Approximating multi-skill blocking systems by HyperExponential Decomposition

We consider multi-class blocking systems in which jobs require a single processing step. There are groups of servers that can each serve a different subset of all job classes. The assignment of jobs occurs according to some fixed overflow policy. We are interested in the blocking probabilities of each class. This model can be used for call centers, tele-communication and computer networks. An approximation method is presented that takes the burstiness of the overflow processes into account. This is achieved by assuming hyperexponential distributions of the inter-overflow times. The approximations are validated with simulation and we make a comparison to existing approximation methods. The overall blocking probability turns out to be approximated with high accuracy by several methods. However, the individual blocking probabilities per class are significantly more accurate for the method that is introduced in this paper. keywords: multi-class blocking system, blocking probability, Equivalent Random Method, Hayward-Fredericks Method, Interrupted Poisson Process Method, call center, hyperexponential distribution, decomposition, overflow routing correspondence to: A. Pot