Analysis of Single-Server Retrial Queuing Models with Batch Arrivals and Server Vacations: Numerical Simulation and Performance Evaluation
DOI:
https://doi.org/10.29070/9cg43m95Keywords:
Retrial Queuing Systems, Batch Arrivals, Server Vacations, Single-Server Model, Numerical Simulation, Performance Evaluation, Stochastic Modeling, service optimizationAbstract
This paper gives a rigorous analytical and numerical examination of single-server retrial queuing systems defined by batch arrivals and server vacation rules. Such models are extremely applicable in service contexts where clients, upon finding the server busy, enter a retry orbit and attempt service after random time periods. The addition of batch arrivals replicates realistic consumer behavior in applications like telephony, manufacturing, and service centers. Server vacations offer another degree of operational complexity, representing circumstances when the server may be offline owing to planned breaks or maintenance.
We establish the mathematical formulation of the system under steady-state circumstances and obtain performance indicators including mean system size, average waiting time, and server usage. Using numerical simulations, we explore the implications of retry rates, batch size distributions, and vacation rules on system performance. The findings give useful insights for enhancing service efficiency and resource allocation. The model acts as a powerful tool for decision-makers intending to boost customer satisfaction and system dependability in retrial-based queueing contexts.
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