As parallelism becomes critically important in the semiconductor technology, high-performance computing, and cloud applications, parallel network systems will increasingly follow suit. Today, parallelism is an essential architectural feature of 40/100/400 Gigabit Ethernet standards, whereby high speed Ethernet systems are equipped with multiple parallel network interfaces. This creates new network topology abstractions and new technology requirements: instead of a single high capacity network link, multiple Ethernet end-points and interfaces need to be considered together with multiple links in form of discrete parallel paths. This new paradigm is enabling implementations of various new features to improve overall system performance. In this paper, we analyze the performance of parallel network systems with network coding. In particular, by using random LNC (RLNC), - a code without the need for decoding, we can make use of the fact that we have codes that are both distributed (removing the need for coordination or optimization of resources) and composable (without the need to exchange code information), leading to a fully stateless operation. We propose a novel theoretical modeling framework, including derivation of the upper and lower bounds as well as an expected value of the differential delay of parallel paths, and the resulting queue size at the receiver. The results show a great promise of network system parallelism in combination with RLNC: with a proper set of design parameters, the differential delay and the buffer size at the Ethernet receiver can be reduced significantly, while the cross-layer design and routing can be greatly simplified.