In this review, we describe historical and recent developments towards tackling a century-long challenge in teletraffic theory, namely the evaluation of blocking probability in overflow systems with mutual overflow. Such systems have many applications in a variety of telecommunications and service systems, including wireless communications, cloud computing, intensive care, and emergency services, and various methods have been developed over the past century to address this challenge. In particular, the recent development of the Information Exchange Surrogate Approximation (IESA) provides significantly increased accuracy and robustness compared to previous approximation methods of its kind while also providing high computational efficiency not available via simulation or exact analysis. To the best of our knowledge, IESA is the first approximation method to combine high levels of accuracy, robustness, and computational efficiency when evaluating blocking probability in overflow systems with mutual overflow, and thus forms a major breakthrough in this century-long effort.

In systems and networks where overflow is penalized, careful planning is required to prevent a small increase in the offered load from suddenly triggering a system collapse. In this work, we consider an overflow loss system where the service time distribution of a request is dependent on the number of overflows. We propose a novel admission control policy for improving the stabilization and performance of such a system based on a new information exchange mechanism (IEM) for congestion information, in which only a small amount of congestion information is carried by each request and is propagated via the overflow of requests. This avoids the need for an external mechanism for propagating congestion information. Furthermore, IEM is fully compatible with trunk reservation, a simple, classical, yet effective method of admission control in overflow loss systems and networks. Despite the very limited amount of communication overhead required by IEM (only a few bits per request), numerical results demonstrate that the combination of IEM with trunk reservation provides greater performance and stability than trunk reservation alone. We also present a computationally efficient analytical performance evaluation method based on IEM and demonstrate numerically that it is asymptotically exact and generally quite accurate. Therefore, the analytical method can be used for system design and planning.

In mobile cellular design, one important quality-of-service metric is the blocking probability. Using computer simulation for studying blocking probability is quite time-consuming. Furthermore, existing teletraffic models such as the Information Exchange Surrogate Approximation (IESA) only give a rough estimate of blocking probability. Another common approach, direct blocking probability evaluation using neural networks (NN), performs poorly when extrapolating to network conditions outside of the training set. This paper addresses the shortcomings of existing teletraffic and NN-based approaches by introducing a hybrid approach, namely IESA-NN. In IESA-NN, an NN is used to estimate a tuning parameter, which is in turn used to estimate the blocking probability via a modified IESA approach. In other words, the teletraffic approach IESA still forms the core of IESA-NN, with NN techniques used to improve the accuracy of the approach via the tuning parameter. Simulation results show that IESA-NN performs better than previous approaches based on NN or teletraffic theory alone. In particular, even when the NN cannot produce a good value for the tuning parameter, for example when extrapolating to network conditions not experienced in the training set, the final IESA-NN estimate is generally still accurate due to bounds set by the underlying teletraffic theory.