End-to-End Delay Modeling for Embedded VNF Chains in 5G Core Networks

In this paper, an analytical end-to-end (E2E) packet delay modeling is established for multiple traffic flows traversing an embedded virtual network function (VNF) chain in fifth generation communication networks. The dominant-resource generalized processing sharing is employed to allocate both computing and transmission resources among flows at each network function virtualization (NFV) node to achieve dominant-resource fair allocation and high resource utilization. A tandem queueing model is developed to characterize packets of multiple flows passing through an NFV node and its outgoing transmission link. For analysis tractability, we decouple packet processing (and transmission) of different flows in the modeling and determine average packet processing and transmission rates of each flow as approximated service rates. An M/D/1 queueing model is developed to calculate packet delay for each flow at the first NFV node. Based on the analysis of packet interarrival time at the subsequent NFV node, we adopt an M/D/1 queueing model as an approximation to evaluate the average packet delay for each flow at each subsequent NFV node. The queueing model is proved to achieve more accurate delay evaluation than that using a G/D/1 queueing model. Packet transmission delay on each embedded virtual link between consecutive NFV nodes is also derived for E2E delay calculation. Extensive simulation results demonstrate the accuracy of our proposed E2E packet delay modeling, upon which delay-aware VNF chain embedding can be achieved.