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Analysis of junior servers approaching a senior server in the multi-server queueing-inventory system
K Jeganathan1, V Anzen Koffer1, K Prasanna Lakshmi2
1Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, Tamil Nadu, 600005, India.
Scientific Reports
|May 6, 2025
Summary
Introducing a senior server into multi-server queueing-inventory systems significantly boosts efficiency. This model, using state-dependent service rates, outperforms traditional systems, enhancing business profit.
Area of Science:
- Operations Research
- Queueing Theory
Background:
- Multi-server queueing-inventory systems face challenges with junior server service disruptions.
- Junior servers require senior server assistance, creating potential bottlenecks.
Purpose of the Study:
- To analyze a multi-server queueing-inventory system with a senior server providing support to junior servers.
- To evaluate the system's performance using state-dependent service rates and compare it with homogeneous rates.
Main Methods:
- Modeling the system as a quasi-birth-and-death process.
- Computing the steady-state probability vector.
- Establishing convexity in expected total cost for both homogeneous and state-dependent service rates.
Main Results:
- State-dependent service rates demonstrate superior operational efficiency over homogeneous rates.
- Analysis of expected waiting times and the number of junior servers in various states.
- The proposed model with a senior server is more efficient than traditional multi-server models.
Conclusions:
- Implementing a senior server enhances the overall efficiency of multi-server queueing-inventory systems.
- State-dependent service rates are crucial for optimizing system performance and increasing business profit.
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