Queueing Inventory System with Multiple Service Nodes and Addressed Retrials from a Common Orbit

Rasmi K (), Jacob M J (), Alexander Dudin () and A. Krishnamoorthy ()
Additional contact information
Rasmi K: National Institute of Technology Calicut
Jacob M J: National Institute of Technology Calicut
Alexander Dudin: Belarusian State University
A. Krishnamoorthy: Department of Mathematics, CMS College

Methodology and Computing in Applied Probability, 2024, vol. 26, issue 1, 1-15

Abstract: Abstract In this paper, we consider a queueing inventory model with K service nodes located apart making it impossible to know the status of the other service nodes. The primary arrival of customers follows Marked Markovian Arrival Process and the service times are exponentially distributed. If a customer arriving at a node finds the server busy or the inventory level to be zero, he joins a common orbit with infinite capacity. An orbital customer shall choose a service node at random according to some predetermined probability distribution dependent on the orbit size. Each service node is assigned with a continuous review inventory replenished according to an (s, S) policy with lead time. This scenario is modeled as a level dependent quasi birth and death process which belongs to the class of asymptotically quasi-Teoplitz Markov chains. Steady-state probabilities and some important performance measures are obtained. A cost function is introduced and employed for computing the optimal values of reorder levels and replenishment rates.

Keywords: Retrial queue; MMAP[K]; QBD; Asymptotically quasi-Toeplitz Markov chain; Cost optimization (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-023-10071-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:26:y:2024:i:1:d:10.1007_s11009-023-10071-w

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-023-10071-w

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().