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Neutron Diffraction Study Oxygen Dissolution Alpha(sub 2)-Ti3Al

Rietveld refinements of neutron powder diffraction data on alpha(sub 2)-Ti3Al have been performed to determine the crystal structure as a function of interstitial oxygen (O) concentration for three alloys with a Ti/Al ratio of approximately equal to 2.34 and O concentrations of 0.25%, 3.99% and 7.71%. The structures of the allows are hexagonal in space group P6(sub 3)/mmc where Ti and Al atoms populate unique sites with excess Al at the Ti site and O atoms occupy octahedral interstitial sites surrounded by six Ti sites. The length of the c-axis was found to increase linearly as the O occupancy of the interstitial sites increased; this lattice lengthening effect was much less pronounced along the alpha axis. Correspondingly, the increases in the lengths of Ti-Al and Ti-Ti bonds with a major component of their direction parallel to the c-axis were roughly an order of magnitude greater than the increases in the lengths of Ti-al and Ti-Ti bonds more closely aligned with the alpha-axis. Densities calculated form the lattice parameters and occupancy factors fall in the range (4.118 plus or minus 0.004) grams per cubic centimeter to (4.194 plus or minus 0.004) grams per cubic centimeter, and exhibit a nearly linear increase with oxygen concentration. Measured densities of (4.113 plus or minus 0.001) grams per cubic centimeter, (4.146 plus or minus 0.009) grams per cubic centimeter, and (4.191 plus or minus 0.002) grams per cubic centimeter for these alloys agree with the results of the refinements.

Jones, Camille Y.↗

NASA technical advances in aircraft occupant safety

A NASA program to improve aircraft safety is discussed in terms of three areas of concentration: unexpected turbulence encounters, fire, and crash impact. To provide warning of clear air turbulence (CAT) so that the pilot can take evasive action, a laser Doppler system is described, which functions by measuring backscatter frequency radiation occurring in aerosols ahead of the aircraft. The system was found able to detect CAT, but at shorter than optimal ranges (10 km as opposed to 32 km). Fire safety has focused on both the early detection of fires through improved sensing methods, and on the development of fire-retardant materials, i.e., intumescent char-forming protective coatings. Crashworthiness is discussed in terms of the development of a survivable crash envelope and improved seat and restraint systems. To evaluate an aircraft for crashworthiness, finite-element computer programs are currently being developed which analyze both aircraft structural configurations and the intrinsic strength of aircraft materials.

Enders, J. H.↗

Determination of crash test pulses and their application to aircraft seat analysis

Deceleration time histories (crash pulses) from a series of twelve light aircraft crash tests conducted at NASA Langley Research Center (LaRC) were analyzed to provide data for seat and airframe design for crashworthiness. Two vertical drop tests at 12.8 m/s (42 ft/s) and 36 G peak deceleration (simulating one of the vertical light aircraft crash pulses) were made using an energy absorbing light aircraft seat prototype. Vertical pelvis acceleration measured in a 50 percentile dummy in the energy absorbing seat were found to be 45% lower than those obtained from the same dummy in a typical light aircraft seat. A hybrid mathematical seat-occupant model was developed using the DYCAST nonlinear finite element computer code and was used to analyze a vertical drop test of the energy absorbing seat. Seat and occupant accelerations predicted by the DYCAST model compared quite favorably with experimental values.

Alfaro-Bou, E.↗

Material selection and evaluation of new encapsulation compounds for electric cables for launch support system

Eight urethane compounds were evaluated as possible replacement for the existing encapsulating compoounds for electrical cables for the Launch Support System at Kennedy Space Center (KSC). The existing encapsulating compound, PR-1535, contains the curative MOCA 4-4'-Methylene-BIS (2-chloroaniline), which is a suspect carcinogen and hence may be the subject of further restrictions of its use by the Occupational Safety and Health Administration (OSHA). The samples made in the configuration of cable joints and in the form of disks were evaluated for flammability and hypergolic compatibility. These also underwent accelerated weatherability tests that measured the residual hardness of the exposed samples. Three candidates and the existing compound passed the hardness test. Of these, only one candidate and the existing compound passed the flammability test. The thermal and hydrolytic stability (weatherability) of these samples was studied using thermogravimetric analysis (DSC) techniques. The TMA and DSC data correlated with the residual hardness data; whereas, the TGA data showed no correlation. A hypergolic compatibility test will be conducted on the compound V-356-HE80, which passed both the flammability and accelerated weatherability tests.

Ray, Asit K.↗

Users' Guide to Vinci: Personal Computer Software for Planning Image-based Measurements in Wind Tunnels

Vinci is software that can be used to plan image-based measurements in wind tunnels. It allows the user to plan the placement of cameras and the choice of lenses well in advance of a test, thereby reducing the set-up time and cost when tunnel occupancy begins. It can also be used post-test to display data (pressure-sensitive paint, particle image velocimetry, model deformation) in context with the test article. Vinci is self-contained and runs on personal computers under Windows operating systems. No other software is required. Test articles are represented by CFD-like surface grids that may be read from an external file or created within the program as a combination of simple geometric shapes. The user controls the position and orientation of the test article through a Graphical User Interface (GUI) and may add many additional objects, including tunnel walls and windows, a wide variety of simple geometric shapes, mirrors, lamps, and laser sheets. The application computes simulated images from up to 40 cameras. Images are based on pinhole projection. Each camera is defined by the sensor size and the focal length of the lens. All camera parameters, including position and point angles, are controlled through the GUI. Simulated images are displayed in a window of the GUI and may be saved as bitmaps.

Users’ Guide, Image Planning, Wind Tunnels, Softwa↗

Occupational safety considerations with hydrazine

Hydrazine is a reducing agent that is most commonly used as a propellant and as an oxygen scavenger in boilers. Hydrazine is extremely irritating and has been demonstrated to produce both acute and chronic toxicity. As a result, the established permissible inhalation exposure limits are very low, and respiration protection is required whenever vapors are present. Liquid hydrazine penetrates the skin and produces a chemical burn; therefore, some protective measures must also be taken to protect the skin from liquid contact. Often, however, a cumbersome, whole-body protective suit is worn to protect against skin contact with vapor as well. To what extent it is actually necessary to protect skin from vapor penetration had not previously been demonstrated. In an attempt to answer this question, we conducted a study with rats to compare the dermal penetration of hydrazine vapor with inhalation. Pharmacokinetic modeling was used to compare body burdens resulting from these different routes of exposure. The analysis concluded that the vapor concentration during a skin-only exposure would have to be at least 200 times higher than that during inhalation to achieve the same body burden. This type of estimation illustrates the use of predictive toxicology in occupational exposures.

Clewell, Harvey J., III↗

NASA Commercial Crew Program and Medical Operational Challenges

This abstract is submitted as part of the USSPACECOM Command Surgeon’s panel demonstrating the medical capabilities and challenges involved in human space flight support operations. BACKGROUND: NASA embarked on the Commercial Crew Program to launch astronauts into low-earth orbit from US soil and dock with the International Space Station (ISS). The eventual industry providers selected were SpaceX (SpX) and Boeing. These commercial transportation systems are vital to ensure crew availability on ISS for research and discovery. OVERVIEW: NASA/SpaceX Demo-2 (DM2) mission launched from the Kennedy Space Center in 2020 as the historic first crewed test-flight of the Crew Dragon spacecraft with two NASA Astronauts onboard. DM2 represented the first flight in 9-years from US soil since STS-135 in 2011. The 63-day mission ended with splashdown in the Gulf of Mexico, the first US water recovery in 45-years since Apollo-Soyuz. Validation of system hardware and operations allowed four-person crews to launch on subsequently missions (Crew-1, Crew-2, Crew-3, Crew-4, Crew-5 to date), which included International Partner crewmembers. DISCUSSION: A multitude of operational, training, medical, and technical issues needed to be addressed between NASA Medical Operations, the commercial provider SpaceX, and the Department of Defense. These included Flight rule development, occupant protection, pressurized suit testing, communication plans during mission phases, and emergency simulations for supporting Flight Surgeons and Biomedical Engineers. In providing crew experience with expected launch and entry G-force profile, Centrifuge training was established. Preventive health measures via the Health Stabilization Program were especially vital during the global COVID-19 pandemic. Unique aspects arise for SpX Dragon parachute splashdown and shipboard recovery operations in the Atlantic Ocean and Gulf of Mexico. The new Commercial Crew Program is indeed a wonderfully challenging and exciting era for human spaceflight.

Joseph Dervay↗

NASA Commercial Crew Program and Medical Operational Challenges

BACKGROUND: NASA embarked on the Commercial Crew Program to launch astronauts into low-earth orbit from US soil and dock with the International Space Station (ISS). The eventual industry providers selected were SpaceX (SpX) and Boeing. These commercial transportation systems are vital to ensure crew availability on ISS for research and discovery. OVERVIEW: NASA/SpaceX Demo-2 (DM2) mission launched from the Kennedy Space Center in 2020 as the historic first crewed test-flight of the Crew Dragon spacecraft with two NASA Astronauts onboard. DM2 represented the first flight in 9-years from US soil since STS-135 in 2011. The 63-day mission ended with splashdown in the Gulf of Mexico, the first US water recovery in 45-years since Apollo-Soyuz. Validation of system hardware and operations allowed four-person crews to launch on subsequently missions (Crew-1, Crew-2, Crew-3, Crew-4, Crew-5 to date), which included International Partner crewmembers. DISCUSSION: A multitude of operational, training, medical, and technical issues needed to be addressed between NASA Medical Operations, the commercial provider SpaceX, and the Department of Defense. These included Flight rule development, occupant protection, pressurized suit testing, communication plans during mission phases, and emergency simulations for supporting Flight Surgeons and Biomedical Engineers. In providing crew experience with expected launch and entry G-force profile, Centrifuge training was established. Preventive health measures via the Health Stabilization Program were especially vital during the global COVID-19 pandemic. Unique aspects arise for SpX Dragon parachute splashdown and shipboard recovery operations in the Atlantic Ocean and Gulf of Mexico. The new Commercial Crew Program is indeed a wonderfully challenging and exciting era for human spaceflight.

Joseph P Dervay↗

Differences in Pre and Post Vascular Patterning of Retinas from ISS Crew Members and HDT Subjects by VESGEN Analysis

Accelerated research by NASA [1] has investigated the significant risks for visual and ocular impairments Spaceflight Associated Neuro-Ocular Syndrome /Visual Impairment/Intracranial Pressure (SANS/VIIP) incurred by microgravity spaceflight, especially long-duration missions. Our study investigates the role of blood vessels in the incidence and etiology of SANS/VIIP within the retinas of Astronaut crewmembers pre-and post-flight to the International Space Station (ISS) by NASA's VESsel GENeration Analysis (VESGEN). The response of retinal vessels in crewmembers to microgravity was compared to that of retinal vessels to Head-Down Tilt (HDT) in subjects undergoing 70-Day Bed Rest. The study tests the proposed hypothesis that cephalad fluid shifts missions, resulting in ocular and visual impairments, are necessarily mediated in part by retinal blood vessels, and are therefore accompanied by significant remodeling of retinal vasculature.Vascular patterns in the retinas of crew members and HDTBR subjects extracted from 30° infrared (IR) Heidelberg Spectralis® images collected pre/postflight and pre/post HDTBR, respectively, were analyzed by VESGEN (patent pending). a mature, automated software developed as a research discovery tool for progressive vascular diseases in the retina and other tissues [2]. The weighted, multi-parametric VESGEN analysis generates maps of branching arterial and venous trees and quantification by parameters such as the fractal dimension (Df, a modern measure of vascular space-filling capacity), vessel diameters, and densities of vessel length and number classified into specific branching generations by vascular physiological branching rules [2,3]. The retrospective study approved by NASA’s Institutional Review Board included six HDT subjects (NASA Flight Analogs Research Unit [FARU] Campaign 11; for example, [4]) and eight ISS crewmembers monitored by routine occupational surveillance who provided their study consents to NASA’s Lifetime Surveillance of Astronaut Health (LSAH). For the initial blinded VESGEN phase, ophthalmic retinal images were masked as to subject identity and pre- and post-status. In the second unblinded phase, VESGEN results were analyzed according to the pre- and post-status of left and right retinas matched to each subject. To complete our study, vascular results will be subjected to NASA biostatistical analysis and correlated with other ophthalmic and medical findings. Preliminary results for changes in the pre- to post-status of vascular patterning in the retinas of crewmembers and HDT subjects are strikingly opposite. By Df and other vascular branching measures, the space-filling capacity of arterial and venous trees decreased in a substantial subset of crewmembers (11/16 retinas). In contrast, vascular densities increased in a substantial subset of HDT subjects by the same parameters (6/10 retinas, currently excluding one anomalous subject). To conclude the study, biostatistical and medical analyses will be of critical importance for investigating the validity of these vascular findings. Vascular densities appeared to decrease in the retinas of crewmembers following ISS Missions, and increase in subjects after HDT. The vascular increases and decreases most likely derive primarily from limits of resolution to the ophthalmic imaging that does not capture the smallest vessels, rather than from vessel growth or atrophy. Differences in arterial and venous response to cephalad fluid shifts induced by ISS and HDT may have resulted from a long-duration conditioning phenomenon (for example, 6-month ISS missions compared to 70-day HDT), or the presence of gravity in HDT compared to microgravity onboard the ISS. To conclude our study, the biostatistical and medical analyses will be of critical importance for investigating the validity and significance of the VESGEN findings.

Murray, M. C.↗

Microbial Anomalies Encountered on the International Space Station

Microorganisms in our living environments are unavoidable. A community of microbes arrived in space with the delivery of the first element of the International Space Station (ISS), attached to hardware and on the bodies of the humans tasked with the initial assembly missions. The risk that microorganisms could cause adverse effects in the health of both the human occupants of the ISS as well as the physical integrity of the station environment and life support systems has been both a driver and a function of engineering and operational controls. Scientists and engineers at NASA have gone to extensive measures to control microbial growth at levels safe for the crewmembers and the spacecraft environment. Many of these measures were initiated with the design of the spacecraft and its systems. Materials used in the ISS were tested for resistance to fungi, such as mold and a paint with a fungus-killing chemical was also used. Controlling the humidity of the air in the Station is also an effective way of discouraging microbe growth. The breathing air is reconditioned by the Environmental Control Life Support System (ECLSS) prior to distribution, utilizing High Efficiency Particulate Air (HEPA) filtration. Requirements restricting the accumulation of water condensate in the air handlers and habitable volume of the ISS were other safeguards added. Water for drinking and food rehydration is disinfected or filtered. A robust in-flight housekeeping regimen for the ISS significantly reduces inappropriate growth of microorganisms and includes a regular cleaning of accessible surfaces with disinfectant wipes. Most of these requirements were suggested by microbiologists to mitigate and possibly prevent many microbiological risks. In addition to these controls, before flight monitoring and analyses of the cabin air, exposed surfaces, water and food, consumables, and crew members are conducted to mitigate microbial risk to the crew and spacecraft. Many microbial risks are much easier to identify and resolve before launch than during space flight. Although the focus has been on prevention of microbiologically related, not all problems can be anticipated. A number of microbial anomalies have occurred on ISS. This paper will discuss the occurrences, root-cause investigations, and mitigation steps taken to remediate the contamination.

Bruce, Rebekah J.↗

Reform of general education and vocational training in the U.S.S.R.

Extensive school reform measures were initiated in the U.S.S.R. in 1984. The essence of the reform is to improve the quality of instruction, improve the content of education, strengthen the Marxist-Leninist world view, and ensure that all secondary school graduates master an occupation.

Spearman, M. L.↗

High-Temperature Thermometer Using Cr-Doped GdAlO3 Broadband Luminescence

A new concept has been developed for a high-temperature luminescence-based optical thermometer that both shows the desired temperature sensitivity in the upper temperature range of present state-of-the-art luminescence thermometers (above 1,300 C), while maintaining substantial stronger luminescence signal intensity that will allow these optical thermometers to operate in the presence of the high thermal background radiation typical of industrial applications. This objective is attained by using a Cr-doped GdAlO3 (Cr:GdAlO3) sensor with an orthorhombic perovskite structure, resulting in broadband luminescence that remains strong at high temperature due to the favorable electron energy level spacing of Cr:GdAlO3. The Cr:GdAlO3 temperature (and pressure) sensor can be incorporated into, or applied onto, a component s surface when a non-contact surface temperature measurement is desired, or alternatively, the temperature sensor can be attached to the end of a fiber-optic probe that can then be positioned at the location where the temperature measurement is desired. In the case of the fiber-optic probe, both the pulsed excitation and the luminescence emission travel through the fiber-optic light guide. In either case, a pulsed light source provides excitation of the luminescence, and the broadband luminescence emission is collected. Real-time temperature measurements are obtain ed using a least-squares fitting algorithm that determines the luminescence decay time, which has a known temperature dependence established by calibration. Due to the broad absorption and emission bands for Cr:GdAlO3, there is considerable flexibility in the choice of excitation wavelength and emission wavelength detection bands. The strategic choice of the GdAlO3 host is based on its high crystal field, phase stability, and distorted symmetry at the Cr3+ occupation sites. The use of the broadband emission for temperature sensing at high temperatures is a key feature of the invention and is novel since broadband luminescence emission normally shows severe thermal quenching. The tightly bound AlO6 octahedra in GdAlO3 results in a larger energy barrier to nonradiative decays than in other materials and therefore makes using broadband emission for temperature sensing possible at high temperatures. This approach results in a substantial increase in temperature capability. For example, the most commonly used Cr-doped crystal used for luminescence-based temperature measurements, ruby, has only been demonstrated up to 600 C, whereas the Cr:GdAlO3 optical thermometer under development has already been shown to exhibit useful luminescence up to 1,300 C. Because GdAlO3 is non-reactive and is stable in harsh, high-temperature environments, sensors composed of Cr:GdAlO3 will be very well suited for remote high-temperature measurements in engine or industrial environments where its intense high-temperature luminescence will stand out above significant thermal radiation background levels.

Eldridge, Jeffrey↗

Surveying Clay Mineral Diversity in the Murray Formation, Gale Crater, Mars

The CheMin XRD instrument aboard Mars Science Laboratory (MSL) has documented clay minerals in various drill samples during its traverse of Gale Crater's floor and ascent of Mt. Sharp. The most recent samples, named Marimba, Quela and Sebina were acquired from the Murray Formation in the Murray Buttes region of lower Mt. Sharp. Marimba and Quela come from a approx. 30 m package of finely laminated lacustrine mudstones. Sebina comes from an overlying package of heterolithic mudstone-sandstones. Clay minerals make up approx.15-25 wt.% of the bulk rock with similar contributions to XRD patterns in all three samples. Broad basal reflections at approx. 10deg 2(theta) CoK(alpha) indicate the presence of 2:1 group clay minerals. The 02(lambda) clay mineral band lies at approx. 22.9deg 2(theta), a region typically occupied by Fe-bearing dioctahedral 2:1 clay minerals like nontronite or Fe-illite. The low humidity within the CheMin instrument, which is open to the martian atmosphere, promotes loss of interlayer H2O and collapse of smectite interlayers making them difficult to distinguish from illites. However, based on the low K content of the bulk samples, it appears that smectitic clay minerals are dominant. Peak dehydroxylation of the Marimba sample measured by the SAM instrument on MSL occurred at 610C and 780C. Fe-bearing smectites are not consistent with these dehydroxylation temperatures. Thus, we suggest that a mixture of dioctahedral and trioctahedral smectite phases are present giving the appearance of intermediate octahedral occupancy in XRD. Dioctahedral smectites have not previously been reported in Gale Crater by MSL. Earlier in the mission, relatively clay mineral rich samples (approx. 20 wt.%) from lacustrine mudstones in Yellowknife Bay (YKB) were found to contain ferrian saponites. It is proposed that YKB saponites formed via isochemical aqueous alteration of detrital olivine close to the time of sediment deposition, under anoxic to poorly oxidizing conditions. In terrestrial settings where alteration sequences of basaltic rocks or sediments are observed, first-stage alteration clay minerals are typically trioctahedral smectite species, as reported from YKB. In later alteration stages trioctahedral clay minerals are replaced by dioctahedral clays as a result of removal and/or oxidation of Fe2+ and Mg. Observed changes in clay mineralogy between YKB and Murray Buttes samples correspond with differences in bulk mineralogy, including: 1) a transition from magnetite to hematite as the main Fe-oxide, 2) increasing abundances of Ca-sulfates and 3) a reduction in the quantity of reactive mafic minerals. This mineralogical change indicates an increasing degree of aqueous alteration and oxidation of mafic detritus in the upper part of the Murray Formation. These results broaden the spectrum of mineralogical facies documented by MSL. Together sedimentology and mineralogy indicate a long-lasting, dynamic fluvial-lacustrine system encompassing a range aqueous geochemical processes under varying redox conditions. Future work is needed to unravel the influence of global and local controls on the range of ancient conditions observed at Gale Crater.

MSL↗

Determining the amount of physical activity needed for long-term weight control

OBJECTIVE: To evaluate prospectively the influence of habitual physical activity on body weight of men and women and to develop a model that defines the role of physical activity on longitudinal weight change. DESIGN AND SETTING: Occupational cohort study conducted for a mean of 5.5 y. SUBJECTS: A total of 496 (341 male and 155 female) NASA/Johnson Space Center employees who completed the 3 month education component of the employee health-related fitness program and remained involved for a minimum of 2 y. MEASUREMENTS: Body weights were measured at baseline (T1) and follow-up (T2), and habitual physical activity was obtained from the mean of multiple ratings of the 11-point (0-10) NASA Activity Scale (NAS) recorded quarterly between T1 and T2. Other measures included age, gender, VO(2 max) obtained from maximal treadmill testing, body mass index (BMI), and body fat percentage. RESULTS: Multiple regression demonstrated that mean NAS, T1 weight, aging and gender all influence long-term T2 weight. T1 age was significant for the men only. Independently, each increase in mean NAS significantly (P<0.01) reduced T2 weight in men (b=-0.91 kg; 95% CI:-1.4 to-0.42 kg) and women (b=-2.14 kg; 95% CI:-2.93 to-1.35 kg). Mean NAS had a greater effect on T2 weight as T1 weight increased, and the relationship was dose-dependent. CONCLUSIONS: Habitual physical activity is a significant source of long-term weight change. The use of self-reported activity level is helpful in predicting long-term weight changes and may be used by health care professionals when counseling patients about the value of physical activity for weight control.

Exercise↗

Full-Scale Drop Test of a Fokker F28 Wingbox Fuselage Section

During the summer of 2017, a vertical drop test was conducted on a partial section of a Fokker F28 MK4000 aircraft as a part of a joint NASA/FAA effort to investigate the performance of transport category aircraft under realistic crash conditions. Ten Anthropomorphic Test Devices (ATDs, a.k.a. crash test dummies) ranging from 5th to 95th percentile sizes were used for the collection and comparison of occupant loads. Additionally, overhead bin mass simulators were added to achieve a realistic fuselage configuration. The section was dropped with a downward facing pitch angle onto a sloping soil surface in order to simulate a local horizontal velocity in the airframe. Instrumentation consisting of accelerometers was installed to measure floor, seat track, ATD, and overhead bin acceleration responses. Self-contained data recorders logging accelerations and rotational rates were also used on the seat tracks and lower structure as evaluations for crash recording devices in potential future use cases. The right side of the section was painted with a stochastic black and white speckle pattern for use in full field photogrammetric imaging techniques. Results collected from the airframe accelerometers will be presented, and deformation and failures of the test article structure will be discussed. Finally, an examination of the test article motion will be presented using derived components of local velocities with their effect on the impact acceleration and airframe response.

Littell, J. D.↗

In situ x-ray and neutron powder diffraction study of LaNi5-xSnx-H systems

This paper will present results of in situ XRD measurements of LaNi4.75Sn0.25 .during the initial absorption-desorption cycle, These measurements were performed under a similar condition to that for LaNi4.75Al0.25 previously reported [1]. The data were analyzed by the Rietveld method. Lattice parameter change and strain formation accompanying hydride phase formation and decomposition will be discussed. In addition, results of in situ neutron diffraction of LaNi4.78Sn0.22, focusing on hydrogen occupation in the hydride phase, will be presented.

metal hydrides↗

Analysis of Phase-Type Stochastic Petri Nets With Discrete and Continuous Timing

The Petri net formalism is useful in studying many discrete-state, discrete-event systems exhibiting concurrency, synchronization, and other complex behavior. As a bipartite graph, the net can conveniently capture salient aspects of the system. As a mathematical tool, the net can specify an analyzable state space. Indeed, one can reason about certain qualitative properties (from state occupancies) and how they arise (the sequence of events leading there). By introducing deterministic or random delays, the model is forced to sojourn in states some amount of time, giving rise to an underlying stochastic process, one that can be specified in a compact way and capable of providing quantitative, probabilistic measures. We formalize a new non-Markovian extension to the Petri net that captures both discrete and continuous timing in the same model. The approach affords efficient, stationary analysis in most cases and efficient transient analysis under certain restrictions. Moreover, this new formalism has the added benefit in modeling fidelity stemming from the simultaneous capture of discrete- and continuous-time events (as opposed to capturing only one and approximating the other). We show how the underlying stochastic process, which is non-Markovian, can be resolved into simpler Markovian problems that enjoy efficient solutions. Solution algorithms are provided that can be easily programmed.

Jones, Robert L.↗