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