A Multi-Server Retrial Queueing Inventory System With Asynchronous Multiple Vacations
K. Jeganathan, T. Harikrishnan, K. Prasanna Lakshmi, D. Nagarajan

TL;DR
This paper models a complex multi-server queueing system with asynchronous vacations and customer retrials, analyzing its steady-state behavior, stability, and costs through matrix geometric methods.
Contribution
It introduces a novel multi-server queueing-inventory model with asynchronous server vacations and retrials, providing stability conditions and performance analysis using matrix geometric approximation.
Findings
Derived stability conditions for the system.
Computed performance measures including waiting times.
Analyzed the impact of system parameters on customer loss rate.
Abstract
This article deals with asynchronous server vacation and customer retrial facility in a multi-server queueing-inventory system. The Poisson process governs the arrival of a customer. The system is comprised of c identical servers, a finite-size waiting area, and a storage area containing S items. The service time is distributed exponentially. If each server finds that there are an insufficient number of customers and items in the system after the busy period, they start a vacation. Once the servers vacation is over and it recognizes there is no chance of getting busy, it goes into an idle state if the number of customers or items is not sufficient, otherwise, it will take another vacation. Furthermore, each server's vacation period occurs independently of the other servers. The system accepts a (s, Q) control policy for inventory replenishment. For the steady state analysis, the Marcel…
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Taxonomy
TopicsAdvanced Queuing Theory Analysis
