Transaction confirmation in proof-of-work blockchains: Auctions, delays and droppings

Blockchains based on Proof-of-Work (PoW) reward miners thanks to an auction among the transactions that ask to be confirmed. Each block contains the transactions offering the highest fee per Byte among those pending in the queue called Mempool. Various types of queueing models have been proposed to study this auction mechanism but most of them have some simplifying assumptions, e.g, fixed block capacity or stochastic stability of the system. In this work, we first propose a queueing model for the Mempool that takes into account the variable block capacity of real systems as well as the priority among the transactions due to the offered fees. We compare this more accurate model with those known in the literature. Then, we investigate a problem that received little attention from the literature: the transaction dropping. Indeed, when the workload intensity is higher than the maximum throughput (a very frequent situation in bitcoin network), miners need to evict some transactions from the Mempool. In this context, we investigate the relation between the dropping probability and the offered fee