Download Analyzing markov chains using kronecker products : theory by Tugrul Dayar PDF

By Tugrul Dayar

Advent -- Preliminaries -- Iterative tools -- Decompositional equipment -- Matrix-Analytic equipment -- Conclusion.653Computer technology

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0; 0; 0; 0; 0; 0; 0; 2/ 2 N since queue 8 has an Erlang service distribution with five phases. 0; 0; 0; 0; 0; 0; 1; 1/ 2 N since queue 7 has a hyperexponential service distribution with two phases and queue 8 is as mentioned previously. H C K 1/ choose K. 5) using the values in the routing probability matrix, P . 0; 0/ D 0 for h D 1; : : : ; 7. In other words, no phase change in the service process is possible without an arrival if the queue is empty. Similarly, the second summation has a single term that contributes to the result since nh D 0 50 4 Decompositional Methods for h D 1; : : : ; 7.

Consider our three-dimensional problem with parameter set . 0;0/ D 1. 16), respectively. 1/ . 0; 1/. 3/ diagonal of QQ 0;1 since Q1 D Q1 D I . Q1 e/ D I . 0;1/;1 D e as suggested previously. 0;0/;k D e for k D 1; : : : ; 4. 0;1/ 00 01 10 D 11 20 21 0 B B B B B B B @ 0 0 1 1 2 0 1 0 1 0 5 3 2 6 8 2 4 9 3 2 4 6 12 4 7 5 4 6 2 2 1 1 C C C C C: 2C C 3A 25 2 In the next step, similar operations will be carried out at level 1 unless the aggregated CTMC is solved exactly, upon which backtracking from recursion starts for iteration m.

H/ D N pD1 Sp for h D 1; 2. 3; 3/g: pD1 vii. 2/ having a subset of size 3. h/ D N pD1 Sp for h D 1; 2. 2; 3/g: pD1 viii. 2/ each having a subset of size 2. h/ D pD1 Sp for h D 1; 2. 2; 2/g: pD1 As observed, excluding the isomorphic cases there are eight different ways in which one can obtain jSj D 5 from a two-dimensional product state space using 2 Ä N Ä 5 partitions. However, there are certain state-space sizes that never lead to jSj D 5 no matter how the state spaces are partitioned. 2/ j D 4, for instance.

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