  In this paper, we propose two models for scaling the transaction throughput
in Proof-of-Work (PoW) based blockchain networks. In the first approach, a
mathematical model has derived for optimal transaction throughput for PoW based
longest chain rule blockchain. In this approach, the blockchain Peer-to-Peer
(P2P) network is considered as Erd\"os-R\'enyi random network topology. This
approach is however limited by the block creation rate, the results suggest
that the rate beyond an optimal point can result in unfairness in the system.
The second approach is a new consensus protocol proposed by considering the
ledger as a Directed Acyclic Graph (DAG) called blockDAG instead of a chain of
blocks. In this framework, we follow a two-step strategy that makes the system
robust enough to handle the double-spend attacks. The first step involves the
development of an unsupervised learning graph clustering algorithm for
separating the blocks created by an attacker. In the second step, the attackers
blocks are eliminated and the remaining blocks are arranged in topological
order by honest clients which makes the blockDAG system suitable for smart
contract applications found in Internet of Things (IoT) services. The
Simulation results demonstrate a significant improvement in the transaction
throughput compared to bitcoin.
