Research and optimization of semi-Markov queueing models

Abstract

Algorithmization of the quality of queuing systems is carried out in order to optimize the work, constructing the revenue functional on the trajectories of a managed semi-Markov process while managing the system’s structure. In particular, we consider both semi-Markov and Markov queuing systems with control of several parameters (characteristics of the system). The task is to find the optimal management strategy. The proposed algorithms of investigation and the characteristics of the queuing systems’ operation $M/M/n^{\ast }/N^{\ast }$, $\mathit{BSMAP}/M_k/n_k/N_k$, $M/G^{\ast }/n/N^{\ast }$, obtained in explicit form can be used to study systems when managing both discontinuous and continuous system parameters.

Keywords:

• Semi-markov process
• queueing system
• optimization
• optimal control

Disclosure statement

No potential conflict of interest was reported by the authors.