Today's telecommunication network infrastructure and services are dramatically changing due partially to the rapid increase in the amount of traffic generation and its transportation. This rapid change is also caused by the increased demand for a high quality of services and the recent interest in green networking strengthened by cutting down carbon emission and operation cost. Access networks generate short electronic packets of different sizes, which are aggregated into larger optical packets at the ingress edge nodes of the optical backbone network. It is transported transparently in the optical domain, reconverted into the electronic domain at the egress edge nodes, and delivered to the destination access networks. Packet aggregation provides many benefits at the level of MAN, and core networks such as, increased spectral efficiency, energy efficiency, optimal resource utilisation, simplified traffic management which significantly reduces protocol and signalling overhead. However, packet aggregation introduces performance bottleneck at the edge node as the packets from the access networks are temporarily stored in the aggregation buffers during the packet aggregation process. In this article, we apply the diffusion approximation model and other stochastic modelling methods to analytically evaluate the performance of a new packet aggregation mechanism which was developed specifically for an N-GREEN (Next Generation of Routers for Energy  Efficiency) metro network. We obtain the distribution of the packets' queue in the aggregation buffer, which influences the distribution of the waiting time (delay) experienced by packets in the aggregation buffer. We then, demonstrate the influence of the probability $p$ of successfully inserting the packet data units from the aggregation queue to the optical ring within a defined timeslot $\Delta$. We also discuss the performance evaluation of the complete ring by deriving the utilisation of each link.