A.P. Samoylenko, D.E. Rud

Optimal telecommunication system traffic management organization is unfeasible without usage of proper mathematical models. The most methodologically elaborated mathematical apparatus is queuing theory, however, the information flows nature restrictions make real telecommunication systems (TS) functioning analysis more complicated. One of such restrictions is the single arrival input information flow assumption. The purpose of this research is an attempt to synthesize and study the TS model functioning in a wide range of protocol data unit (PDU) batch size for TS traffic management implementation. The batch arrival input flow is approximated by the additive model of normalized simple (Poisson) flows. The TS functional description by n-dimensional Markovian model of queuing system is proposed and attended by the static mode functioning queuing system М 3/М 3/5 study example. The result of study is obtaining the system М 3/М 3/m and М 4/М 4/m static state probabilities expressions, validity of which is proven by potential possibility of their reduction to the known Erlang system type М /М /m formula. The expressions obtained can be generalized for describing the М n/М n/m queuing systems. The absolute throughput is used as the main TS operating efficiency rate. It also can be used as an objective function for optimal TS management. The М 3/М 3/m queuing system with failures graph family A(m) analysis make possible to draw a conclusion about the range of service devices quantity m and the batch arrival traffic nature influence on TS performance. The recommendations for optimal TS resources management are given. An approach to the evaluation of the necessary capacity buffer memory, based on the average value of PDU quantity in the system is proposed.