THESIS
2021
1 online resource (xi, 87 pages) : illustrations (some color)
Abstract
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
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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.
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