Priority queueing model with balking and reneging

This investigation deals with two levels, single server preemptive priority queueing model with discouragement behaviour (balking and reneging) of customers. Arrivals to each level are assumed to follow a Poisson process and service times are exponentially distributed. The decision to balk / renege is made on the basis of queue length only. Two specific forms of balking behaviour are considered. The system under consideration is solved by using a finite difference equation approach for solving the governing balance equations of the queueing model, with infinite population of level 1 customer. The steady state probability distribution of the number of customers in the system is obtained

Unreliable Server Retrial Queue with Optional Service and Multi-Phase Repair

In this paper, the retrial unreliable server queue with batch arrivals is considered. The arrival rates of the units are different and dependent upon the joining probabilities according to the server status. On arrival, if unit finds the busy server, he may retry for the service after a random duration of time. The server facilitates the essential service and optional service, if opted after essential service. Moreover, the server is unreliable and subject to the breakdown while rendering essential/optional service. The failed server may immediately undergo for the compulsory multiphase repair or may wait to start the repair due to any technical reasons. The server can also avail the optional vacation under the Bernoulli schedule after finish the service of each unit or may continue to serve the next unit. The variables corresponding to elapsed times of general distributed service process, retrial process, repair process and vacation duration, as supplementary variables and used to frame the governing equations. By using the probability generating functions of joint distributions of the units at different states of the server, the performance characteristics of the system are derived. To validate the results, the sensitivity analysis has been performed by taking the numerical illustration

Klippel Trenaunay Weber syndrome with unilateral polycystic kidney disease: a rare presentation

Klippel Trenaunay Weber syndrome (KTWS) is a rare disease characterized by hemihypertrophy, variceal enlargement of the veins, and arteriovenous (AV) malformations. Renal involvement in KTWS is not known except in rare case reports. Herein, we present a case of KTWS with unilateral polycystic kidney. A 52-year-old male was admitted due to pain left lumbar region for the last three months. The physical findings were increased diameter and increased length of the left leg compared with the right one, diffuse variceal enlargements on left leg, portwine stain on left side on neck, thorax, abdomen, left upper limb and left lower limb and a few hemangiomatous lesions on the left leg. Radiographic findings were cystic lesions in the left kidney, varicose veins in left leg, and hypertrophy of the soft tissues of the proximal left leg. Color Doppler of left lower limb showed incompetence of the saphenofemoral junction. He was diagnosed to have KTWS with these findings. Renal function tests of the patient were in the normal range. Patient’s only complain was left lumbar region pain, mild in intensity. Patient was managed symptomatically

Performance analysis of bulk arrival queue with balking, optional service, delayed repair and multi-phase repair

In this investigation, single repairable server queueing system with bulk input and state dependent rates is analyzed by considering the general distributions for the repair, delay to repair and service processes. The server is capable of rendering two stages of the service in which the first stage service is essential and the second stage service is optional. During the repair, the server has to undergo through m-different compulsory phases of the repair. To examine the steady state behavior and to obtain the various performance indices of the system, the probability generating functions of the queue size distributions are derived by using the supplementary variable technique. By setting the appropriate parameters, some special cases are discussed. The sensitivity analysis is performed by facilitating the numerical results for the suitable illustration. Keywords: Bulk arrival, Unreliable server, Balking, Second optional service, Delayed repair, Queue size, Mathematics subject classification: 60K25, 68M2

MX/G/1 unreliable retrial queue with option of additional service and Bernoulli vacation

In this paper, retrial queue with unreliable server and bulk arrivals is investigated. The server is capable of providing m-optional services and any one of these available services, may be rendered to the customer after the first essential service if the customer opts for the same. It is assumed that the server may fail while rendering any phase of service and undergoes for the immediate repair. After the completion of the service of a customer, the server may either take a vacation for a random period or may continue to provide the service to the other customers waiting in the queue. The supplementary variables corresponding to service time, repair time and retrial time are incorporated to determine the queue size distribution. To examine the effect of different parameters on the performance measures of the system, the numerical illustration is given which is supported by numerical simulation and sensitivity analysis

Age–sex differences in the global burden of lower respiratory infections and risk factors, 1990–2019: results from the Global Burden of Disease Study 2019

Summary Background The global burden of lower respiratory infections (LRIs) and corresponding risk factors in children older than 5 years and adults has not been studied as comprehensively as it has been in children younger than 5 years. We assessed the burden and trends of LRIs and risk factors across all age groups by sex, for 204 countries and territories. Methods In this analysis of data for the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019, we used clinician-diagnosed pneumonia or bronchiolitis as our case definition for LRIs. We included International Classification of Diseases 9th edition codes 079.6, 466–469, 470.0, 480–482.8, 483.0–483.9, 484.1–484.2, 484.6–484.7, and 487–489 and International Classification of Diseases 10th edition codes A48.1, A70, B97.4–B97.6, J09–J15.8, J16–J16.9, J20–J21.9, J91.0, P23.0–P23.4, and U04–U04.9. We used the Cause of Death Ensemble modelling strategy to analyse 23 109 site-years of vital registration data, 825 site-years of sample vital registration data, 1766 site-years of verbal autopsy data, and 681 site-years of mortality surveillance data. We used DisMod-MR 2.1, a Bayesian meta-regression tool, to analyse age–sex-specific incidence and prevalence data identified via systematic reviews of the literature, population-based survey data, and claims and inpatient data. Additionally, we estimated age–sex-specific LRI mortality that is attributable to the independent effects of 14 risk factors. Findings Globally, in 2019, we estimated that there were 257 million (95% uncertainty interval [UI] 240–275) LRI incident episodes in males and 232 million (217–248) in females. In the same year, LRIs accounted for 1·30 million (95% UI 1·18–1·42) male deaths and 1·20 million (1·07–1·33) female deaths. Age-standardised incidence and mortality rates were 1·17 times (95% UI 1·16–1·18) and 1·31 times (95% UI 1·23–1·41) greater in males than in females in 2019. Between 1990 and 2019, LRI incidence and mortality rates declined at different rates across age groups and an increase in LRI episodes and deaths was estimated among all adult age groups, with males aged 70 years and older having the highest increase in LRI episodes (126·0% [95% UI 121·4–131·1]) and deaths (100·0% [83·4–115·9]). During the same period, LRI episodes and deaths in children younger than 15 years were estimated to have decreased, and the greatest decline was observed for LRI deaths in males younger than 5 years (–70·7% [–77·2 to –61·8]). The leading risk factors for LRI mortality varied across age groups and sex. More than half of global LRI deaths in children younger than 5 years were attributable to child wasting (population attributable fraction [PAF] 53·0% [95% UI 37·7–61·8] in males and 56·4% [40·7–65·1] in females), and more than a quarter of LRI deaths among those aged 5–14 years were attributable to household air pollution (PAF 26·0% [95% UI 16·6–35·5] for males and PAF 25·8% [16·3–35·4] for females). PAFs of male LRI deaths attributed to smoking were 20·4% (95% UI 15·4–25·2) in those aged 15–49 years, 30·5% (24·1–36·9) in those aged 50–69 years, and 21·9% (16·8–27·3) in those aged 70 years and older. PAFs of female LRI deaths attributed to household air pollution were 21·1% (95% UI 14·5–27·9) in those aged 15–49 years and 18·2% (12·5–24·5) in those aged 50–69 years. For females aged 70 years and older, the leading risk factor, ambient particulate matter, was responsible for 11·7% (95% UI 8·2–15·8) of LRI deaths. Interpretation The patterns and progress in reducing the burden of LRIs and key risk factors for mortality varied across age groups and sexes. The progress seen in children younger than 5 years was clearly a result of targeted interventions, such as vaccination and reduction of exposure to risk factors. Similar interventions for other age groups could contribute to the achievement of multiple Sustainable Development Goals targets, including promoting wellbeing at all ages and reducing health inequalities. Interventions, including addressing risk factors such as child wasting, smoking, ambient particulate matter pollution, and household air pollution, would prevent deaths and reduce health disparities

Population-level risks of alcohol consumption by amount, geography, age, sex, and year: a systematic analysis for the Global Burden of Disease Study 2020

Background The health risks associated with moderate alcohol consumption continue to be debated. Small amounts of alcohol might lower the risk of some health outcomes but increase the risk of others, suggesting that the overall risk depends, in part, on background disease rates, which vary by region, age, sex, and year. Methods For this analysis, we constructed burden-weighted dose-response relative risk curves across 22 health outcomes to estimate the theoretical minimum risk exposure level (TMREL) and non-drinker equivalence (NDE), the consumption level at which the health risk is equivalent to that of a non-drinker, using disease rates from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2020 for 21 regions, including 204 countries and territories, by 5-year age group, sex, and year for individuals aged 15-95 years and older from 1990 to 2020. Based on the NDE, we quantified the population consuming harmful amounts of alcohol. Findings The burden-weighted relative risk curves for alcohol use varied by region and age. Among individuals aged 15-39 years in 2020, the TMREL varied between 0 (95% uncertainty interval 0-0) and 0.603 (0.400-1.00) standard drinks per day, and the NDE varied between 0.002 (0-0) and 1.75 (0.698-4.30) standard drinks per day. Among individuals aged 40 years and older, the burden-weighted relative risk curve was J-shaped for all regions, with a 2020 TMREL that ranged from 0.114 (0-0.403) to 1.87 (0.500-3.30) standard drinks per day and an NDE that ranged between 0.193 (0-0.900) and 6.94 (3.40-8.30) standard drinks per day. Among individuals consuming harmful amounts of alcohol in 2020, 59.1% (54.3-65.4) were aged 15-39 years and 76.9% (73.0-81.3) were male. Interpretation There is strong evidence to support recommendations on alcohol consumption varying by age and location. Stronger interventions, particularly those tailored towards younger individuals, are needed to reduce the substantial global health loss attributable to alcohol

Population-level risks of alcohol consumption by amount, geography, age, sex, and year: a systematic analysis for the Global Burden of Disease Study 2020

Background: The health risks associated with moderate alcohol consumption continue to be debated. Small amounts of alcohol might lower the risk of some health outcomes but increase the risk of others, suggesting that the overall risk depends, in part, on background disease rates, which vary by region, age, sex, and year. Methods: For this analysis, we constructed burden-weighted dose–response relative risk curves across 22 health outcomes to estimate the theoretical minimum risk exposure level (TMREL) and non-drinker equivalence (NDE), the consumption level at which the health risk is equivalent to that of a non-drinker, using disease rates from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2020 for 21 regions, including 204 countries and territories, by 5-year age group, sex, and year for individuals aged 15–95 years and older from 1990 to 2020. Based on the NDE, we quantified the population consuming harmful amounts of alcohol. Findings: The burden-weighted relative risk curves for alcohol use varied by region and age. Among individuals aged 15–39 years in 2020, the TMREL varied between 0 (95% uncertainty interval 0–0) and 0·603 (0·400–1·00) standard drinks per day, and the NDE varied between 0·002 (0–0) and 1·75 (0·698–4·30) standard drinks per day. Among individuals aged 40 years and older, the burden-weighted relative risk curve was J-shaped for all regions, with a 2020 TMREL that ranged from 0·114 (0–0·403) to 1·87 (0·500–3·30) standard drinks per day and an NDE that ranged between 0·193 (0–0·900) and 6·94 (3·40–8·30) standard drinks per day. Among individuals consuming harmful amounts of alcohol in 2020, 59·1% (54·3–65·4) were aged 15–39 years and 76·9% (73·0–81·3) were male. Interpretation: There is strong evidence to support recommendations on alcohol consumption varying by age and location. Stronger interventions, particularly those tailored towards younger individuals, are needed to reduce the substantial global health loss attributable to alcohol. Funding: Bill & Melinda Gates Foundation