Abstract

Blockchain is well known as a database technology supporting digital currencies, such as Bitcoin, Ether, and Ripple. Regarding the mining process as a vacation, and the block-verification process as a service, we establish a type of non-exhaustive queueing model with a limited batch service and a possible zero-transaction service. By selecting the beginning instant of a block-verification process as a regeneration point and using the method of a generating function, we obtain the stationary probability distribution for the number of transactions in the system at the regeneration points. Then, we derive the average number of transactions and the average confirmation time of transactions in the blockchain system. Finally, we provide numerical results with analysis and simulation to demonstrate how the average number of transactions and the average confirmation time of transactions in the blockchain system change with the mining parameter.

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