This thesis investigates two issues in stochastic models for real applications.

In the first part, we consider a blockchain system. A blockchain system, such as Bitcoin or Ethereum, validates electronic transactions and stores them in a chain of blocks without a central authority. Miners with computing power compete for the right to create blocks according to a pre-set protocol and, in return, earn fees paid by users who submit transactions. Such a system essentially operates as a single server queue with batch services based on a fee-based priority discipline, albeit with distinctive features due to the security concerns caused by decentralization. That is, a transaction is confirmed only after a number of additional blocks are subsequently extended to the block containing it, which co...[ Read more ]

This thesis investigates two issues in stochastic models for real applications.

In the first part, we consider a blockchain system. A blockchain system, such as Bitcoin or Ethereum, validates electronic transactions and stores them in a chain of blocks without a central authority. Miners with computing power compete for the right to create blocks according to a pre-set protocol and, in return, earn fees paid by users who submit transactions. Such a system essentially operates as a single server queue with batch services based on a fee-based priority discipline, albeit with distinctive features due to the security concerns caused by decentralization. That is, a transaction is confirmed only after a number of additional blocks are subsequently extended to the block containing it, which complicates the interplay between miners and users. In our study, we build a stochastic model to analyze how miners’ participation decisions interact with users’ participation and fee decisions in equilibrium, and identify the optimal protocol design when the goal is to maximize total throughput or users’ utility. Our analyses show that miners and users may end up in either a vicious or virtuous cycle, depending on the initial system state. We validate our model and analytical results using data from Bitcoin.

In the second part, we study how to efficiently match drivers and riders with different price options in a ride-hailing system. We establish a three-stage queueing model for the ride-hailing system and derive the stochastic system dynamics. We further consider the fluid approximations in the heavy traffic regime and prove the convergence of fluid scaled processes to the limits and the convergence of the fluid limits to a unique equilibrium. Finally, we provide optimal conditions for the matching decisions in fluid equilibrium for maximizing the platform’s revenue or the proportion of completed services.