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 noncongested 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.