The effect of service time variability on maximum queue lengths in M^X/G/1 queues

We study the impact of service-time distributions on the distribution of the maximum queue length during a busy period for the M^X/G/1 queue. The maximum queue length is an important random variable to understand when designing the buffer size for finite buffer (M/G/1/n) systems. We show the somewhat surprising result that for three variations of the preemptive LCFS discipline, the maximum queue length during a busy period is smaller when service times are more variable (in the convex sense).Comment: 12 page

Controls on Highly Siderophile Element Concentrations in Martian Basalt: Sulfide Saturation and Under-Saturation

Highly siderophile elements (HSE; Re, Au and the platinum group elements) in shergottites exhibit a wide range from very high, similar to the terrestrial mantle, to very low, similar to sulfide saturated mid ocean ridge basalt (e.g., [1]). This large range has been difficult to explain without good constraints on sulfide saturation or under-saturation [2]. A new model for prediction of sulfide saturation places new constraints on this problem [3]. Shergottite data: For primitive shergottites, pressure and temperature estimates are between 1.2-1.5 GPa, and 1350-1470 C [4]. The range of oxygen fugacities is from FMQ-2 to IW, where the amount of Fe2O3 is low and thus does not have a significant effect on the S saturation values. Finally, the bulk compositions of shergottites have been reported in many recent studies (e.g., [5]). All of this information will be used to test whether shergottites are sulfide saturated [3]. Modeling values and results: The database for HSE partition coefficients has been growing with many new data for silicates and oxides [6-8] to complement a large sulfide database [9- 11]. Combining these data with simple batch melting models allows HSE contents of mantle melts to be estimated for sulfide-bearing vs. sulfide-free mantle. Combining such models with fractional crystallization modeling (e.g., [12]) allows HSE contents of more evolved liquids to be modeled. Most primitive shergottites have high HSE contents (and low S contents) that can be explained by sulfide under-saturated melting of the mantle. An exception is Dhofar 019 which has high S contents and very low HSE contents suggesting sulfide saturation. Most evolved basaltic shergottites have lower S contents than saturation, and intermediate HSE contents that can be explained by olivine, pyroxene, and chromite fractionation. An exception is EET A79001 lithology B, which has very low HSE contents and S contents higher than sulfide saturation values . evidence for sulfide saturation during late fractional crystallization. These results show that shergottite HSE contents are controlled by silicates, oxides, and sulfides. In addition, the mantle producing the most primitive shergottites did not contain near chondritic relative ratios of the HSEs like the terrestrial mantle, and did not experience a late chondritic veneer

FCFS Parallel Service Systems and Matching Models

We consider three parallel service models in which customers of several types are served by several types of servers subject to a bipartite compatibility graph, and the service policy is first come first served. Two of the models have a fixed set of servers. The first is a queueing model in which arriving customers are assigned to the longest idling compatible server if available, or else queue up in a single queue, and servers that become available pick the longest waiting compatible customer, as studied by Adan and Weiss, 2014. The second is a redundancy service model where arriving customers split into copies that queue up at all the compatible servers, and are served in each queue on FCFS basis, and leave the system when the first copy completes service, as studied by Gardner et al., 2016. The third model is a matching queueing model with a random stream of arriving servers. Arriving customers queue in a single queue and arriving servers match with the first compatible customer and leave immediately with the customer, or they leave without a customer. The last model is relevant to organ transplants, to housing assignments, to adoptions and many other situations. We study the relations between these models, and show that they are closely related to the FCFS infinite bipartite matching model, in which two infinite sequences of customers and servers of several types are matched FCFS according to a bipartite compatibility graph, as studied by Adan et al., 2017. We also introduce a directed bipartite matching model in which we embed the queueing systems. This leads to a generalization of Burke's theorem to parallel service systems

Allan Hills 76005 Polymict Eucrite Pairing Group: Curatorial and Scientific Update on a Jointly Curated Meteorite

Allan Hills 76005 (or 765) was collected by the joint US-Japan field search for meteorites in 1976-77. It was described in detail as "pale gray in color and consists of finely divided macrocrystalline pyroxene-rich matrix that contains abundant clastic fragments: (1) Clasts of white, plagioclase-rich rocks. (2) Medium-gray, partly devitrified, cryptocrystalline. (3) Monomineralic fragments and grains of pyroxene, plagioclases, oxide minerals, sulfides, and metal. In overall appearance it is very similar to some lunar breccias." Subsequent studies found a great diversity of basaltic clast textures and compositions, and therefore it is best classified as a polymict eucrite. Samples from the 1976-77, 77-78, and 78-79 field seasons (76, 77, and 78 prefixes) were split between US and Japan (NIPR). The US specimens are currently at NASA-JSC, Smithsonian Institution, or the Field Museum in Chicago. After this initial finding of ALH 76005, the next year s team recovered one additional mass ALH 77302, and then four additional masses were found during the third season ALH 78040 and ALH 78132, 78158 and 78165. The joint US-Japan collection effort ended after three years and the US began collecting in the Trans-Antarctic Mountains with the 1979-80 and subsequent field seasons. ALH 79017 and ALH 80102 were recovered in these first two years, and then in 1981-82 field season, 6 additional masses were recovered from the Allan Hills. Of course it took some time to establish pairing of all of these specimens, but altogether the samples comprise 4292.4 g of material. Here will be summarized the scientific findings as well as some curatorial details of how specimens have been subdivided and allocated for study. A detailed summary is also presented on the NASA-JSC curation webpage for the HED meteorite compendium

Depletion of Vandium in Planetary Mantles: Controlled by Metal, Oxide, or Silicate?

Vanadium concentrations in planetary mantles can provide information about the conditions during early accretion and differentiation. Because V is a slightly siderophile element, it is usually assumed that any depletion would be due to core formation and metal-silicate equilibrium. However, V is typically more compatible in phases such as spinel, magnesiowuestite and garnet. Fractionation of all of these phases would cause depletions more marked than those from metal. In this paper consideration of depletions due to metal, oxide and silicate are critically evaluated

Allan Hills 76005 polymict eucrite pairing group: curatorial and scientific update on a jointly curated meteorite.

第2回極域科学シンポジウム/第34回南極隕石シンポジウム 11月17日（木） 国立国語研究所 2階講

Practitioner\u27s Corner: Ken Markowitz on Serving as an Environmental Advocate

From my past experience with Ken Markowitz, a 1989 graduate of WCL, I characterized him as dedicated to both the profession of environmental law and the school as an alumnus. When I contacted him about doing this interview, he confirmed my past impressions of him, by quickly responding to my invitation with a reply of any time. Ken seems always willing to help out students despite being extremely busy running his own public interest consulting firm, EarthPace LLC, in Washington DC. Ken\u27s firm advises organizations on using the Web and other emerging technologies to heighten public awareness of earth science and the law. Dramatically, technology can assist people in making more conscientious, cost-effective decisions regarding the environment

Volatile Element Depletion of the Moon The Roles of Pre-Cursors, Post-Impact Disk Dynamics, and Core Formation

The compositional and isotopic similarity of Earths primitive upper mantle (PUM) and the Moon has bolstered the idea that the Moon was derived from the proto-Earth, but the Moons inventory of volatile lithophile elements Na, K, Rb and Cs are lower than in Earths PUM by a factor of 4 to 5. The abundances of fourteen other volatile elements exhibit siderophile behavior (volatile siderophile elements or VSE; P, As, Cu, Ag, Sb, Ga, Ge, Bi, Pb, Zn, Sn, Cd, In, and Tl) that could be used to evaluate whether the Moon was derived from the proto-Earth, and whether their depletion can be attributed to volatility or core formation. In this study, newly available core-mantle partitioning data are used, together with bulk Moon compositions, protolunar disk dynamics modelling to test the hypothesis that the Moon was derived from PUM-like material. At lunar core formation conditions, As, Sb, Ag, Ge, Bi, Sn are siderophile, whereas P, Cu, Ga, Pb, Zn, Cd, In and Tl are all weakly siderophile or lithophile. Most of the VSE can be explained by a combination of known processes pre-cursor volatile depletion, melt-gas dynamics and equilibria in the protolunar disk, and core formation. Explaining this whole group of volatile elements may require a combination of mixing and separation of the newly formed Moon from remnant gas rich in the highest volatility VSEs. This large group of volatile elements informs a wide temperature range and offers a powerful test of melt-gas segregation mechanisms in the protolunar disk and lunar formation hypotheses