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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.

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|May 6, 2025
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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.

Keywords:
Infinite waiting hallJunior serversMatrix geometric methodQueueing-inventory systemSenior server

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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.