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Additional resources for Analyzing markov chains using kronecker products : theory and applications
3)], plus a diagonal correction (first term) so as to sum up the rows to zero. 3), including the case h D l, which implies n D m, there are three possibilities. First, the departure of a customer from a queue is an arrival at a queue with a larger index (h < l). Second, the departure of a customer from a queue is an arrival at a queue with a smaller index (h > l). Third, the departure of a customer from a queue is an arrival at the same queue (h D l). ). 8; 9; 9; 6; 6; 9; 9; 7/. K; K; K; K; K; K; K; K/ since ch D minfK; bh g and bh 6 for h D 1; : : : ; H .
3) start with an initial approximation. At each iteration, they multiply the current approximation with a particular matrix to obtain a new approximation with the objective that the approximations eventually converge to the true solution [83, 130]. These methods are the building blocks of all advanced iterative methods. The matrix used in the iterative multiplication process is obtained at the outset by splitting the coefficient matrix of the linear system, which is Q in our setting. Therefore, we begin by splitting the smaller matrices that form the Kronecker products as in  and show how classical iterative methods can be formulated in terms of these smaller matrices.
3; 4/g: pD1 iii. 2/ having two subsets of size 2. h/ D N pD1 Sp for h D 1; 2. 2; 4/g: pD1 iv. 2/ having a subset of size 3. h/ D pD1 Sp for h D 1; 2. 2; 4/g: pD1 v. 2/ having a subset of size 4. 2/ S j D 10, but f1; 2; 3; 4g, and S D pD1 Sp for h D 1; 2. 2 Handling Unreachable States 43 vi. 2/ each having a subset of size 2. 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.