Blockchain Queuing Model with Non-Preemptive Limited-Priority

Blockchain technology has recently obtained widespread attention. And it is being regarded as potentially even more disruptive than the Internet, whose usage includes large areas of applications ranging from crypto currency, financial services, reputation system, Internet of Things, sharing economy to public and social services. The existing works of blockchain primarily are focused on key components and potential applications. However, in the existing blockchain systems, the waiting time of transactions is too long. Furthermore, it may produce serious consequences because many important transactions are not handled timely. To solve the problem, in the paper, the blockchain Queuing model with non-preemptive limited-priority is established, which considers the different transactions having different priority when being mined. There are two classes of transactions in the model, one is high-priority transaction with pay or with prior interest, the other is low-priority transaction without pay or without prior interest. And high-priority transactions can be mined preferentially when mining process is not occupied. If low-priority transaction is being mined, the arriving high-priority transaction will wait for the mining accomplishment. Through the analysis of the model, we compute average waiting time, average staying time and average length of queue. From simulation of the model, we find that transactions with pay or with prior interest and increase service rate of mining are effective for reducing waiting time. Besides, the two factors mutually reinforce to shorten waiting time. Finally, we conclude this paper and point out the direction of future research.