  Future mobile networks supporting Internet of Things are expected to provide
both high throughput and low latency to user-specific services. One way to
overcome this challenge is to adopt Network Function Virtualization (NFV) and
Multi-access Edge Computing (MEC). Besides latency constraints, these services
may have strict function chaining requirements. The distribution of network
functions over different hosts and more flexible routing caused by service
function chaining raise new challenges for end-to-end performance analysis. In
this paper, as a first step, we analyze an end-to-end communications system
that consists of both MEC servers and a server at the core network hosting
different types of virtual network functions. We develop a queueing model for
the performance analysis of the system consisting of both processing and
transmission flows. We propose a method in order to derive analytical
expressions of the performance metrics of interest. Then, we show how to apply
the similar method to an extended larger system and derive a stochastic model
for such systems. We observe that the simulation and analytical results
coincide. By evaluating the system under different scenarios, we provide
insights for the decision making on traffic flow control and its impact on
critical performance metrics.
