Information exchange surrogates for approximation of blocking probabilities in overflow loss systems

Abstract

Overflow loss systems are an important class of teletraffic models. Evaluation of blocking probabilities in such systems involving mutual overflow effects is a difficult problem. In the literature, decoupling a given system into independent subsystems is typically regarded as a scalable, though non-robust, approach to the problem. This paper presents a new method that is based on a radically different idea from that of the conventional approach. Firstly a surrogate model that, in a systematic way, approximately captures the state dependencies due to the overflow model is designed. Secondly it is observed that approximation of the blocking probability of the surrogate model provides a good approximation to the blocking probability in the original model. We introduce important concepts underpinning this surrogate-based approximation method, and demonstrate its effectiveness by applying it to an overflow model that incorporates mutual overflow effects common to various applications of overflow loss systems. Unlike the conventional approach that requires a fixed-point solution of the blocking probability with no guarantee of the convergence and uniqueness, our new method provides a unique solution in a fixed number of iterations. Extensive and statistically reliable experiments demonstrate that the new method yields significantly and consistently better results compared to the conventional approach, improving the accuracy by orders of magnitude in many instances and yet requiring less computational effort.

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