Performance Evaluation of Internet Router and Steady State Vector.

      Аннотация: Seminal studies on the network traffic, revealed the certain statistical property (self-similar nature) of network traffic, and how they degrades the network performance. Markovian models are well recognized as the appropriate self-similar traffic models. Markovian arrival process (MAP) has been proposed to emulate self similarity over the desired time-scales. Markov modulated Poisson process (MMPP) a particular case of MMPP emulating self-similar traffc over different time scale is fitted by several authors using second order statistics. The two state Circulant Markov modulated Poisson process which is restricted version of two state MMPP. The CMMPP emulating self-similar traffic is fitted by equating the variance. The mean waiting time and packet loss behavior are calculated by using the models of CMMPP/M/1 CMMPP/M/1/K queuing systems wherein service time is taken to be deterministic exponential distributions. It is clear from the numerical results the time scale do have collision on delay packet loss probability. Loss probability of packets increases if H and Traffic intensity is increase. This type of analysis is useful in dimensioning the router.

Ключевые слова: Circulant stochastic matrices, Hurst parameter, self-similar traffic, traffic intensity, steady state probability vector, block triangular matrix, block skew symmetric matrix, TSS method, convergence analysis. CMMPP, mean waiting time, packet loss probability, timescale