Performance measures of a call admission control in mobile networks using SWN
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Aggregated bounding Markov processes applied to the analysis of tandem queues
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Stochastic Monotonicity in Queueing Networks
EPEW '09 Proceedings of the 6th European Performance Engineering Workshop on Computer Performance Engineering
Accuracy of strong and weak comparisons for network of queues
MMB&DFT'10 Proceedings of the 15th international GI/ITG conference on Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance
Strong and Weak orderings for an accurate resource dimensioning
VECoS'11 Proceedings of the Fifth international conference on Verification and Evaluation of Computer and Communication Systems
Strong and weak stochastic bounds for multidimensional Markov chains
International Journal of Critical Computer-Based Systems
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We present in this paper a mathematical method based on stochastic comparisons of Markov chains in order to compute in a mobile network performance measures that are important QoS parameters for users: the dropping handover of voice and the blocking probability of a new voice call. The key idea of this methodology is that given a complex system represented by a multi-dimensional Markov chain which is too large to be solved, we propose to reduce the state space, and so to define a new Markov chain which is a simplified version of the original one. This reduced Markov chain is defined as an aggregated one, which represents a stochastic bound for performance measures written as increasing reward function on the stationary distribution. The main steps of the construction of the aggregated Markov chain applied into mobile networks are presented in this paper. As the number of mobile users with different kinds of applications increases, the associated model is more complex and it can be represented by multi-dimensional continuous time Markov chain with a very large size. Thus, we define an aggregated Markov chain represented by a multi-dimensional birth and death process which is very easy to solve. We have proved that there is a weak ordering between the original Markov chain and the aggregated one using increasing set formalism. We have computed upper bounds of dropping handover and blocking probability for different values of input parameters. Numerical results prove that upper bounds give good results and so the stochastic methodology is an interesting mathematical tool for the performance evaluation of complex systems.