Optimal control of a removable and non-reliable server in an infinite and a finite \(M/H_2/1\) queueing system
The paper deals with a single removable and non-reliable server in a queuing system with either infinite or finite capacity. The server is turned on when \(N\) or more costumers are present in the system and turned off when none is present. While the server is turned on and working, it is subject of breakdowns according to a Poisson process. Objectives of the paper are to construct steady-state models for both the infinite and the finite system capacity, to determine the stability condition to reach steady-state and to formulate the cost function. The cost function includes the holding costs for each waiting costumer in the system, the costs for keeping the server alive, the costs for turning the server on or off, the breakdown costs for failed server and the fixed costs for every lost costumer. The authors determine the optimal \(N\)-policy in respect of cost minimization. The results are completed by a sensitivity analysis for an infinite and a finite system capacity and different cost factors.
scientific article; zbMATH DE number 1389075