| Meaning: |
Modeling of sources with multiple states e.g., at the call level |
| Description: |
State machine with \(m\) states.
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Markovian process with the rate \(\lambda_i\) in the state \(i\)
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Markovian process for modulation with the transition rate \(q_{ij}\) from
state \(i\) to state \(j\)
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According to definition: \(q_{ii} = -\sum\limits_{i \neq i} = q_{ij}\).
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Special case of the MAP with \(d_{ii} = \lambda_i\), \(d_{ij} = 0 \forall (i
\neq j)\) and \(i_{ij} = q_{ij} - d_{ij}\)
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| Parameters: |
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number of states \(m\)
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arrival rates \(\lambda_i\) in the states
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transition rates \(q_{ij}\)
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| Characteristic values: |
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sojourn time \(S_i\) in the state \(i\) is negative exponentially distributed
with the mean value \(E[S_i] = \frac{1}{\sum\limits_{i \neq i} q_{ij}} =
\frac{-1}{q_{ii}}\)
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sojourn probabilities \(P_i\) from linear equation system \(\sum\limits_i
q_{ji} \cdot P_j = 0 \forall i \mbox{ , } \sum\limits_i P_i = 1\)
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average arrival rate: \(\lambda = \sum\limits_i P_i \cdot \lambda_i \)
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| Parser example: |
[...].distribution = MMPPDistribution
[...].distribution.States = 2
[...].distribution.EventRates = [0.1 0.9]
[...].distribution.RMAP = [[-0.001 0.001] [0.001 -0.001]]
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| References: |
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P. J. KÜHN: Reminder on queueing theory for ATM networks. Telecommunication
Systems, No. 5, 1996, pp. 1-24.
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G. D. STAMOULIS, M. E. ANAGNOSTOU, A. D. GEORGANTAS: Traffic source models
for ATM networks: a survey. Computer Communications, Vol. 17, No. 6, Juni,
1994.
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H. HEFFES, D. M. LUCANTONI: A Markov modulated charcterization of packetized
voice and data traffic and related statistical multiplexer performance. IEEE
Journal on Selected Areas in Communications, Vol. SAC-4, No. 6, 1986, pp.
856-868.
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