Jing-Yu Ma

Jing-Yu Ma, Li Xia, Quan-Lin Li

In this paper, we propose a novel dynamic decision method by applying the sensitivity-based optimization theory to find the optimal energy-efficient policy of a data center with two groups of heterogeneous servers. Servers in Group 1 always work at high energy consumption, while servers in Group 2 may either work at high energy consumption or sleep at low energy consumption. An energy-efficient control policy determines the switch between work and sleep states of servers in Group 2 in a dynamic way. Since servers in Group 1 are always working with high priority to jobs, a transfer rule is proposed to migrate the jobs in Group 2 to idle servers in Group 1. To find the optimal energy-efficient policy, we set up a policy-based Poisson equation, and provide explicit expressions for its unique solution of performance potentials by means of the RG-factorization. Based on this, we characterize monotonicity and optimality of the long-run average profit with respect to the policies under different service prices. We prove that the bang-bang control is always optimal for this optimization problem, i.e., we should either keep all servers sleep or turn on the servers such that the number of working servers equals that of waiting jobs in Group 2. As an easy adoption of policy forms, we further study the threshold-type policy and obtain a necessary condition of the optimal threshold policy. We hope the methodology and results derived in this paper can shed light to the study of more general energy-efficient data centers.

Jing-Yu Ma, Quan-Lin Li

In this paper, we provide a novel dynamic decision method of blockchain selfish mining by applying the sensitivity-based optimization theory. Our aim is to find the optimal dynamic blockchain-pegged policy of the dishonest mining pool. To study the selfish mining attacks, two mining pools is designed by means of different competitive criterions, where the honest mining pool follows a two-block leading competitive criterion, while the dishonest mining pool follows a modification of two-block leading competitive criterion through using a blockchain-pegged policy. To find the optimal blockchain-pegged policy, we set up a policy-based continuous-time Markov process and analyze some key factors. Based on this, we discuss monotonicity and optimality of the long-run average profit with respect to the blockchain-pegged reward and prove the structure of the optimal blockchain-pegged policy. We hope the methodology and results derived in this paper can shed light on the dynamic decision research on the selfish mining attacks of blockchain selfish mining.

Quan-Lin Li, Jing-Yu Ma, Yan-Xia Chang et al.

In this paper, we develop a more general framework of block-structured Markov processes in the queueing study of blockchain systems, which can provide analysis both for the stationary performance measures and for the sojourn times of any transaction and block. Note that an original aim of this paper is to generalize the two-stage batch-service queueing model studied in Li et al. \cite{Li:2018} both ``from exponential to phase-type" service times and ``from Poisson to MAP" transaction arrivals. In general, the MAP transaction arrivals and the two stages of PH service times make our blockchain queue more suitable to various practical conditions of blockchain systems with crucial random factors, for example, the mining processes, the block-generations, the blockchain-building and so forth. For such a more general blockchain queueing model, we focus on two basic research aspects: (1) By using the matrix-geometric solution, we first obtain a sufficient stable condition of the blockchain system. Then we provide simple expressions for the average number of transactions in the queueing waiting room, and the average number of transactions in the block. (2) However, comparing with Li et al. \cite{Li:2018}, analysis of the transaction-confirmation time becomes very difficult and challenging due to the complicated blockchain structure. To overcome the difficulties, we develop a computational technique of the first passage times by means of both the PH distributions of infinite sizes and the $RG$-factorizations. Finally, we hope that the methodology and results given in this paper will open a new avenue to queueing analysis of more general blockchain systems in practice, and can motivate a series of promising future research on development of lockchain technologies.