Distributed Decentralized Chain (DDC) and k-Queue Variable Bulk Arrival and Static Bulk Service Model

This paper proposes a quantitative model for a new blockchain technology that distributes public ledger in a decentralized manner, referred to as Distributed Decentralized chain (DDC). A clique of k nodes in the P2P network participates in storing a complete copy of blockchain instead of having every node carry an entire copy. The proposed model is k-Queue Variable Bulk Arrival and Static Bulk Service queueing model (k-VBASBS), in which the state is defined by (i,k), where i is the number of slots from 0 upto n in a block on the current node, and k is the number of distributed nodes to store a complete copy of a chain of blocks. Without loss of generality and practicality, it is assumed that there are two different transaction posting rates assumed to take into account the overhead of inter-node (i.e., μ(inter-node)) control-hopping versus the one of the original intra-node posting rate (i.e., μ(intra-node)), and μ(inter-node)μ<<(intra-node). Based on the proposed k-VBASBS model, the average waiting time, space requirement, and throughput of the transactions will be simulated for the performance, and the dependability will be also modeled and simulated by the vulnerability to 51% attack.