| Summary: | This paper extends the <i>k</i>-out-of-<i>n</i>:<i>G</i> reliability system to a multi-server queue. We study a multi-server reliability-queuing model with the <i>N</i>-policy of repair. The queuing system considered here has <i>n</i> servers, each of which has identically and exponentially distributed service times with parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>. Servers are subject to breakdown at an exponential rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>. The repair process follows the <i>N</i>-policy of repair. Although these servers work independently of each other, service can be provided only when <i>k</i> functional servers are available in the system. We study the model in the steady state, using the matrix analytic method. We evaluate some associated performance measures and provide graphical/numerical illustrations. We consider an optimization problem, and the results of the study are presented.
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