Comparison of Analysis Methods for the Joint Connection-Level and Packet-Level Performance Evaluation of VoIP Traffic Networks

Abstract

In this paper, the performance of different mathematical models for the joint connection-level and packet-level numerical evaluation of systems with Voice over Internet Protocol (VoIP) traffic are studied and compared. The evaluation focuses on computational running time, memory requirements, and accuracy of performance metrics. System dynamics are captured by a Markov chain and its corresponding state transition probability matrix, which represents the probabilities of transitioning, frame by frame, from one system state to another. In VoIP environments, many transitions between valid states are not possible, resulting in a state transition probability matrix with many zero-value elements. Generally, the computational complexity of solving Markov chains depends on the number of valid states and the number of non-zero elements in the state transition probability matrix. The evaluated analysis methods utilize the following techniques, either separately or in combination: Time-Scale Decomposition Technique (TSDT) and the strategy of Limiting the Number of State Transitions(LNST). TSDT aims to reduce the dimensionality of the analysis and the cardinality of the valid state space, while LNST seeks to minimize the number of non-zero elements in the state transition probability matrix by eliminating unlikely state transitions. Numerical results show that the method combining TSDT with the LNST strategy (M-TSDT&LNST) reduces computational running time by up to 110 times compared to the method using minimal approximation (the reference method). Despite this substantial reduction, the relative differences in system Erlang capacity and connection-level (packet-level) performance metrics between M-TSDT&LNST and the reference method remain below 1.6% and 1.4% (3.8%), respectively.

Keywords

• VoIP systems
• performance analysis
• computational complexity
• joint connection and packet level