V. D. Dinopoulou^*, M. N. Katehakis^**, C. Melolidakis^*

 ^*Dept. of Production Engineering and Management,
Technical University of Crete, GR-73100 Chania, Greece
**Dept. of Management Science, Graduate School of Management, Rutgers University, U.S.A.

Abstract

We consider a continously operating system consisting of N -out-of-, subsystems connected in parallel. The components of all subsystems are assumed identical with life times independent exponentially distributed random variables and the system is maintained by a single repaiman. In the present paper, we examine the optimal repair allocation policy for highly reliable systems. In particular, we show that there exists (and we describe it explicitly) an easy to compute index type repair allocation policy, which maximizes the reliability of the system at any time instant t. This policy is unique and depends only on the state and the structure of the system (and not on the failure and repair rates). Finally, we give the corresponding (“dual”) queueing network problem and the corresponding policy which controls that network optimally. In particular, we explicitly give the job assignment policy which maximizes the probability that at least one processor of the network is at full capacity.

Keywords: Controlled Markov Processes, Reliability, Queueing System.