The Correlation Structure of the Output of an ATM Multiplexer
نویسندگان
چکیده
In this paper we study the correlation structure of the output process of an ATM multiplexer. We consider two special cases : (i) the output process of the D-BMAP/D/1/N queue, a generic model for an ATM multiplexer and (ii) a process which results from a renewal process which shares the output link of a multiplexer with other connections. Both output processes belong to the versatile class of discrete-time Markovian arrival processes (D-MAP’s). We derive an expression for the Index of Dispersion for Counts (IDC) and for the Index of Dispersion for Intervals (IDI) of a D-MAP. Two classes of D-MAP’s are considered depending on the eigenvalues of the transition matrix : those with an aperiodic transition matrix and those with a periodic transition matrix. For both cases we derive a closed form formula for the limit of the IDC (which coincides with the limit of the IDI) and for the convergence rate of the covariance sequence. These results are then applied to the two special cases of output processes.
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