The analysis of unreliable M[X]/G/1 queuing system with loss,vacation and two delays of verification |
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Authors: | Hafida Saggou Ines Sadeg El-Bay Bourennane |
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Institution: | 1. Laboratory of RIIMA, Faculty of Mathematics, USTHB, PB 32 El Alia 16111 Algiers, Algeria;2. Laboratory LE2I UMR CNRS 6306, University of Bourgogne, Dijon, France |
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Abstract: | This paper considers an MX]/G/1 queue with breakdowns, repair, Bernoulli vacation, two delays and geometric loss. In this paper, a special attention is given to the limiting distribution of system states. We obtain simplified expressions for the Probability Generating Functions (PGFs) of the joint distribution of server state and system size. Some performance measures were derived from the analysis of the steady state probabilities. PGF of a departure point system size distribution is developed. Particular cases of the studied system were investigated. The effect of system parameters on the main performance measures are illustrated and discussed. |
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Keywords: | Batch arrivals Random breakdowns Verification time Vacation time geometric loss Supplementary variable method |
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