The <i>k</i>-out-of-<i>n</i>:<i>G</i> System Viewed as a Multi-Server Queue

Abstract

This paper extends the k-out-of-n:G reliability system to a multi-server queue. We study a multi-server reliability-queuing model with the N-policy of repair. The queuing system considered here has n servers, each of which has identically and exponentially distributed service times with parameter μ. Servers are subject to breakdown at an exponential rate γ. The repair process follows the N-policy of repair. Although these servers work independently of each other, service can be provided only when k 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.

Keywords

• reliability
• <i>k</i>-out of <i>n</i> system
• <i>N</i>-policy
• HAP system
• breakdown