Abstract
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.
The publication has been prepared with the support of the RUDN University Program 5-100 and funded by RFBR according to the research projects No. 17-07-00142.
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Efrosinin, D., Gudkova, I., Stepanova, N. (2019). Performance Analysis and Optimal Control for Queueing System with a Reserve Unreliable Server Pool. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2019. Communications in Computer and Information Science, vol 1109. Springer, Cham. https://doi.org/10.1007/978-3-030-33388-1_10
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DOI: https://doi.org/10.1007/978-3-030-33388-1_10
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