A Queueing Inventory System with Server Working Breakdown
K. Prasanna Lakshmi1, K. Jeganathan2, V. Kamal Nasir3, L. Niyaz Ahmed4, M. Abdul Reiyas5
1K. Prasanna Lakshmi*, Department of Mathematics with Computer Applications, Ethiraj College for Women, Chennai, India.
2K. Jeganathan, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai, India.
3L. Niyaz Ahmed, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai, India.
4V. Kamal Nasir, Department of Mathematics, New College, Chennai.
5M. Abdul Reiyas, Department of Food Trade and Business Management, College of Food and Dairy Technology, TANUVAS, Chennai.
Manuscript received on September 16, 2019. | Revised Manuscript received on 24 September, 2019. | Manuscript published on October 10, 2019. | PP: 3351-3354 | Volume-8 Issue-12, October 2019. | Retrieval Number: L25721081219/2019©BEIESP | DOI: 10.35940/ijitee.L2572.1081219
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: This paper considers a single server inventory queueing system with two types of server breakdowns, say Type 1(T1) breakdown and Type 2 (T2) breakdowns, and working breakdown. T1 breakdown occurs in regular service period whereas T2 breakdown occurs in the duration of working breakdown. The inter arrival time between any two customers and the times of occurrences of both types of breakdowns are all independent exponential distributions. The commencement of repairing process of T1 breakdown follows Bernoulli’s whereas the commencement of repairing process of T2 breakdown is instantaneous. By using matrix method, we obtain the steady state probability vector of the finite capacity queueing inventory system. Finally, the numerical examination of model sensitiveness is performed.
Keywords: Server Working Breakdown, Markovian Inventory, (s,Q) policy.
Scope of the Article: Numerical Modelling of Structures