This paper reviews the applicability of simplified bandwidth requirement estimators that need only the mean and the peak rates of traffic flows as input, instead of the full statistical description of the traffic required by their original form. The estimators approximate the effective bandwidth function, the key component of the bandwidth requirement estimate, with the logarithmic moment generating function of an on-off source. It is demonstrated that this on-off type approximation has to be used with care as it results in a loss of information about the traffic streams. This is manifested in the reduction of the advanced bandwidth estimator method of the many sources asymptotics into the basic Chernoff-type technique. As a consequence bandwidth requirement estimators built on the onoff type approximation overlook the multiplexing gain occurring in the buffers, which results in overly conservative estimates close or equal to the peak rate when applied to traffic aggregates.
A new general solution method is derived for the general
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/1 type processes --- for the steady-state distribution of infinite block-structured Markov chains with repetitive structure. While matrix inversion is needed in each iterational step of other general (and of more special) matrix analytical procedures, the method presented here uses matrix addition and matrix multiplication only. In exchange, the computational complexity and the memory requirement is increasing in each iterational step of the proposed method. This paper, however, lays priority on the theoretical aspect of the general solution.
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