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Aerospace Instrument-Making

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Numerical Analysis of Multi-server Queue with Vacation, Setup and Vacation Delay Times
Lokhvitsky V.A., Khabarov R.S., Yakovlev E.L.

An approach to obtaining the probabilities of the state, initial moments of the waiting time and stay of
requests in a multi-channel queueing system of the M/H2
/n type with hyperexponential times of service
of requests, warming up, cooling and delay of the start of cooling is proposed. The parameters of the
hyperexponential distribution in the general case can be complex, which allows setting arbitrary values of
the variation coeffi cients of the specifi ed distributions (including less than one). The results of numerical
calculations are presented in comparison with the results of simulation modeling, which confi rm the high
accuracy and correctness of the proposed solution. The code with the implementation of the method and
calculation examples is available at the link [1].
Keywords: instrument walks, warming up, cooling down, delay in warming up, mass service systems, queue theory, simulation
modeling.


DOI: 10.25791/aviakosmos.1.2025.1456

Pp. 44-57.

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