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All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Validation of On-Orbit Methodology for the Assessment of Cardiac Function and Changes in the Circulating Volume Using Ultrasound and Braslet-M Occlusion Cuffs

The objective of this joint U.S. - Russian project was the development and validation of an in-flight methodology to assess a number of cardiac and vascular parameters associated with circulating volume and its manipulation in long-duration space flight. Responses to modified Valsalva and Mueller maneuvers were measured by cardiac and vascular ultrasound (US) before, during, and after temporary volume reduction by means of Braslet-M thigh occlusion cuffs (Russia). Materials and Methods: The study protocol was conducted in 14 sessions on 9 ISS crewmembers, with an average exposure to microgravity of 122 days. Baseline cardiovascular measurements were taken by echocardiography in multiple modes (including tissue Doppler of both ventricles) and femoral and jugular vein imaging on the International Space Station (ISS). The Braslet devices were then applied and measurements were repeated after >10 minutes. The cuffs were then released and the hemodynamic recovery process was monitored. Modified Valsalva and Mueller maneuvers were used throughout the protocol. All US data were acquired by the HDI-5000 ultrasound system aboard the ISS (ATL/Philips, USA) during remotely guided sessions. The study protocol, including the use of Braslet-M for this purpose, was approved by the ISS Human Research Multilateral Review Board (HRMRB). Results: The effects of fluid sequestration on a number of echocardiographic and vascular parameters were readily detectable by in-flight US, as were responses to respiratory maneuvers. The overall volume status assessment methodology appears to be valid and practical, with a decrease in left heart lateral E (tissue Doppler) as one of the most reliable measures. Increase in the femoral vein cross-sectional areas was consistently observed with Braslet application. Other significant differences and trends within the extensive cardiovascular data were also observed. (Decreased - RV and LV preload indices, Cardiac Output, LV E all maneuvers, LV Stroke Volume). Conclusions: This Study: 1) Addressed specific aspects of operational space medicine and space physiology, including assessment of circulating volume disturbances 2) Expanded the applications of diagnostic ultrasound imaging and Doppler techniques in microgravity. 3) Used respiratory maneuvers against the background of acute circulating volume manipulations which appear to enhance our ability to noninvasively detect volume-dependency in a number of cardiac and vascular parameters. 4) Determined that Tei index is not clinically changed therefore contractility not altered in the face of reduced preload. 5) Determined that increased Femoral Vein Area indicating blood being sequestered in lower extremities correlates with reduced preload and cardiac output. 6) That Braslet may be the only feasible means of acutely treating high pressure pulmonary edema in reduced gravity environments.

Hamilton, Douglas↗
NASA NTRS1974

Program to study optimal protocol for cardiovascular and muscular efficiency

Training programs necessary for the development of optimal strength during prolonged manned space flight were examined, and exercises performed on the Super Mini Gym Skylab 2 were compared with similar exercises on the Universal Gym and calisthenics. Cardiopulmonary gains were found negligible but all training groups exhibited good gains in strength.

Olree, H. D.↗
NASA NTRS1975

Program to study optimal protocol for cardiovascular and muscular efficiency

Two possible ways to minimize the effects of deconditioning in space are; To achieve a very high level of conditioning immediately prior to flight, and to provide a regimen in the capsule which will maintain a moderate degree of fitness. It was determined that running and riding a bicycle ergometer at comparable heart rates produced similar gains in physical fitness variables. It was found that subjects who exercised at a 180 heart rate made greater gains in physical fitness than did those exercising at a 140 or 160 heart rate. When the length of the workout was varied, subjects exercising sixty minutes per day made greater gains than those exercising twenty or forty minutes per day. Subjects who discontinued training slowly deconditioned, but a moderate level of fitness could be maintained by exercising at a pulse rate of 160 beats per minute for twenty minute periods three times a week. Subjects who overtrained twice daily to near exhaustion increased in fitness.

Olree, H. D.↗
NASA NTRS2003

Ultrasound in space

Physiology of the human body in space has been a major concern for space-faring nations since the beginning of the space era. Ultrasound (US) is one of the most cost effective and versatile forms of medical imaging. As such, its use in characterizing microgravity-induced changes in physiology is being realized. In addition to the use of US in related ground-based studies, equipment has also been modified to fly in space. This involves alteration to handle the stresses of launch and different power and cooling requirements. Study protocols also have been altered to accommodate the microgravity environment. Ultrasound studies to date have shown a pattern of adaptation to microgravity that includes changes in cardiac chamber sizes and vertebral spacing. Ultrasound has been and will continue to be an important component in the investigation of physiological and, possibly, pathologic changes occurring in space or as a result of spaceflight.

Review, Tutorial↗
NASA NTRS2017

Mapping by VESGEN of Blood Vessels in the Retinas of Astronauts Pre- and Post-Flight to the ISS

Research by NASA [1] established that significant risks for visual and ocular impairments associated with increased intracranial pressure (VIIP) are incurred by microgravity spaceflight, especially long-duration missions. It is well established in physiology and pathology that a fundamental role of the microvasculature is to mediate fluid transfers and remodel actively in response to environmental, immune and other stresses. We therefore hypothesize that remodeling of retinal blood vessels necessarily occurs during accommodation of microgravity-induced fluid shifts prior to subsequent development of visual and ocular impairments. Potential contributions of retinal vascular remodeling to VIIP etiology are therefore being investigated by NASA's innovative VESsel GENeration Analysis (VESGEN) software for two studies: (1) U.S. crew members before and after ISS missions, and (2) head-down tilt in human subjects before and after 70 days of bed rest. We anticipate that results of the two studies will be complete by the Investigators Workshop (January 22, 2017). METHODS: For the 2013 NASA NRA award, we are concluding the analysis of 30 degree infrared (IR) Heidelberg Spectralis images of retinal blood vessels by VESGEN (patents pending), a mature, automated software developed as a translational and basic vascular research discovery tool, particularly for retinal vascular disease. Subjects of our retrospective study include eight ISS crew members monitored for routine occupational surveillance pre- and post-flight, who provided their study consents to NASAs Lifetime Surveillance of Astronaut Health (LSAH) in coordination with approval of the VESGEN retrospective study protocol by NASAs Institutional Review Board (IRB). The ophthalmic retinal images (average image resolution, approximately 5.6 microns per pixel) are blinded as to pre and post ISS status until the second portion of our study, when VESGEN results will be correlated with other ophthalmic and medical findings for the crew members. Due to image resolution challenges, a novel Matlab tool was developed for aligning pre and post images, and comparing (querying) the two images for differences in the morphology of small vessels. RESULTS: During the past year, LSAH approved the release of all astronaut retinal images to our study for VESGEN analysis. Substantial progress on the initial blinded portion of the study is in place. We anticipate that VESGEN analysis of the 32 Spectralis IR retinal images will be complete for presentation at the 2017 IWS meeting. CONCLUSIONS: Modified retinal vascular patterning may offer early-stage predictions of ocular changes resulting in decreased visual acuity for the VIIP syndrome. Novel insights provided by VESGEN into progressively pathological and blinding vascular remodeling in the human retina currently help to guide other NIH- and NASA-supported therapeutic studies of retinal disease and modeling of the VIIP risk. Results of our vascular investigation of the retinas of astronauts pre- and post-flight may help advance the understanding of both healthy and pathological adaptations to fluid shifts in microgravity associated with the VIIP syndrome. Preliminary results indicate that imaging of higher resolution, such as the new OCT angiography (OCT-A) technology, will be required to determine conclusively the role of the smaller retinal and choroidal vessels in VIIP etiology.

VESGEN↗
NASA NTRS2007

Implementation of the NASA AG-Bed Rest Pilot

To examine the efficacy of artificial gravity (AG) as a countermeasure to spaceflight deconditioning, intermittent AG produced by a horizontal short-radius centrifuge (SRC) was utilized on human test subjects deconditioned by bed rest. This poster will present the subject screening, study design, logistics, and implementation of the 41 day pilot study conducted at the University of Texas Medical Branch, Galveston, TX bed rest facility. An extensive screening process was employed to exclude subjects that were dissimilar to the U.S. astronaut population. Candidates underwent a modified U.S. Air Force Class III physical and tests of bone density, cardiovascular fitness, vestibular system function, psychological fitness and centrifuge tolerance. 15 subjects completed the study; 7 control and 8 AG treatment. All provided written consent to volunteer after the nature of the study and its hazards were clearly explained to them. Standard conditions were strictly regulated; Ta = 72 +/- 2 F, humidity = 70 +/- 5%, light/dark cycle 16h:8h. All fluid intake (minimum 28.5 ml/kg body weight/day) and urine output was monitored. Caloric intake was adjusted as necessary to maintain body weight. Carbohydrate, fat and protein were provided in a ratio of 55:30:15. Phosphorus intake was 1400 mg/d, sodium intake was 2 mmol/kg/d, potassium intake was 1.3 mmol/kg/d, and dietary calcium intake was 1000 mg/d. A physician examined each subject daily. During the first 11 days of the study protocol, subjects were ambulatory, but confined to the facility. Subjects participated in multiple baseline tests of bone, muscle, cardiovascular, sensory-motor, immunological, and psychological function. On the 12th day, subjects entered the bed rest phase of the study, during which they were confined to strict 6? head down tilt bed rest for 21 days. Beginning 24 hrs into this period, treatment subjects received 1 hour daily exposures to artificial gravity which was produced by spinning the subjects on a 3.0 m radius SRC. They were oriented radially in the supine position so that the centrifugal force was aligned with their long body axis, and while spinning, they #stood# on a force plate, supporting the centrifugal loading (2.5 g at the feet, 1.0 g at the heart). The subject station allowed free translation over approximately 10 cm to ensure full loading of the lower extremities and to allow for anti-orthostatic muscle contractions. Control subjects were positioned on the centrifuge but did not spin. Following the bed rest phase, subjects were allowed to ambulate again, but remained within the facility for an additional 9 days and participated in multiple follow-up tests of physiological function.

Warren, L. E.↗
NASA NTRS2012

Virtual Ultrasound Guidance for Inexperienced Operators

Medical ultrasound or echocardiographic studies are highly operator-dependent and generally require lengthy training and internship to perfect. To obtain quality echocardiographic images in remote environments, such as on-orbit, remote guidance of studies has been employed. This technique involves minimal training for the user, coupled with remote guidance from an expert. When real-time communication or expert guidance is not available, a more autonomous system of guiding an inexperienced operator through an ultrasound study is needed. One example would be missions beyond low Earth orbit in which the time delay inherent with communication will make remote guidance impractical. The Virtual Ultrasound Guidance system is a combination of hardware and software. The hardware portion includes, but is not limited to, video glasses that allow hands-free, full-screen viewing. The glasses also allow the operator a substantial field of view below the glasses to view and operate the ultrasound system. The software is a comprehensive video program designed to guide an inexperienced operator through a detailed ultrasound or echocardiographic study without extensive training or guidance from the ground. The program contains a detailed description using video and audio to demonstrate equipment controls, ergonomics of scanning, study protocol, and scanning guidance, including recovery from sub-optimal images. The components used in the initial validation of the system include an Apple iPod Classic third-generation as the video source, and Myvue video glasses. Initially, the program prompts the operator to power-up the ultrasound and position the patient. The operator would put on the video glasses and attach them to the video source. After turning on both devices and the ultrasound system, the audio-video guidance would then instruct on patient positioning and scanning techniques. A detailed scanning protocol follows with descriptions and reference video of each view along with advice on technique. The program also instructs the operator regarding the types of images to store and how to overcome pitfalls in scanning. Images can be forwarded to the ground or other site when convenient. Following study completion, the video glasses, video source, and ultrasound system are powered down and stored. Virtually any equipment that can play back video can be used to play back the program. This includes a DVD player, personal computer, and some MP3 players.

Caine, Timothy↗
NASA NTRS2010

MACHETE: Environment for Space Networking Evaluation

Space Exploration missions requires the design and implementation of space networking that differs from terrestrial networks. In a space networking architecture, interplanetary communication protocols need to be designed, validated and evaluated carefully to support different mission requirements. As actual systems are expensive to build, it is essential to have a low cost method to validate and verify mission/system designs and operations. This can be accomplished through simulation. Simulation can aid design decisions where alternative solutions are being considered, support trade-studies and enable fast study of what-if scenarios. It can be used to identify risks, verify system performance against requirements, and as an initial test environment as one moves towards emulation and actual hardware implementation of the systems. We describe the development of Multi-mission Advanced Communications Hybrid Environment for Test and Evaluation (MACHETE) and its use cases in supporting architecture trade studies, protocol performance and its role in hybrid simulation/emulation. The MACHETE environment contains various tools and interfaces such that users may select the set of tools tailored for the specific simulation end goal. The use cases illustrate tool combinations for simulating space networking in different mission scenarios. This simulation environment is useful in supporting space networking design for planned and future missions as well as evaluating performance of existing networks where non-determinism exist in data traffic and/or link conditions.

Jennings, Esther H.↗
NASA NTRS1997

Effect of Daily Supine LBNP Exercise on Gastrointestinal Motility During Antiorthostatic Bedrest in Normal Subjects

Space flight alters gastrointestinal (GI) function in general, and GI motility, in particular. This can decrease appetite, affect the body's ability to absorb nutrients, fluids and electrolytes, and contribute to a negative energy balance. Antiorthostatic bed rest (ABR) has been used to simulate microgravity-induced physiological changes in human subjects. The objective of this investigation is to determine if daily supine lower body negative pressure (LBNP) exercise will maintain GI motility at near normal levels during ABR. Eight subjects participated in the study protocol consisting of an ambulatory phase scheduled before bedrest periods and two 14 day bed rest (6 deg head-down tilt) periods, once with and another time without exercise. Supine treadmill running in an LBNP chamber was used for exercise. Mouth-to-cecum transit time (MCTT) of lactulose was measured indirectly using the rise in breath hydrogen level after oral administration of lactulose (20 g) following a standard low-fiber breakfast. GI motility during ambulatory and ABR periods was assessed using MCTT data. Results of this Study indicate that GI motility during ABR without exercise decreased by 45% [MCTT +/- S.E.M. 56.2 +/- 6.0 (Ambulatory); 87.3 +/- 8.3 (ABR)]. Supine LBNP exercise did not significantly alter this reduction in GI motility during ABR [MCTT +/- S.E.M. 81.3 +/- 4.2 (Exercise); 87.3 +/- 8.3 (No Exercise)]. These results suggest that supine LBNP exercise may not be an effective countermeasure for microgravity-induced decrements in GI motility and function.

Putcha, Lakshmi↗
NASA NTRS2012

Extreme Tele-Echocardiography: Methodology for Remote Guidance of In-Flight Echocardiography Aboard the International Space Station

Methods: In the year before launch of an ISS mission, potential astronaut echocardiographic operators participate in 5 sessions to train for echo acquisitions that occur roughly monthly during the mission, including one exercise echocardiogram. The focus of training is familiarity with the study protocol and remote guidance procedures. On-orbit, real-time guidance of in-flight acquisitions is provided by a sonographer in the Telescience Center of Mission Control. Physician investigators with remote access are able to relay comments on image quality to the sonographer. Live video feed is relayed from the ISS to the ground via the Tracking and Data Relay Satellite System with a 2- second transmission delay. The expert sonographer uses these images, along with twoway audio, to provide instructions and feedback. Images are stored in non-compressed DICOM format for asynchronous relay to the ground for subsequent off-line analysis. Results: Since June, 2009, a total of 27 resting echocardiograms and 5 exercise studies have been performed during flight. Average acquisition time has been 45 minutes, reflecting 26,000 km of ISS travel per study. Image quality has been adequate in all studies, and remote guidance has proven imperative for fine-tuning imaging and prioritizing views when communication outages limit the study duration. Typical resting studies have included 27 video loops and 30 still-frame images requiring 750 MB of storage. Conclusions: Despite limited crew training, remote guidance allows research-quality echocardiography to be performed by non-experts aboard the ISS. Analysis is underway and additional subjects are being recruited to define the impact of microgravity on cardiac structure and systolic and diastolic function.

Martin, David S.↗
NASA NTRS2011

Extreme Tele-Echocardiography: Methodology for Remote Guidance of In-flight Echocardiography Aboard the International Space Station

Echocardiography is ideally suited for cardiovascular imaging in remote environments, but the expertise to perform it is often lacking. In 2001, an ATL HDI5000 was delivered to the International Space Station (ISS). The instrument is currently being used in a study to investigate the impact of long-term microgravity on cardiovascular function. The purpose of this report is to describe the methodology for remote guidance of echocardiography in space. Methods: In the year before launch of an ISS mission, potential astronaut echocardiographic operators participate in 5 sessions to train for echo acquisitions that occur roughly monthly during the mission, including one exercise echocardiogram. The focus of training is familiarity with the study protocol and remote guidance procedures. On-orbit, real-time guidance of in-flight acquisitions is provided by a sonographer in the Telescience Center of Mission Control. Physician investigators with remote access are able to relay comments on image optimization to the sonographer. Live video feed is relayed from the ISS to the ground via the Tracking and Data Relay Satellite System with a 2 second transmission delay. The expert sonographer uses these images along with two-way audio to provide instructions and feedback. Images are stored in non-compressed DICOM format for asynchronous relay to the ground for subsequent off-line analysis. Results: Since June, 2009, a total of 19 resting echocardiograms and 4 exercise studies have been performed in-flight. Average acquisition time has been 45 minutes, reflecting 26,000 km of ISS travel per study. Image quality has been adequate in all studies, but remote guidance has proven imperative for fine-tuning imaging and prioritizing views when communication outages limit the study duration. Typical resting studies have included 12 video loops and 21 still-frame images requiring 750 MB of storage. Conclusions: Despite limited crew training, remote guidance allows research-quality echocardiography to be performed by non-experts aboard the ISS. Analysis is underway and additional subjects are being recruited to define the impact of microgravity on cardiac structure and systolic and diastolic function.

Martin, David↗
NASA NTRS1983

Advanced Platform Systems Technology study. Volume 3: Supporting data

The overall study effort proceeded from the identification of 106 technology topics to the selection of 5 for detail trade studies. The technical issues and options were evaluated through the trade process. Finally, individual consideration was given to costs and benefits for the technologies identified for advancement. Eight priority technology items were identified for advancement. Supporting data generated during the trade selection and trade study process were presented. Space platform requirements, trade study and cost benefits analysis, and technology advancement planning are advanced. The structured approach used took advantage of a number of forms developed to ensure that a consistent approach was employed by each of the diverse specialists that participated. These forms were an intrinsic part of the study protocol.

Source record↗
NASA NTRS2008

Gastrointestinal Physiology During Head Down Tilt Bedrest in Human Subjects

Introduction: Gastrointestinal (GI) motility plays a key role in the physiology and function of the GI tract. It directly affects absorption of medications and nutrients taken by mouth, in addition to indirectly altering GI physiology by way of changes in the microfloral composition and biochemistry of the GI tract. Astronauts have reported nausea, loss of appetite and constipation during space flight all of which indicate a reduction in GI motility and function similar to the one seen in chronic bed rest patients. The purpose of this study is to determine GI motility and bacterial proliferation during -6 degree head down tilt bed rest (HTD). Methods: Healthy male and female subjects between the ages of 25-40 participated in a 60 day HTD study protocol. GI transit time (GITT) was determined using lactulose breath hydrogen test and bacterial overgrowth was measured using glucose breath hydrogen test. H. Pylori colonization was determined using C13-urea breath test (UBIT#). All three tests were conducted on 9 days before HDT, and repeated on HDT days 2, 28, 58, and again on day 7 after HDT. Results: GITT increased during HTD compared to the respective ambulatory control values; GITT was significantly lower on day 7 after HTD. A concomitant increase in bacterial colonization was also noticed during HDT starting after approximately 28 days of HDT. However, H. Pylori proliferation was not recorded during HDT as indicated by UBIT#. Conclusion: GITT significantly decreased during HDT with a concomitant increase in the proliferation of GI bacterial flora but not H. pylori.

Vaksman, Z.↗
NASA NTRS2006

Transferring Files Between the Deep Impact Spacecrafts and the Ground Data System Using the CCSDS File Delivery Protocol (CFDP): A Case Study

The CCSDS File Delivery Protocol (CFDP) Standard could reshape ground support architectures by enabling applications to communicate over the space link using reliable-symmetric transport services. JPL utilized the CFDP standard to support the Deep Impact Mission. The architecture was based on layering the CFDP applications on top of the CCSDS Space Link Extension Services for data transport from the mission control centers to the ground stations. On July 4, 2005 at 1:52 A.M. EDT, the Deep Impact impactor successfully collided with comet Tempel 1. During the final 48 hours prior to impact, over 300 files were uplinked to the spacecraft, while over 6 thousand files were downlinked from the spacecraft using the CFDP. This paper uses the Deep Impact Mission as a case study in a discussion of the CFDP architecture, Deep Impact Mission requirements, and design for integrating the CFDP into the JPL deep space support services. Issues and recommendations for future missions using CFDP are also provided.

CCSDS File Delivery Protocol (CFDP)↗
NASA NTRS1991

Effects of space environment on structural materials - A preliminary study and development of materials characterization protocols

A preliminary study of materials exposed in space in LEO for nearly six years in the NASA Long-Duration Exposure Facility is presented. It is demonstrated that it will be necessary to isolate surface debris and reaction products from materials exposed in space. Replication techniques originally designed for electron microscopy examination of surfaces can be applied to lift off and isolate such surface features. Debris and reaction products were examined through a variety of analytical techniques, including the surface morphology by SEM, and internal microstructures by STEM and TEM, EDS, and SAD. The results illustrate the role that atomic oxygen and micrometeorites play in surface alteration and reaction in LEO space environments, as well as the role of debris created from other proximate materials.

Miglionico, C.↗
NASA NTRS2012

The Agricultural Model Intercomparison and Improvement Project (AgMIP): Protocols and Pilot Studies

The Agricultural Model Intercomparison and Improvement Project (AgMIP) is a major international effort linking the climate, crop, and economic modeling communities with cutting-edge information technology to produce improved crop and economic models and the next generation of climate impact projections for the agricultural sector. The goals of AgMIP are to improve substantially the characterization of world food security due to climate change and to enhance adaptation capacity in both developing and developed countries. Analyses of the agricultural impacts of climate variability and change require a transdisciplinary effort to consistently link state-of-the-art climate scenarios to crop and economic models. Crop model outputs are aggregated as inputs to regional and global economic models to determine regional vulnerabilities, changes in comparative advantage, price effects, and potential adaptation strategies in the agricultural sector. Climate, Crop Modeling, Economics, and Information Technology Team Protocols are presented to guide coordinated climate, crop modeling, economics, and information technology research activities around the world, along with AgMIP Cross-Cutting Themes that address uncertainty, aggregation and scaling, and the development of Representative Agricultural Pathways (RAPs) to enable testing of climate change adaptations in the context of other regional and global trends. The organization of research activities by geographic region and specific crops is described, along with project milestones. Pilot results demonstrate AgMIP's role in assessing climate impacts with explicit representation of uncertainties in climate scenarios and simulations using crop and economic models. An intercomparison of wheat model simulations near Obregón, Mexico reveals inter-model differences in yield sensitivity to [CO2] with model uncertainty holding approximately steady as concentrations rise, while uncertainty related to choice of crop model increases with rising temperatures. Wheat model simulations with midcentury climate scenarios project a slight decline in absolute yields that is more sensitive to selection of crop model than to global climate model, emissions scenario, or climate scenario downscaling method. A comparison of regional and national-scale economic simulations finds a large sensitivity of projected yield changes to the simulations' resolved scales. Finally, a global economic model intercomparison example demonstrates that improvements in the understanding of agriculture futures arise from integration of the range of uncertainty in crop, climate, and economic modeling results in multi-model assessments.

Rosenzweig, C.↗
NASA NTRS1992

Guaranteeing synchronous message deadlines with the timed token medium access control protocol

We study the problem of guaranteeing synchronous message deadlines in token ring networks where the timed token medium access control protocol is employed. Synchronous capacity, defined as the maximum time for which a node can transmit its synchronous messages every time it receives the token, is a key parameter in the control of synchronous message transmission. To ensure the transmission of synchronous messages before their deadlines, synchronous capacities must be properly allocated to individual nodes. We address the issue of appropriate allocation of the synchronous capacities. Several synchronous capacity allocation schemes are analyzed in terms of their ability to satisfy deadline constraints of synchronous messages. We show that an inappropriate allocation of the synchronous capacities could cause message deadlines to be missed even if the synchronous traffic is extremely low. We propose a scheme called the normalized proportional allocation scheme which can guarantee the synchronous message deadlines for synchronous traffic of up to 33 percent of available utilization. To date, no other synchronous capacity allocation scheme has been reported to achieve such substantial performance. Another major contribution of this paper is an extension to the previous work on the bounded token rotation time. We prove that the time elapsed between any consecutive visits to a particular node is bounded by upsilon TTRT, where TTRT is the target token rotation time set up at system initialization time. The previous result by Johnson and Sevcik is a special case where upsilon = 2. We use this result in the analysis of various synchronous allocation schemes. It can also be applied in other similar studies.

Agrawal, Gopal↗