The purpose of this paper is to obtain product form solution for retrial – queueing – inventory system. We study an M/M/1 retrial queue with a storage system driven by an (s,S) policy. When server is idle, external arrivals enter directly to an orbit. Inventory replenishment lead time is exponentially distributed. The interval between two successive retrials is exponentially distributed and only the customer at the head of the orbit is permitted to access the server. No customer is allowed to join the orbit when the storage system is empty and also when the serer is busy. We first derive the stationary joint distribution of the queue length and the on-hand inventory in explicit product form. Using the joint distribution, we investigate long-run performance measures such as distribution of number of customers served, number of arrivals, number of customers lost during an interval of random duration and a cost function. The optimal pair (s,S) is numerically investigated.
Mots-clés : queueing-inventory, stochastic decomposition, retrial
@article{RO_2020__54_1_81_0, author = {Shajin, Dhanya and Krishnamoorthy, A.}, title = {Stochastic decomposition in retrial queueing-inventory system}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {81--99}, publisher = {EDP-Sciences}, volume = {54}, number = {1}, year = {2020}, doi = {10.1051/ro/2018118}, mrnumber = {4052228}, zbl = {1437.90018}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ro/2018118/} }
TY - JOUR AU - Shajin, Dhanya AU - Krishnamoorthy, A. TI - Stochastic decomposition in retrial queueing-inventory system JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2020 SP - 81 EP - 99 VL - 54 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2018118/ DO - 10.1051/ro/2018118 LA - en ID - RO_2020__54_1_81_0 ER -
%0 Journal Article %A Shajin, Dhanya %A Krishnamoorthy, A. %T Stochastic decomposition in retrial queueing-inventory system %J RAIRO - Operations Research - Recherche Opérationnelle %D 2020 %P 81-99 %V 54 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2018118/ %R 10.1051/ro/2018118 %G en %F RO_2020__54_1_81_0
Shajin, Dhanya; Krishnamoorthy, A. Stochastic decomposition in retrial queueing-inventory system. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 1, pp. 81-99. doi : 10.1051/ro/2018118. http://www.numdam.org/articles/10.1051/ro/2018118/
Retrial Queueing Systems. Springer Verlag, Berlin Heidelberg (2008) | DOI | MR | Zbl
and ,A queueing system with heterogeneous impatient customers and consumable items. Int. J. Appl. Math. Comput. Sci. 27 (2017) 367–384. | DOI | MR | Zbl
, and ,The M/M/1 queue with a production-inventory system and lost sales. Appl. Math. Comput. 233 (2014) 534–544. | MR | Zbl
and ,A production-inventory system with a Markovian service queue and lost sales. J. Korean Stat. Soc. 45 (2016) 14–24. | DOI | MR | Zbl
and ,Continuous-type -inventory model with an attached M/M/1 queue and lost sales. Perform. Eval. 125 (2018) 68–79. | DOI
, , and ,Loss systems in a random environment: steady-state analysis. Queueing Syst. 80 (2014) 127–153. | DOI | MR | Zbl
and ,Optimal control policy of an inventory system with postponed demand. RAIRO: OR 50 (2016) 145–155. | DOI | Numdam | MR | Zbl
, and ,On partial and complete blocking set of sets of states in Queueing-inventory model. Appl Comput. Math. 18 (2019) 189–201. | MR | Zbl
, and ,A two-priority single server retrial queue with additional items. To appear in: J. Ind. Manage. Optim. Doi: (2019). | DOI | MR | Zbl
, and ,A survey on inventory models with positive service time. OPSEARCH 48 (2011) 153–169. | DOI | MR
, and ,Stochastic decomposition in production inventory with service time. Eur. J. Oper. Res. 228 (2013) 358–366. | DOI | MR | Zbl
and ,Matrix-geometric Solutions in Stochastic Models: an Algorithmic Approach. The Johns Hopkins University Press, Baltimore [1994 version is Dover Edition] (1981). | MR | Zbl
,Numerical investigation of a multi-server retrial model. Queueing Syst. 7 (1990) 169–190. | DOI | Zbl
and ,Models for integrated production-inventory systems: steady state and cost analysis. Int. J. Prod. Res. 54 (2016) 6174–6191. | DOI
, and ,The M/M/1 queue with inventory, lost sale and general lead times. Queueing Syst. 75 (2013) 65–77. | DOI | MR | Zbl
, and ,M/M/1 queueing systems with inventory. Queueing Syst. 54 (2006) 55–78. | DOI | MR | Zbl
, , , and ,Cité par Sources :