Blockchain is a technology that provides a distributed ledger that stores previous records while maintaining consistency and security. Bitcoin is the first and largest decentralized electronic cryptographic system that uses blockchain technology. It faces a challenge in making all the nodes synchronize and have the same overall view with the cost of scalability and performance. In addition, with miners' financial interest playing a significant role in choosing transactions from the backlog, small fee or small fee per byte value transactions will exhibit more delays. To study the issues related to the system's performance, we developed an $M(t)/M^N/1$ model. The backlog's arrival follows an inhomogeneous Poison process to the system that has infinite buffer capacity, and the service time is distributed exponentially, which removes $N$ transactions at time. Besides validating the model with measurement data, we have used the model to study the reward distribution when miners take transaction selection strategies like fee per byte, fee-based, and FIFO. The analysis shows that smaller fee transactions exhibit higher waiting times, even with increasing the block size. Moreover, the miner transaction selection strategy impacts the final gain.