Abstract—This paper presents two separate Markov models to investigate blocking probabilities in multi-service communications systems, when preemptive scheduling is adopted to implement service differentiation. One is the generalized model, which is built as a multi-dimensional Markov chain, based on a variant of the multi-dimensional Erlang loss model. The other is the hierarchical model, which is constructed as a multi-level Markov chain, based on a combination of one-dimensional Erlang loss models. A detailed comparison when applying these two models to a general R-service communications system is presented. This validates the major advantages of the proposed hierarchical model: the closed form expressions of blocking probabilities; the dramatically reduced computational complexity; and the excellent scalability for analyzing larger systems. Furthermore, the analytical values are compared with simulation results for two- and three-service systems. Results show that the proposed hierarchical model provides a high degree of accuracy in the blocking probabilities under different scenarios, especially when the relative arrival rates of the lower priority classes are high.

Index Terms—Markov chain, preemptive scheduling, multi-service system, service differentiation, blocking probability

Cite: Shuna Yang and Norvald Stol, "Performance Modeling in Multi-Service Communications Systems with Preemptive Scheduling," Journal of Communications, vol. 9, no. 6, pp. 448-460, 2014. Doi: 10.12720/jcm.9.6.448-460