Future applications for next generation mobile networks demand extremely low end-to-end latency and high reliability. Besides new concepts to achieve low latency, there is also a need to prove that the requirements are met and high reliability can be guaranteed under the influence of randomly behaving traffic. Due to the complexity and the ultra-low failure rates, simulations or testbeds are cumbersome or even unfeasible. Thus, this paper aims for a flexible mathematical model that is able to capture the randomness and to analyze the end-to-end latency distribution in networks. The distribution provides not only mean values but also percentiles, which are of key importance for critical communications. Moreover, such a model may help to optimize the network, e. g., by selecting the involved nodes and improving the routing strategy.

Future generations of mobile networks are expected to serve a multitude of applications with different requirements and traffic characterizations. Through network slices, the applications shall be even served on the same physical infrastructure. However, this requires a sophisticated network management, for an efficient sharing of the common resources and for meeting the demanding requirements of applications with very stringent requirements, e.g., ultra-high reliability, low-latency. In this regard, mathematical models can help in understanding and optimizing the network performance. By introducing queuing models for general systems and scheduling policies for heterogeneous traffic, this paper is an important step for accurate modeling of general systems and towards slice configuration and optimization.