Equilibrium delay distribution for queues with random service

The problem which the thesis discusses is that of determining the probability of delay of a demand (customer) in a queueing system in which service is random, i.e. on the completion of a service-time the server obtains the next customer for service by choosing at random from among those waiting. The system is assumed to be in statistical equilibrium arrivals are assumed to follow the Poisson distribution and two distinct assumptions regarding service-time are made, (i) that it follows the negative exponential distribution, (ii) that it is constant. For the case of negative exponential service-time, the work of a number of authors is reviewed: (i) Molina (1927), who derived the equilibrium state probabilities of the system; (ii) Mellor (1942), who was the first to discuss the actual delay distribution, but whose treatment of the problem is incorrect; (iii) Vaulot (1946), who formulated the problem correctly and gave a fundamental differential-difference equation, which he used to find the delay distribution as a Maclaurin series; (iv) Palm (1946), who, independently of Vaulot and almost simultaneously with him, derived the fundamental equation, and discussed methods (involving generating functions) by which it might be solved, the determination of the general form of the distribution by means of the first two moments, and the question of numerical computation; (v) Pollaczek (1946), who used Laplace transforms end contour integration to find an exact expression for the delay distribution function, but In a form too complicated for actual computation; (vi) Riordan (1953), who, in cm attempt to check numerical values obtained by means of a differential analyzer, found a method of evaluating exactly the moments of the distribution, and used them to approximate to the distribution function by a sum of a few exponentials, thus obtaining numerical values comparatively easily; (vii) Le Roy (1937), who discussed the problem In matrix notation and used an approximating process similar to Riordan's. The case in which the number of places in the queue is finite does not appear to have been discussed, and in the next section, which is new, the modifications to the state probabilities and to the fundamental equation for this case are given. The results of act vial solution of the equation, by means of the Sirius digital computer, for 20, 40 and 60 places In the queue are given, and their relation to the results for an unrestricted queue cure discussed. The case of constant service-time has received comparatively little attention, and the section dealing with this first reviews the work of Crommelin (1932), who derived equations satisfied by the equilibrium state probabilities and also obtained an expression for a generating function of these probabilities, and of Burke (1959), gave a very clear analysis of the problem and obtained actual numerical values for the delay distribution, but only for the case of one server. Burke's work appears to be capable of extension, and in the next section, which is new, it is shown that his methods can be used In the case of two servers. There seems to be no record of a Monte Carlo investigation of the constant service-time case, and in the following section, which is also new, the method by which such an investigation was carried out, by means of the Sirius computer, for one and for two servers is described. It is shown that for one server good agreement with Burke's results was obtained. Finelly, it is pointed out that although Burke's methods can probably be extended to more than two servers, Monte Carlo methods offer an easier way of dealing with this problem, and there seems to be no serious difficulty in using them to analyse not only larger systems but also cases in which more realistic assumptions are made regarding the arrival and service-time distributions

The Indian Ocean Deep Meridional Overturning Circulation in Three Ocean Reanalysis Products

The time mean Indian Ocean (IO) deep meridional overturning circulation (MOC) is compared across three ocean reanalysis products (ORAS4, GECCO2, and GFDL). The MOC stream functions obtained by vertically integrating the mass flux across a latitude-depth section in three products are found to be significantly different from each other. Detailed analysis suggests that ORAS4 delivers the best depiction of IO MOC. The inferred IO deep MOC consists of two deep and strong counterclockwise cells located south of 30°S and around 10°S, respectively. The geostrophic component along with the barotropic or external mode dominates the former, and a combination of Ekman and geostrophic components dominates the latter. GECCO2 depicts a steady decline in the northward meridional transport in the bottom layer and a consequent reduction in the MOC strength. The tropical thermocline in GECCO2 responds to this MOC variability leading to rapid and monotonic warming of the tropical IO

Inconsistent Atmosphere‐Ocean Dynamics and Multidecadal Zonal SST Gradient Trends Across the Equatorial Pacific Ocean in Reanalysis Products

Ocean reanalysis products are routinely employed as reality checks in model evaluations and for process studies. This is especially so for critical regions such as the equatorial cold tongue (ECT) in the eastern equatorial Pacific where models suffer a chronic cold bias. ECT is a major player in the Pacific equatorial zonal sea surface temperature (SST) gradient (ΔEWSST) that has a significant impact on oceanic heat uptake and thus global climate. Hence, we investigate the reliability of three ocean reanalysis products for surface flux and ocean dynamic controls on ΔEWSST and Niño3.4 SST trends. We infer that while Niño3.4 SST trends are positive in all products, the signs of ΔEWSST trends do not agree with each other because initial conditions likely play a big role in their evolution. However, for ΔEWSST trends, the effect of initial conditions gets canceled out to some extent. Mixed layer heat budget and trends in ocean dynamic features such as tropical and subtropical cells, equatorial undercurrent, and subsurface temperatures are also diagnosed. We show that two reanalysis products that show a strengthening of ΔEWSST have contradicting trends in their surface heat flux and ocean dynamic contributions. This suggests that without accurate surface heat and momentum fluxes, data assimilation techniques may produce an east–west trend that is inconsistent among each other. Reanalysis products must address these issues considering the importance of this gradient

When someone gets sick, we run to them, not from them”: holding space for solidarity otherwise and the cxxxity in times of COVID-19

Global Challenges (FGGA

Gender Differences in the Relationships between Perceived Stress, Eating Behaviors, Sleep, Dietary Risk, and Body Mass Index

Background: Obesity is a growing epidemic among university students, and the high levels of stress reported by this population could contribute to this issue. Singular relationships between perceived stress; engagement in restrained, uncontrolled, and emotional eating; sleep; dietary risk; and body mass index (BMI) have been reported in the current body of literature; however, these constructs interact with each other, and the complex relationships among them are infrequently examined. Therefore, the aim of the present study was to explore the complex relationships between these constructs using mediation and moderation analyses stratified by gender. Methods: A cross-sectional study, enrolling university students from the United States (U.S.), the Netherlands, South Korea, Malaysia, Ireland, Ghana, and China, was conducted between October 2020 and January 2021 during the COVID-19 pandemic. Perceived stress; maladaptive eating behaviors including restrained, uncontrolled, and emotional eating; sleep duration and quality; dietary risk; and BMI were assessed using validated questionnaires, which were distributed through an online platform. Results: A total of 1392 students completed the online survey (379 male, 973 female, and 40 who self-identified as “other”). Uncontrolled and emotional eating mediated the relationship between perceived stress and dietary risk for both males and females; higher sleep quality weakened this relationship among female students but not males. Emotional eating mediated the relationship between perceived stress and BMI for both males and females, but higher sleep quality weakened this relationship only among females. Conclusions: Our findings suggest that students in higher education are likely to benefit from interventions to reduce uncontrolled and emotional eating. Programs that improve sleep quality, especially during highly stressful periods, may be helpful

Needs and perceptions regarding healthy eating among people at risk of food insecurity: A qualitative analysis

Background: Healthy eating behaviour is an essential determinant of overall health. This behaviour is generally poor among people at risk of experiencing food insecurity, which may be caused by many factors including perceived higher costs of healthy foods, financial stress, inadequate nutritional knowledge, and inadequate skills required for healthy food preparation. Few studies have examined how these factors influence eating behaviour among people at risk of experiencing food insecurity. We therefore aimed to gain a better understanding of the needs and perceptions regarding healthy eating in this target group. Methods: We conducted a qualitative exploration grounded in data using inductive analyses with 10 participants at risk of experiencing food insecurity. The analysis using an inductive approach identified four core factors influencing eating behaviour: Health related topics; Social and cultural influences; Influences by the physical environment; and Financial influences. Results: Overall, participants showed adequate nutrition knowledge. However, eating behaviour was strongly influenced by both social factors (e.g. child food preferences and cultural food habits), and physical environmental factors (e.g. temptations in the local food environment). Perceived barriers for healthy eating behaviour included poor mental health, financial stress, and high food prices. Participants had a generally conscious attitude towards their financial situation, reflected in their strategies to cope with a limited budget. Food insecurity was mostly mentioned in reference to the past or to others and not to participants' own current experiences. Participants were familiar with several existing resources to reduce food-related financial strain (e.g. debt assistance) and generally had a positive attitude towards these resources. An exception was the Food Bank, of which the food parcel content was not well appreciated. Proposed interventions to reduce food-related financial strain included distributing free meals, facilitating social contacts, increasing healthy food supply in the neighbourhood, and lowering prices of healthy foods. Conclusion: The insights from this study increase understanding of factors influencing eating behaviour of people at risk of food insecurity. Therefore, this study could inform future development of potential interventions aiming at helping people at risk of experiencing food insecurity to improve healthy eating, thereby decreasing the risk of diet-related diseases

Biocompatibility of implantable materials: an oxidative stress viewpoint

Oxidative stress occurs when the production of oxidants surpasses the antioxidant capacity in living cells. Oxidative stress is implicated in a number of pathological conditions such as cardiovascular and neurodegenerative diseases but it also has crucial roles in the regulation of cellular activities. Over the last few decades, many studies have identified significant connections between oxidative stress, inflammation and healing. In particular, increasing evidence indicates that the production of oxidants and the cellular response to oxidative stress are intricately connected to the fate of implanted biomaterials. This review article provides an overview of the major mechanisms underlying the link between oxidative stress and the biocompatibility of biomaterials. ROS, RNS and lipid peroxidation products act as chemo-attractants, signalling molecules and agents of degradation during the inflammation and healing phases. As chemo-attractants and signalling molecules, they contribute to the recruitment and activation of inflammatory and healing cells, which in turn produce more oxidants. As agents of degradation, they contribute to the maturation of the extracellular matrix at the healing site and to the degradation of the implanted material. Oxidative stress is itself influenced by the material properties, such as by their composition, their surface properties and their degradation products. Because both cells and materials produce and react with oxidants, oxidative stress may be the most direct route mediating the communication between cells and materials. Improved understanding of the oxidative stress mechanisms following biomaterial implantation may therefore help the development of new biomaterials with enhanced biocompatibility

Analysis and design of low-noise amplifiers in silicon-germanium hetrojunction bipolar technology for radar and communication systems

This thesis presents an overview of the simulation, design, and measurement of state-of-the-art Silicon-Germanium Hetro-Junction Bipolar Transistor (SiGe HBT) low-noise amplifiers (LNAs). The LNA design trade-off space is presented and methods for achieving an optimized design are discussed. In Chapter 1, we review the importance of LNAs and the benefits of SiGe HBT technology in high frequency amplifier design. Chapter 2 introduces LNA design and basic noise theory. A graphical LNA design approach is presented to aid in understanding of the high-frequency LNA design process. Chapter 3 presents an LNA design optimization method for power constrained applications. Measured results using this design technique are highlighted and shown to have record performance. Lastly, in Chapter 4, we highlight cryogenic noise performance and present measured results from cryogenic operation of SiGe HBT LNAs. We demonstrate in this thesis that SiGe HBT LNAs have the capability to meet the demanding needs for next generation wireless systems. The aim of the analysis presented herein is to provide designers with the fundamentals of designing SiGe HBT LNAs through relevant design examples and measured results.M.S