High computational power consumption is a significant problem in a Proof-of-Work blockchain. Restricting the total mining power or the number of miners is a possible solution to save computational power consumption. However, reducing the mining power or the number of miners raises concerns about fairness and security. In this paper, we propose a stochastic lightweight blockchain called SLChain in which a random subset of miners is selected to mine the next block. In the proposed SLChain, the power consumption is significantly reduced while maintaining fairness among miners, robustness to multiple types of attacks, and block time consistency. Furthermore, the proposed SLChain can mitigate selfish mining attacks. We derive an analytical model to calculate the rewards earned by selfish miners. Simulations are conducted to study the accuracy of the proposed analytical model. From the numerical results, we found that the profitable threshold of selfish mining attacks increases from 25% to 29.29% in the proposed SLChain. In summary, the proposed stochastic lightweight blockchain can simultaneously reduce computational power consumption, maintain fairness and security levels, ensure block time consistency, and mitigate selfish mining attacks simultaneously.

Selfish mining poses significant security challenges to Proof-of-Work (PoW) blockchains by allowing strategic miners to gain disproportionate rewards through protocol deviation. While the impact of a single selfish miner has been extensively studied, the security implications of multiple independent selfish miners remain insufficiently understood. This paper presents an accurate and efficient analytical model for security evaluation of PoW blockchains under multiple independent selfish mining behaviors. The blockchain dynamics are modeled as a Markov chain with a novel state aggregation approximation, enabling closed-form estimation of miner rewards. Numerical results show that the proposed model achieves high accuracy, with deviations typically less than 5.09% compared to simulations in a blockchain with two selfish miners. In a blockchain with more than two selfish miners, the proposed analytical model yields more accuracy approximation leading to less than 2% error. We also propose a truncation mechanism to reduce the number of states in the proposed Markov chain. Numerical results show that the proposed analytical model with truncation significantly reduce the computation time while the accuracy is still maintained. Two use cases are presented: determining the profitable threshold of total selfish mining power and analyzing reward dis-proportionality between strong and weak selfish miners. The proposed model provides a practical framework for quantifying incentive-driven security risks and evaluating their impact on blockchain fairness and decentralization.

Selfish mining presents a significant threat to Proof-of-Work blockchains by compromising fairness among miners and wasting computational resources through the generation of stale blocks. Detecting and mitigating selfish mining attacks is crucial to maintain blockchain security and efficiency. While the presence of stale blocks is commonly used as an indicator of selfish mining, merely identifying the attacker’s existence is insufficient. A more valuable goal is to estimate the extent of the attack, specifically the selfish mining rate. In this paper, we propose two analytical models that can precisely calculate stale block ratios in blockchains with one or two selfish miners. These models provide closed-form functions that compute stale block ratios given selfish mining rates. We then derive inverse functions to estimate the selfish mining rate based on observed stale block ratios. Simulation results demonstrate that our analytical models can effectively calculate stale block ratios, with an average discrepancy of only 3.12% compared to simulation results. Furthermore, our estimation approach accurately predicts selfish mining rates, with a mean error of 2.82%. Estimating the selfish mining rate with high accuracy enables better identification of malicious attacks, enhances fairness, optimizes resource allocation, and supports the development of more robust security mechanisms in blockchain networks.

This paper presents a two-stage DTMC modeling approach to analyze tip count distributions in generalized IOTA tangles, where each new transaction approves multiple previous tips under a uniform random tip selection strategy. The first stage transforms the continuous-time IOTA tangle into a slotted one, while the second stage constructs a discrete-time Markov chain (DTMC) model for the slotted tangle. The proposed approach derives the steady-state distribution of the tip count and estimates the mean transaction confirmation time via Little’s law. Simulation results validate its accuracy, with average relative error below 6.6%. The proposed framework provides a practical tool for understanding and optimizing the performance of generalized IOTA tangles, supporting the design of tip selection algorithms that improve throughput, enhance security, and reduce confirmation delays.

Sharding is a promising technology to enhance the scalability of a Proof-of-Work (PoW) blockchain by dividing the nodes or miners into multiple disjoint groups (shards). Each shard processes a subset of transactions so that the throughput can be significantly improved. However, since the number of nodes or the total mining rate in a shard becomes much smaller, previous works claimed that sharding mechanisms decrease security level of a blockchain. In this paper, we mathematically show that the claim is not necessarily true for all types of attacks. We consider both the majority and selfish mining attacks in a sharded blockchain. Three key metrics are generally utilized to evaluate the effectiveness of security attacks, namely, the probability of single shard takeover ($P_{S S T}$) for majority attack, expected fraction of rewards earned by selfish miners$(E R)$and profitable threshold$(P T)$for selfish mining attack. These metrics are formulated and obtained via mathematical analyses, numerical methods, or simulations. We show that the security level decreases with the increasing number of shards in terms of$P_{S S T}$in majority attacks and$P T$in selfish mining attacks. However, in the case of selfish mining attacks, increasing the number of shards does not necessarily reduce the security level of a sharded blockchain, as measured by$E R$.

In this paper, we study the rewards in a Proof-of-Work blockchain with two selfish miners. We analyze the rewards from both network and miner’s perspectives. A simulator is implemented to study the behaviors and rewards between the miners. We first observed that the required total selfish mining rate for selfish miners to be profitable increases when the gap between the two mining rates of selfish miners decreases. When the two selfish miners have same mining rates, the required total selfish mining rate is close to 42% which is a lower bound to guarantee the profitability of selfish miners. We also compared the distributions of rewards earned by selfish miners with different mining rates. Simulations show that the strong selfish miner will be more profitable than the weak one. If the strong selfish miner has dominant mining rate, he will earn most of the rewards and the network becomes unstable. Finally, we derive an inequality to guarantee the stability of the blockchain network with two selfish miners.

In a Proof-of-Work blockchain with multiple selfish miners, can we accurately and efficiently calculate the reward earned by each miner? The problem is fundamental but difficult to be solved since the miners interact with each other dynamically. This paper proposes an accurate analytical model of a Proof-of-Work blockchain with multiple selfish miners and the earned rewards can be obtained via closed-form expressions. Compared to the simulation results, our proposed analytical model is able to yield accurate calculation of the reward earned by each miner. In most situations, the differences are less than 5%. We also show that our proposed analytical model performs closer to the simulation results than some previous approaches do. The analytical model can be easily extended to a blockchain with more than two selfish miners. Therefore, our proposed analytical model provides a theoretical framework for future researches on various selfish mining strategies.

Excessive dynamic IR-drop degrades the circuit performance and may lead to functional failure. Existing IR-drop fixing techniques at the placement stage do not consider the time-variant property and thus cannot handle dynamic IR-drop hotspots well. In current practice, designers perform Engineer Change Order (ECO) to move out these hotspot cells based on their experience. In this paper, we present a novel dynamic IR-drop ECO optimization and prediction framework by wise cell movement. We first spread high demand current cells in a global view to stagger their current waveforms. Then, we further move IR hotspot cells close to power/ground (PG) vias for minimizing the resistance from PG pads to their PG pins. Moreover, we propose an accurate machine learning-based dynamic IR-drop prediction model to guide the final cell movement. The features of our model capture power ground network characteristics, timing information, and cumulative current drawn by cells, thus leading to a general model applicable to ECO. Experimental results show that our proposed model precisely predicts dynamic IR-drop after cell movement, and our optimization scheme can substantially alleviate dynamic IR-drop without timing degradation.

This paper proposes a connection-level active rerouting algorithm in all-optical WDM networks with traffic grooming and alternate routing to reduce the connection blocking probability. The main idea of the proposed rerouting algorithm is to reroute the existing connections to a predefined routing path, which is called the best rerouting path, between the source-destination pair. The best rerouting path is obtained by solving a non-linear optimization problem in which the objective function is to minimize the approximate blocking rate. After obtaining best rerouting path, the rerouting algorithm is devised to immigrate the connections to the best rerouting path when a connection finishes transmission. Simulation results show that the proposed rerouting algorithm yields lower connection blocking probability than the case without rerouting algorithms. Besides, we also found that the rerouting overhead produced by the proposed algorithm is very small. The results show that the proposed rerouting algorithm is able to produce low connection blocking probability with small rerouting overhead.

Most of Internet traffics are generated by peer-to-peer(P2P) file sharing applications. The main idea of P2P file sharing applications is that when a peer contributes a file with higher rate, the rate that the peer is able to download files from other peers will also be high. The mechanism works well in a bandwidth symmetric network. However, when a peer shares a large amount of files to other peers via asymmetric networks such as ADSL networks, the queueing delay of general packets will be very long due to the shortage of upload bandwidth. When the ADSL router connects more than one client, one client which contributes the P2P files may cause the packets from other clients wait for a very long time in the ADSL router. Furthermore, the packets may be timeout. In this paper, we proposed a queueing scheme in ADSL router to solve the problem. The main idea of the proposed queueing scheme is to send out the general packets first as well as P2P packets are able to be sent in a bounded queueing delay. Simulation results show that the proposed queueing scheme may send out the packets efficiently and the average queueing delay is smaller than the first-come first-served algorithm. We also show that the throughput of the proposed queueing scheme is higher than other queueing schemes proposed before.

The roadside unit (RSU) plays an important role in VANET environments for privacy conservation. In order to conserve the privacy of a vehicle, the issued certificate must be updated frequently via RSUs. If a certificate expires without being updated, the services for the vehicle will be terminated. Therefore, deploying as more as possible RSUs will ensure that the certificate can be updated before it expires. However, the cost for allocating an RSU is very high. In this paper, we consider the roadside unit allocating problem such that the certificates can be updated before it expired. Previous researches focus on the roadside unit placement problem in a small city in which for any origination-destination pair the certificate is limited to update at most once. The scalable RSUs placement problem in which more than once certificate updates are required is discussed in this paper. The RSUs allocation problem is formulated and is proved as an NP-hard problem. We proposed two scalable roadside unit placement algorithms which works well for a large city. Simulation results show that the proposed algorithms yields lower number of required RSUs than the simple method named the most shortest path counts first method.

This paper proposes a new fixed-alternate routing algorithm for all-optical WDM networks without wavelength conversion in order to reduce the connection blocking probability. The key idea in the proposed fixed-alternate routing algorithm is to try to route the traffics in approximately the optimal way. The multiple routing paths between each source-destination pair are arranged and used in descending order according to the traffic intensities obtained by solving a nonlinear multicommodity flow optimization problem. It is well known that finding the connection blocking probability is a very difficult task. Therefore, an objective function closely related to the connection probability is devised and used to formulate a nonlinear multicommodity flow optimization problem. Simulations are performed to study the performance of the proposed fixed-alternate routing algorithm. Our simulation results show that sorting the routing paths according to the optimally assigned traffic intensities in the proposed fixed-alternate routing algorithm can effectively reduce the connection blocking probability compared with sorting the routing paths according to hop counts in a typical fixed-alternate routing algorithm. In general, in all-optical WDM networks, a connection request that goes through a longer path experiences higher connection blocking probability than a connection request that goes through a shorter path. This is known as the fairness problem. Our simulation results show that the proposed algorithm yields better fairness than a typical fixed-alternate routing algorithm.

In all-optical WDM networks, splitters at branch nodes are used to realize multicast trees. It is expensive to place splitters at all of the nodes in an all-optical WDM network. To reduce the cost, splitters can be placed at a subset of nodes. The problem of selecting a subset of nodes to place the splitters such that certain performance measure is optimized is called the splitter placement problem. Splitter placement problems in all-optical WDM networks in which a single light tree is constructed to realize each multicast connection have been studied in previous researches. This paper studies the splitter placement problem in all-optical WDM networks in which a light forest consisting of a collection of light trees is used to realize a multicast connection. The goal is to place a given number of splitters in the network such that the average per link wavelength resource usage of multicast connections is minimized. An upper bound and a lower bound on the per link average wavelength resource usage for a given number of multicast connections are derived. Two splitter placement methods are proposed for this problem. The two proposed splitter methods are shown to yield significant lower average wavelength resource usage than the random placement method. One of the methods is shown to produce near minimum average wavelength resource usage.