Authors:
Kalyanaraman. R,DOI NO:
https://doi.org/10.26782/jmcms.2022.05.00004Keywords:
Markovian queue,heterogeneous server,breakdown,repair,steady-state solution,matrix-Geometric method,Abstract
In this paper, we consider a system with two heterogeneous servers Markovian queue. In which the system breakdown occurs when the system is in busy mode. Immediately the system undergoes repair. After completion of the repair, the system either undergoes optional repair mode or becomes busy mode based on a Bernoulli schedule. It is assumed that the number of repairs follows the Poisson process and the repair periods follow an exponential distribution. The model has been solved in steady-state using the matrix analytic method. Some performance measures and numerical results are obtained.Refference:
I. Cheng, C.Y., and Liu, H.H., (2010) The-finite – time -period preventive maintenance policies with failiure rate reduction under a warranty consideration, Journal of the Chinese institute of industrial Engineers, v.27, 81-89.
II. Desmit, J.H.A., (1983) A numerical solution for the multi server queue with hyper exponential service times, Oper. Res. Lett, v.2, 217-224.
III. Durilk,I., (2005) Inżynieria zarządzania Cz. II – strategie wytwarzania.Gdańsk: Wydawnictwo Placet.
IV. Heffer, J.C., (1969) Steady state solution of the M/Ek/C (F1F0) queuing system, CORSJ. v.7, 16-30.
V. Kalyanaraman, R., and Senthilkumar, R., (2018a) Heterogeneous server Markovian queue with switching of service modes,Annamalai University Science Journal, v.51(1), 1-8.
VI. Kalyanaraman, R., and Senthilkumar, R., (2018b) Heterogeneous server Markovian queue with restricted Admissibility and with Reneging, Mathematical Sciences International Research Journal, v.7 (1), 309-315.
VII. Kalyanaraman, R., and Senthilkumar, R., (2018c) Heterogeneous server Markovian queue with restricted Admissibility of customers,Journal of Applied Mathematics Analysis and Applications, v.7(1), 85-97.
VIII. Latouche, G and Neuts, M.F., (1980) Efficient algorithmic solutions to exponential tandem queues with blocking, SIAM J. Algebraic Discrete Math., v.1, 93-106.
IX. Lucantoni, D.M., (1979) A GI/M/C queue with a different service rate for customers who need not wait an algorithmic solution, Technical Rep. Univ. of Delware, USA.
X. Mitrany, I.L., and Avi-Itzhak, B., (1968) A many-server queue with service interruptions. Operations Research, v.16, pp. 628-638.
XI. Neuts, M.F., (1978) Markov chains with applications in queueing theory which have a matrix-geometric invariant probability vector, Adv. Appl. Probab., 10, 185-212.
XII. Neuts, M.F., (1981) Matrix-Geometric solution in stochastic models,Vol 2 of John Hopkins series in the Mathematical Sciences,John Hopkins University press, Baltimore,Md,USA. J. Mech. Cont. & Math. Sci., Vol.-17, No.-5, May (2022) pp 43-55 Kalyanaraman. R 55
XIII. Neuts, M.F., and Lucantoni, D.M., (1979) A Markovian queue with N servers subject to breakdowns and repairs. Management Science, v.25, pp. 849-861.
XIV. Schouten, F.A.V.D.D., and Wartenhorst, P., (1993) A two machine repair model with variable repair rate,Noval Research Logistics, v.40, 495-23.
XV. Sheng, Li .Lv., Jing, Bo.Li., and De, Quan.Yue., (2011) Unreliable multiserver machine repairable system with variable breakdown rates,Journal of the Chinese Institute Industrial Engineers, V.28(5), pp-400-409.
XVI. Singh, V.P., (1970) Two servers Markovian queues with balking, Heterogeneous vs Homogeneous servers, Oper.Res., v.18(1), 145-159.
XVII. Singh, V.P., (1973) Queue dependence-servers, Jr. of Eng. Maths, v.7 (2), 123-126.
XVIII. Vinod, B., (1985) Unreliable queueing systems. Computers and Operations Research, v.12, pp. 322-340.
XIX. Wang, K.H., and Chang, Y.C., (2002) Cost analysis of a finite M/M/R queueing system with balking, reneging and server breakdowns. Mathematical Methods of Operations Research, v.56, 169-180.
XX. Wartenhosrt, P., (1995) N parallel Queueing systems with server breakdowns and repair. European Journal of Operational Research, v.82, pp. 302-322.
XXI. Witold BIAŁY and Juraj RUŽBARSKÝ (2018) Breakdown Cause and Effect Analysis. Case Study, Management Systems in Production Engineering, v.26 (2), pp. 83-87.
XXII. Wu, C.H., Lee, W.C., Ke, J.C., and Liu,T.H., (2014) Optimization analysis of on unreliable multi server queue with a controllable repair policy, Computer and Operation research, v.49, pp-83-96.