<p>Many organizations extend their business by opening new branches at different places as customer’s need and company’s growth (for example, Honda bike and Hyundai car showrooms, Apollo Pharmacy, and so on). According to this real-life phenomenon, this article discusses the integrated queueing-inventory system with its two branches. We consider two branches namely, branch 1 and branch 2. Arrivals for both branches occur according to the Markovian arrival process and are independent. Both branches have a dedicated single server and finite waiting hall. If the inventory level reaches zero in any branch, the corresponding waiting customer is allowed either go to the other branch or infinite size orbit. This type of service process is called diverted services. If there is a space in branch 1 or branch 2, the retrial customer can decide to join in any branch under the Bernoulli schedule. Additionally, this article adopts the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$(s_1, Q_1)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>s</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mn>1</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> ordering policy for branch 1 and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$(s_2, Q_2)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>s</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mn>2</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> ordering policy for branch 2. Since we applied Neuts matrix geometric method to solve the stationary probability solution, we derived stability condition, rate matrix <i>R</i>. The necessary system performance metrics are found for the branching queueing-inventory system. Furthermore, some numerical illustrations are explained to show how the diverted service option helps to reduce the customer loss rate, waiting time, and increases the arrival rate at the time of zero inventory in the branching queueing-inventory system.</p>

Integrated branching queueing-inventory system with diverted service

期刊论文
发表日期：

2025年2月28日

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V. Vinitha,
S. Amutha,
Gyanendra Prasad Joshi,
M. Kameswari,
N. Anbazhagan

摘要

Many organizations extend their business by opening new branches at different places as customer’s need and company’s growth (for example, Honda bike and Hyundai car showrooms, Apollo Pharmacy, and so on). According to this real-life phenomenon, this article discusses the integrated queueing-inventory system with its two branches. We consider two branches namely, branch 1 and branch 2. Arrivals for both branches occur according to the Markovian arrival process and are independent. Both branches have a dedicated single server and finite waiting hall. If the inventory level reaches zero in any branch, the corresponding waiting customer is allowed either go to the other branch or infinite size orbit. This type of service process is called diverted services. If there is a space in branch 1 or branch 2, the retrial customer can decide to join in any branch under the Bernoulli schedule. Additionally, this article adopts the $(s_1, Q_1)$ $(s_{1}, Q_{1})$ ordering policy for branch 1 and $(s_2, Q_2)$ $(s_{2}, Q_{2})$ ordering policy for branch 2. Since we applied Neuts matrix geometric method to solve the stationary probability solution, we derived stability condition, rate matrix R. The necessary system performance metrics are found for the branching queueing-inventory system. Furthermore, some numerical illustrations are explained to show how the diverted service option helps to reduce the customer loss rate, waiting time, and increases the arrival rate at the time of zero inventory in the branching queueing-inventory system.