Recent advances in ad hoc Wireless Mesh Networks (WMN) has posited it as a strong candidate in Smart Grid's Neighbourhood Area Network (NAN) for Advanced Metering Infrastructure (AMI). However, its abysmal capacity and poor multi-hoping performance in harsh dynamic environment will require an improvement to its protocol stacks in order for it to effectively support the variable requirements of application traffic in Smart Grid. This paper presents a classification of Smart Grid traffics and examines the performance of HWMP (which is the default routing protocol of the IEEE 802.11s standard) with the Optimised Link State Routing (OLSR) protocol in a NAN based ad hoc WMN. Results from simulations in ns-3 show that HWMP does not outperform OLSR. This indicates that cross layer modifications can be developed in OLSR protocol to address the routing challenges in a NAN based ad hoc WMN.