1,2Department of Mathematics, IFTM University, Moradabad-244102, Uttar Pradesh, India
3*Department of Mathematics, NDIM, New Delhi-110062, Delhi, India
Received: 18th Sep, 2025; Revised: 29th Oct, 2025; Accepted: 8th Nov, 2025; Available Online: 1st December, 2025
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 nonstationary healthcare queueing networks.
Keywords: Mass vaccination; Queuing networks; Stochastic stability; Heavy-traffic diffusion; Healthcare operations; Capacity allocation; Pandemic logistics; Optimization.
How to cite this article: Sharma K, Singh BK, Agarwal S. Stochastic Analysis of Queue Dynamics in Multi-Stage Mass Covid-19 Vaccination Networks with Capacity Optimization. Int J Drug Deliv Technol. 2026;16(1): 693-700; DOI: 10.25258/ijddt.16.1.72
Source of support: Nil.
Conflict of interest: None