Optimization of Markovian queuing systems with failures in the MATLAB system

The paper touches upon the optimization task of the multichannel Markov queuing system suffering failures due to a heavy work load, which can be observed in realistic operational conditions for multi-purpose queuing systems. The optimization task is reduced to maximizing the system throughput with the minimum number of maintenance devices required, hence, to reducing the number of failures. To solve the task, MATLAB R2016b system has been used, which provides tools (functions) for minimizing the objective functions of many variables with constraints. The natural constraints are superimposed on the system parameters: intensity of the input flow and intensity of the service, which are positive quantities in the queuing system environment. Taking into account the fact that possibility of failures depends on the number of servicing tools, this number inevitably becomes a real number, and not a whole number, and should be taken as a parameter of the optimization task. The results obtained can be used to test models of queuing systems having failures under peak loads, as well as in cases which can be defined by the ratio of the intensity of Poisson arrivals to the intensity of a single machine processing.