Finite Memory Recursive Solutions in Stochastic Models: Equilibrium and Transient Analysis

G/M/1 and M/G/1-type Markov processes provide natural models for widely differing stochastic phenomena. Efficient recursive solutions for the equilibrium and transient analysis of these processes are therefore of considerable interest. In this direction, a new class of recursive solutions are proposed for the analysis of M/G/l and G/M/l type processes. In this report, the notion of when a process is LEDI-complete, which means it has complete Level Entrance Direction Information, is introduced for G/M/1-type Markov processes. This notion leads to a new class of recursive solutions, called finite-memory recursive solutions, for the equilibrium probabilities of a class of G/M/ 1-type Markov processes. A finite-memory recursive solution of order k has the form πn+k = π W1 +π n+1W2 + ••• +πn+k-1 Wk7 where πn is the vector of limiting probabilities of the states on level n of the process and Wi, 1 \u3c i \u3c k, are square matrices. It is also shown that the concept of LEDI- completeness leads to a finite- memory recursive solution for the transient behavior of this class of G/M/-1- type processes. Such a recursive solution has the form πn+k(s) = ^n(s)W1(s) +π n+i(s)W2(s) + • • • + πn+k-i(s)Wk(s). where π(s) is the Laplace transform of πn(t), the vector of state occupancy probabilities at time t for the states on level n of the process. The relationship between these finite-memory recursive solutions and matrix geometric solutions is also explored. The results are extended to the case where the transition rates are level dependent. It is also briefly explained how a finite memory recursion for the equilibrium and transient probabilities of M/G/l type Markov processes can be obtained

STUDY OF HRCT CHEST FINDINGS AND SEVERITY SCORE IN COVID-19 PATIENTS AND ITS CORRELATION WITH CLINICAL AND LABORATORY PARAMETERS

Objectives: High-resolution computed tomography (HRCT) refers to a CT scan that gives a more precise cross-section image of the lungs than a regular chest CT and chest X-ray. HRCT chest uses specific technologies for better image resolution with exquisite lung details ideal for assessment. This modality can be applied in diagnosing and grading severity in coronavirus disease 2019 (COVID-19) infection. HRCT is more sensitive and accurate in diagnosing diffuse lung disease. Since HRCT can detect even small nodules in the lungs, it can detect severe abnormalities at an early stage of the infection and help to plan appropriate treatment. The aim of the study was to study HRCT chest findings in patients with COVID-19 infection and correlation with clinical and laboratory parameters.   Methods: This was a prospective and retrospective observational study done for duration of 1 year, that is, from June 2020 to May 2021 in the Department of Radio-diagnosis at Shri Sathya Sai Medical College and Research Institute, Tiruporur-Guduvancherry, Main Road, Ammapettai, Nellikuppam, Kancheepuram district on 235 COVID-19 positive patients. Results: The typical findings were ground glass opacity + reticular pattern (GGO +crazy paving) noted 50.2% moderate cases and 13.2% severe cases. The mild group (CT-SS of 1–8) consisted of 56 patients (23.83%), moderate group (CT-SS of 9–12) consisted of 143 (60.85%) patients where as severe group (CT-SS of >13) was composed of 36 (15.32%). Conclusion: HRCT chest plays an important role in early identification of the COVID-19 infection. HRCT severity score helps to the patients in guiding the treatment and monitor disease progression

Resource Management in Fog Networking of Cloud Computing using KNN Algorithm

It is necessary to deploy any application in Cloud environment to reduce the investment cost, maintenance cost and licence of hardware/software. Keeping these benefits, it is advised to go for cloud computing environment for any application deployment. The major challenge in this environment is fault tolerance of resources to support for continuous availability of resources to client for working. Especially in IoT applications, we use Fog networking connecting to cloud computing. In this scenario, it is advised to use KNN (K- Nearest Neighbour) resource identification and allocation algorithm to increase the throughput to user requirement. We are presenting an approach to allocate the required resources with optimal distance resource allocation, so as to improve the throughput of user requirement