Performance Analysis and Optimal Control for Queueing System with a Reserve Unreliable Server Pool

In this paper a Markovian queueing system supplied with main and reserve unreliable service facility which we refer to as pools is introduced. Usage of the reserve pool is controlled by a hysteretic policy that depends on upper and lower threshold levels of queue length to increase and decrease the total service rate. The system is analysed as a process of type quasi-birth-and-death (QBD), and expressions for the stationary state probabilities are derived. For the cost structure we evaluate the long-run average cost per unit of time and determine the optimal hysteretic policy by implementing genetic algorithm. The sensitivity analysis to study the effect of system parameters and threshold levels on the average cost is provided by a number of numerical examples. © 2019, Springer Nature Switzerland AG