**Programmee**: | Young Researchers |

**Code**: | 13.819.18.05A |

**Execution period**: | 2013 – 2014 |

**Institutions**: | Institute of Mathematics and Computer Science |

**Project Leader**: | Bejenari Diana |

**Participants**: |
Mitev Lilia, Ţicu Ionela, Rodica Costea Alina |

### Summary

Within this project will be realized the following objectives:

- determining the matrix form of Kendall functional equation;
- determining the matrix form of generalized Kendall functional equation;
- elaboration of matrix algorithms for determining the k-busy period distribution for queueing systems of Polling type with semi-Markov delays and for generalized priority queuing systems;
- elaboration of numerical algorithms for calculating state probabilities and mean value of waiting time for Polling systems with discrete time;
- elaboration of numerical algorithms for modeling traffic coefficient, queue length distribution for generalized models with semi-Markov exchange of states;
- implementation of the elaborated algorithms.

Methodology support of the research is based on some concepts from probability theory, queueing systems theory, methods of the theory of random processes, etc.

After achieving the proposed objectives are expected the following results:

- obtaining the matrix form of Kendall functional equation and generalized Kendall for determining the k-busy period distribution for queueing systems of Polling type with semi-Markov delays, and for generalized priority queuing systems;
- software numerical algorithms of calculation investigated probabilistic characteristics for these systems for diversification and processing information flow analysis in the activity seaport, for efficiency of the activity maritime terminals, contemporary networks and modern network technologies.