Computing an exact solution for the differential equations,
with differences, system that allows the determination of the M|M|m|m system
transient probabilities is a hard task. The respective complexity grows with m.
The computations are extremely fastidious and the length and the fact that the
expressions obtained are often approximate, and not exact, will not allow the
transient probabilities behavior as time functions characterization. To
overcome these problems, in this work it is analyzed how that system can supply
approximate values to the M|M|m|m queue system, through matrix calculations. It
is also presented an asymptotic method to solve the system that becomes
possible in many cases to obtain simple approximated expressions for those
probabilities using the M|M| ∝ transient probabilities, very
well-known and very much easier to study.
Author(s) Details:
Manuel Alberto M. Ferreira,
ISTAR-IUL - Information Sciences, Technologies and Architecture
Research Center (ISTA-School of Technology and Architecture), Iscte-Instituto
Universitário de Lisboa, Lisboa, Portugal.
Please see the link here: https://stm.bookpi.org/RATMCS-V9/article/view/13326
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