Analysis of queuing-inventory system with phase-type service time under hybrid replenishment policy

Authors

  • Agassi Melikov Baku Engineering University, 120 Hasan Aliyev Street, Khirdalan AZ0101, Azerbaijan
  • Serife Ozkar Balikesir University, Çağış Campus, Balikesir 10145, Turkey

Keywords:

queuing-inventory system, hybrid replenishment policy, phase-type service distribution, matrix-geometric method

Abstract

We investigate a single-server queuing-inventory system with a hybrid replenishment policy. Customer arrivals follow a Poisson process and service times have a phase-type distribution. A hybrid inventory replenishment policy is defined as follows: when the inventory level falls to s, the (s, Q) policy is applied, provided that the number of customers in the system is less than a threshold r; if at this point the customers quantity is greater than or equal to r, the (s, S) policy is applied. The mathematical model of the investigated queuing-inventory system is constructed as a multi-dimensional continuous-time Markov chain. The stability condition is established, and steady-state distribution is calculated using the matrix-geometric method. Numerical results are presented.

Author Biographies

  • Agassi Melikov, Baku Engineering University, 120 Hasan Aliyev Street, Khirdalan AZ0101, Azerbaijan

    doctor of science (engineering), corresponding member of the National Academy of Sciences of Azerbaijan, full professor; vice-rector for scientific affairs and professor at the department of mathematics and computer science, faculty of information and computer technologies

  • Serife Ozkar, Balikesir University, Çağış Campus, Balikesir 10145, Turkey

    PhD (statistics), docent; associate professor at the department of international trade and logistics, faculty of economics and administrative sciences

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Published

2026-09-25

Issue

No. 2 (2026): Journal of the Belarusian State University. Mathematics and Informatics

Section

Probability Theory and Mathematical Statistics

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How to Cite

[1]
Melikov, A. and Ozkar, S. 2026. Analysis of queuing-inventory system with phase-type service time under hybrid replenishment policy. Journal of the Belarusian State University. Mathematics and Informatics. 2 (Sep. 2026), 77–88.