigation. Case studies of the Mediterranean and South China Seas underscore the complexities of investigating isotopic alteration. In an effort to evaluate the evidence for alteration of the sedimentary N isotopic signal and try to quantify the net effect, we have compiled and compared data demonstrating alteration from the published literature. A >100 point comparison of sediment trap and surface sedimentary nitrogen isotope values demonstrates that, at sites located off of the continental margins, an increase in sediment 15N/14N occurs during early burial, likely at the seafloor. The extent of isotopic alteration appears to be a function of water depth. Depth-related differences in oxygen exposure time at the seafloor are likely the dominant control on the extent of N isotopic alteration. Moreover, the compiled data suggest that the degree of alteration is likely to be uniform through time at most sites so that bulk sedimentary isotope records likely provide a good means for evaluating relative changes in the global N cycle

Macronutrient supply, uptake and recycling in the coastal ocean of the west Antarctic Peninsula

Nutrient supply, uptake and cycling underpin high primary productivity over the continental shelf of the west Antarctic Peninsula (WAP). Here we use a suite of biogeochemical and isotopic data collected over five years in northern Marguerite Bay to examine these macronutrient dynamics and their controlling biological and physical processes in the WAP coastal ocean. We show pronounced nutrient drawdown over the summer months by primary production which drives a net seasonal nitrate uptake of 1.83 mol N m-2 yr-1, equivalent to net carbon uptake of 146 g C m-2 yr-1. High primary production fuelled primarily by deep-sourced macronutrients is diatom-dominated, but non-siliceous phytoplankton also play a role. Strong nutrient drawdown in the uppermost surface ocean has the potential to cause transient nitrogen limitation before nutrient resupply and/or regeneration. Interannual variability in nutrient utilisation corresponds to winter sea ice duration and the degree of upper ocean mixing, implying susceptibility to physical climate change. The nitrogen isotope composition of nitrate (δ15NNO3) shows a utilisation signal during the growing seasons with a community-level net isotope effect of 4.19 ± 0.29‰. We also observe significant deviation of our data from modelled and observed utilisation trends, and argue that this is driven primarily by water column nitrification and meltwater dilution of surface nitrate. This study is important because it provides a detailed description of the nutrient biogeochemistry underlying high primary productivity at the WAP, and shows that surface ocean nutrient inventories in the Antarctic sea ice zone can be affected by intense recycling in the water column, meltwater dilution and sea ice processes, in addition to utilisation in the upper ocean