Giuliano Casale, Eddy Zheng Zhang, Evgenia Smirni
We propose a trace fitting algorithm for Markovian Arrival Processes (MAPs) that
can capture statistics of any order of interarrival times between measured events.
By studying real traffic and workload traces often used in performance evaluation
studies, we show that matching higher order statistical properties, in addition to
first and second order descriptors, results in increased queueing prediction accuracy
with respect to algorithms that only match the mean, the coefficient of variation,
and the autocorrelations of the trace. This result supports the approach of modeling
traces by the interarrival time process instead of the counting process that is more
frequently used in previous work.
We proceed by first characterizing the general properties of MAPs using a spectral
approach. Based on this result, we show how different MAPs can be combined to-
gether using Kronecker products to define a larger MAP with predefined properties
of interarrival times. We then devise an algorithm that is based on this Kronecker
composition and can accurately fit data traces. This MAP fitting algorithm uses
nonlinear optimization that can be customized to fit an arbitrary number of mo-
ments and to meet the desired cost-accuracy tradeoff. Numerical results of the fitting
algorithm on real data, such as the Bellcore Aug89 trace and a Seagate disk drive
trace, indicate that the proposed fitting technique achieves increased prediction
accuracy with respect to other state-of-the-art fitting methods.
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