Semi-Markov Modeling for Network Switch Algorithms

Abstract

Performance oriented issues in stochastic process modelling is an important issue is distributed systems. This paper introduces a mathematical model for the analysis of resource reservation algorithms implemented in Internet Protocol (IP) based network switches (node). Correlating Markov processes in the aspect of network performance analysis has proven to result in solutions with relative complexity. This is attributed to the multiple nodes that constitute a distributed system. Thus, creating a compromise between the solution derivation and the complexity of the system [1,2]. In contrast, in this research an approach to generalize the stochastic characteristics of network nodes has been developed. Thus, a single node is utilized as a representation of the entire network nodes in a distributed system. The Semi-Markov Process (SMP) approach has been applied as a performance analysis approach for extensive network algorithm analysis. In this research, resource reservation algorithms implemented in a class of finite buffer queuing systems have been analyzed. The definition of the network switch states, the limiting probabilities, steady-state derivations and the iterative algorithm for steady state convergence have been developed. The SMP approach utilized proved to provide an accurate performance prediction and representation of resource reservation mechanisms. The reservation algorithm considered in this paper is the deterministic reservation algorithm. The algorithm correlates the average packet delay and packet loss ratio parameters to activate the resource reservation mechanism. The developed models are validated through extensive discrete-event simulation [3]. The performance metrics of the algorithm derived from the SMP is the average packet delay.

[1] Shamala, S.; Othman, M.; Johari, R. and Yazid,M.Y; Analytical Modeling of Dynamic Resource Reservation Algorithms Implemented in IP Switches, International Conference on Research and Education in Mathematics , Malaysia, 2003.
[2] Selvakennedy, S.; Ramani, A.K.; Prakash, V. and Saman, M.Y.; Design of simulation system for performance predictions of WDM Single-hop networks, Malaysian Journal of Computer Science, vol. 11, no. 2, pp. 32-39, 1998.
[3] Shamala, S.; Othman, M.; Johari, R.; Saman, M.Y. Pro-Active QoS Resource Management Schemes for Future Integrated Packet-Switched Networks. Malaysian Journal of Computer Science, vol. 16, no. 2, 2003.