Stochastic Analysis Of Queue Dynamics In Multi-Stage Mass Covid-19 Vaccination Networks With Capacity Optimization Kanika Sharma, B.K. Singh, Shubham Agarwal International Journal of Drug Delivery Technology, 2026 Multi-stage service systems were needed to roll out in the shortest time possible during mass COVID-19 vaccinations in the presence of severe stochastic variations in the arrivals and the service times. In contrast to one-station clinics, vaccination facilities are complex intertwined queueing systems which comprise registration, clinical screening, vaccination, and post-inoculation observation phases. The paper builds a strict dependence on stochastic study of such multi-stage network of vaccinations on the global level. It is a non-stationary open Jackson network with time-varying Poisson arrivals and non-homogeneous service rates. We develop the conditions of global stability through the techniques of fluid limits, obtain the approximations of diffusion with heavy traffic, and study the dynamics of bottlenecks. An optimization problem is developed that involves nonlinear capacity allocation in order to establish optimal staffing at the congested stages subject to labor costs. Original discrete-event simulation experiments help support the theoretical results. The findings can be used in large-scale planning of vaccination and add to the mathematical theory of non-stationary healthcare queueing networks.
Queuing Theory-Based Model for Optimization of Covid-19 Vaccination and Booster Delivery Kanika Sharma, Shubham Agarwal, B.K. Singh International Journal of Experimental Research and Review, 2024 Although queuing theory is commonly utilized in businesses to analyze and model processes involving waiting lines, the healthcare sector sees a difference from other industries when it comes to optimizing fixed resources under alterable demand conditions. To enhance operational effectiveness and cut down on waiting times, hospital operation managers need to be informed on the state of business processes. A scientific method to reduce systemic inefficiencies and raise patient satisfaction is the queuing theory. The objective of this study is to use queuing theory to optimize COVID-19 vaccination and booster delivery. This study discussed two distinct models, one for bigger MV hubs and the other for smaller GP vaccination clinics. The current study demonstrated how these models may be used to anticipate staffing needs to prevent bottlenecks, predict daily throughput given staff capacity limits, and simulate the queuing process. With respectable face validity, we produced accurate estimates of the distributions of given service times and overall processing times. In the future, this may be improved by carrying out a time-use survey to get empirical data on total processing time, which could be compared to the projected processing time of the model and service times for each station, which would help guide the model's inputs.
Statistical Analysis and Distribution of Fermat Pseudoprimes Within the Given Interval Bhawana Fulara, Arvind Bhatt, Deepak Kumar Sharma, Shubham Agarwal, Geeta Mathpal, et al. International Journal of Experimental Research and Review, 2024 Prime numbers are natural numbers that can only be divided by one and the original number. There is more than one of them. Error-correcting codes used in telecommunications are generated using prime numbers. They guarantee automatic message correction both during transmission and reception. Algorithms used in public-key cryptography are built upon primes. They're also employed in the production of pseudorandom numbers. Mathematicians and many other scientific and technological communities have always been fascinated by prime numbers. Additionally, computer engineers can use it to tackle a wide range of real-world problems. The analysis of prime numbers is very important for finding their applications in different fields. The statistical analysis of pseudoprimes within a given interval is carried out in the presented paper and an algorithm of Python program to find the distribution of pseudoprimes has also been generated, which is used to find their distribution with different bases within the given intervals. The data analysis process made use of graphical depiction. The discovery will surely open up new avenues for future number theory study and applications outside of mathematics.
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Distribution of Multi-Reverse Primes within the Given Interval & Their Application in Asymmetric Cryptographic Algorithm International Journal of Applied Engineering and Technology London, 2021
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