Analysis of Stochastic M / M / c / N Inventory System with Queue-Dependent Server Activation, Multi-Threshold Stages and Optional Retrial Facility

T. Harikrishnan, K. Jeganathan, S. Selvakumar, N. Anbazhagan, Woong Cho, Gyanendra Prasad Joshi and Kwang Chul Son
Additional contact information
T. Harikrishnan: Department of Mathematics, Guru Nanak College (Autonomous), Chennai 600042, India
K. Jeganathan: Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, India
S. Selvakumar: Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, India
N. Anbazhagan: Department of Mathematics, Alagappa University, Karaikudi 630003, India
Woong Cho: Department of Software Convergence, Daegu Catholic University, Gyeongsan 38430, Korea
Gyanendra Prasad Joshi: Department of Computer Science and Engineering, Sejong University, Seoul 05006, Korea
Kwang Chul Son: Department of Information Contents, Kwangwoon University, Seoul 01897, Korea

Mathematics, 2022, vol. 10, issue 15, 1-37

Abstract: The purpose of this article is to examine the server activation policy (SAP) in a multi-server queuing-inventory system (MQIS). The queue has a total of c number of multi-threshold stages as well as c -homogeneous servers. The activation of each server begins one by one if there is an adequate queue length and inventory in the system; otherwise, they remain idle. The server deactivation process continues until the queue length exceeds the manageable level (predetermined stages) or there is insufficient stock. In addition, when we assume the length of the two successive threshold levels is one, the server activation policy model becomes a regular multi-server model. The Neuts matrix geometric approach is used to discuss the stability condition, stationary probability vector. The Laplace–Stieltjes transform (LST) is used to analyse the waiting time distributions of the queue and orbital customers. Additionally, significant system performance metrics and sensitivity analysis are used to investigate the effects of various parameters and cost values. In the comparative result between the server activation model (SAM) and without the server activation model (WSAM) on the expected total cost, we obtain the minimised cost in the SAM. Moreover, the results are obtained by assuming that the length of the intervals between the two successive threshold levels is to be taken into account as the non-uniform length. The expected inventory level, reorder rate, and waiting time of a customer in the waiting hall and orbit were explored numerically by the parameter analysis.

Keywords: server activation; server deactivation; multi-threshold stages; waiting time; (0, s) ordering policy; classical retrial policy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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