• Deepa Chauhan

Proposed work aims to analyze Mx/G/1 queuing system for unreliable server queue with two phases of heterogeneous services one after the other to the arriving batch under Bernoulli schedule vacation. The server operates under N-policy according to which he remains idle till queue size becomes N (≥1); i.e. when N customers are accumulated in the system, the server is immediately turn on and provides service. While servicing the customers the server may breakdown and is sent for repair immediately. As soon as the server is repaired, it starts to serve the customers. After completion of both phases of service, the server either goes for a vacation or may continue to serve the next customer, if any. The server’s vacations are based on Bernoulli schedule under a single vacation policy. We obtain explicit queue size distribution at random epoch as well as at the departure epoch under the steady state conditions. The numerical results for various performance measures are summarized in tables and displayed via graphs.

MX/(G1,G2)/1 queue, Bernoulli schedule, Vacation, N-Policy, Unreliable Server, Phase Services, Supplementary variable, Queue Size.

"Performance Analysis of MX/ (G1, G2)/1 Queue with Repairable Server, Bernoulli Vacation Schedule under N-Policy", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.12, Issue 10, page no.a25-a35, October-2025, Available :http://www.jetir.org/papers/JETIR2510003.pdf

"Performance Analysis of MX/ (G1, G2)/1 Queue with Repairable Server, Bernoulli Vacation Schedule under N-Policy", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.12, Issue 10, page no. ppa25-a35, October-2025, Available at : http://www.jetir.org/papers/JETIR2510003.pdf