Browsing by Subject "Lumpability"

Now showing 1 - 2 of 2

Open Access
Analysis of large Markov chains using stochastic automata networks
(2001-07) Oleg, Gusak
This work contributes to the existing research in the area of analysis of finite Markov chains (MCs) modeled as stochastic automata networks (SANs). First, this thesis extends the near complete decomposability concept of Markov chains to SANs so that the inherent difficulty associated with solving the underlying MC car! be forecasted and solution techniques based on this concept car! be investigated. A straightforward approach to finding a nearly completely decomposable (NCD) partitioning of the MC underlying a SAN requires the computation of the nonzero elements of its global generator. This is not feasible for very large systems ever! in sparse matrix representation due to memory and execution time constraints. In this thesis, an efficient decompositional solution algorithm to this problem that is based on analyzing the NCD structure of each component of a giver! SAN is introduced. Numerical results show that the giver! algorithm performs much better than the straightforward approach. Second, this work specifies easy to check lumpability conditions for the generator of a SAN. When there exists a lumpable partitioning induced by the tensor representation of the generator, it is shown that an efficient iterative aggregation-disaggregation algorithm (IAD) may be employed to compute the steady state distribution of the MC underlying the SAN model. The results of experiments with continuous-time arid discrete-time SAN models show that the proposed algorithm performs better than the highly competitive block Gauss- Seidel (BGS) in terms of both the number of iterations arid the time to converge to the solution. having relatively large blocks in lurnpable partitionings is investigated. To overcome difficulties associated with solving large diagonal blocks at each iteration of the IAD algorithm, the recursive implementation of BGS for SANs is employed. The performance of IAD is compared with that of BGS. The results of experiments show that it is possible to tune IAD so that it outperforms BGS.
Open Access
Effects of reordering and lumping in the analysis of discrete-time sans
(Birkhäuser, Basel, 2000) Dayar, Tuğrul; Gardy, D.; Mokkadem, A.
In a recent paper [13],it is shown that discrete-time stochastic automata networks (SANs) are lumpable under rather general conditions. Therein, the authors present an efficient iterative aggregation-disaggregation (IAD) algorithm geared towards computing the stationary vector of discrete-time SANs that satisfy the conditions of lumpability. The performance of the proposed IAD solver essentially depends on two parameters. The first is the order in which the automata are lined up, and the second is the size of the lumped matrix. Based on the characteristics of the SAN model at hand, the user may have some flexibility in the choice of these two parameters. In this paper, we give rules of thumb regarding the choice of these parameters on a model from mobile communications.