Drop behaviour of random early detection with discrete-time batch Markovian arrival process

A matrix-analytic approach is applied to analyse both the long-term and the short-term drop behaviour of a router with an RED scheme. The bursty nature of packet drop is examined by means of conditional statistics with respect to alternating congested and non-congested periods. All of the four related performance measures are derived by conditional statistics, including the long-term drop probability, and the three short-term measures comprising average length of a congested period, average length of a non-congested period, and the conditional packet drop probability during a congested period.