Delays in blockchain networks are mainly related to consensus protocols. Among these protocols, we focus on a specific family of protocols, where the mempool's role in the consensus mechanism is explicitly examined. A mempool is a temporary storage area for transactions waiting to be included in a block. This study investigates the round duration of two mempoolbased protocols: one requiring a single quorum of messages and another demanding two. We perform the delay analysis with two approaches. First, we elaborate on a Markov chain to determine the distribution of the round durations. Second, we establish an analytical model of message delays while assuming an exponential distribution of message propagation delays. Finally, asymptotic analysis is conducted to estimate the time of quorum formation. We end the paper by comparing the simulation results with the theoretical ones. Results show that both results are very close. This research offers valuable insights into the performance characteristics of mempool-based consensus protocols, aiding in the design and optimization of blockchain systems.