A Variable Bulk Arrival and Static Bulk Service Queueing Model for Blockchain

Abstract

This paper proposes a novel embedded Markovian queueing model of the M(1,n)/Mn/1 type in order to establish a theoretical foundation to design a blockchain-based system with specific interest in Ethereum. The model assumes variable bulk arrivals of transactions in Poisson distribution, i.e., M(1,n), where n the number of slots across all the mined transactions and static bulk service of transactions in exponential time, i.e., Mn, for posting in the current block, namely, VBASBP. The primary performance measurements to be taken are the average number of slots no matter how many transactions are mined under the assumption of the maximum number of slots per block as specified by n; the average waiting time per slot; and the throughput in terms of the average number of slots to be processed per time. The variable bulk arrival rate is assumed to vary linearly proportional to the size of the transactions in a multiple of per slot, and the static bulk service is assumed to take place when the number of slots in the mined transactions reaches at n, i.e., a bulk processing of multiple transactions in multiple slots for posting in a block. Numerical simulations are conducted on Matlab to demonstrate the efficacy of the model.