Conference Agenda

We investigate the reliability and cycle analysis for a repairable k-out-of-n:G system with retrial of failed components. Such a model has important practical applications in fully automatic manufacturing system. Models for availability and reliability of the system whose components are all subject to two failure modes are presented.

One failure consists the specific component while there is the total failure-disaster-regarding all components. There is no waiting space for failed components in the system. If a failed component finds the repairman busy and it can not be repaired at once, it will enter into the retrial orbit and try again for repair after some random period of time. Some reliability indexes, including steady-state availability, reliability function and mean time to system first failure, are derived by using vector Markov process and Laplace transform theory. Also we explore the busy cycle and the idle system cycle providing useful results.

Service systems with a finite customer population occur if the maximum number of customers that can arrive is given, e.g., by the tickets that were sold for a flight. There is a trade-off between staffing costs and service quality, i.e., costs related to the waiting time and missing the deadline, e.g., the departure of the flight. From the service operator’s perspective, a key decision is to determine when and how many servers should be provided.

The literature on staffing decisions features constant and time-dependent staffing policies. For queueing systems with a finite customer population, state-dependent policies can exploit the information about the already served customers because it determines the number of customers left from the initial population and thereby the number of future arrivals. The literature encompasses state-dependent policies, where the number of servers can be changed depending on the already arrived, and severed customers. This requires a highly flexible workforce and flexible cost structures because the staffing depends on the realization of the arrival process.

We propose a new staffing policy that considers both servers scheduled according to a time-dependent policy and more expensive but flexible servers that follow a state-dependent policy. We formalize the optimization problem for queueing systems with a finite customer population for all discussed staffing policies. Solutions for the proposed staffing policy are generated by combining complete enumeration with stochastic dynamic programming. Numerical results that provide insights regarding the difference between the policies are presented.