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 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.

Abstract Future mobile services are expected to include various non‐voice oriented services. One important category of non‐voice oriented mobile services is non‐real‐time services. When a mobile user establishes a connection to access non‐real‐time service, the mobile user usually cares about whether the total time to complete its data transfer is within its time tolerance. In addition, different mobile users may have different bandwidth requirements and different tolerances in the total completion time. It is essential for wireless systems to provide various mobile users with different total completion times. In this paper, two quality‐of‐service (QoS) metrics, called stretch ratio and eligibility percentage, are employed at a connection level to present the degree of the length of the total completion time. We devise a measurement based call admission control scheme that provides multiple QoSs for various mobile users which have different requirements of stretch ratios, eligibility percentages, and bandwidths. Extensive simulation results show that the measurement based call admission control scheme not only provides various satisfactory QoSs for mobile users but also produces high throughput. Copyright © 2010 John Wiley & Sons, Ltd.

It is undesired to drop an ongoing call in wireless systems; however, call dropping may occur in two situations, one of which is hand-off between cells in cellular wireless networks, the other of which is channel withdrawal in wireless systems with spectrum leasing. Channel reservation is a common solution to reduce the two types of call dropping. Optimal numbers of reservation channels were separately found before to reduce the two types of call dropping respectively. This paper studies a cellular wireless network which leases spectrum bands from another system. Due to the gain of resource sharing, the two reservations can be combined into a reservation pool, which, however, increases the complexity of selecting the optimal number of the channels in the pool; this selection is further complicated for heterogenous traffic because different traffic types have different tolerances to the exhaustion of channels. Therefore, it is critical to reserve the optimal number of channels in a pool such that the quality-of-services of different types of traffic are satisfied while throughput is maximized. We develop a three-dimensional Markov chain to analyze the performances of the channel reservation in a cellular wireless network with spectrum leasing. Based on the analysis, we use an example to demonstrate that the selected parameters of reservation guarantee the quality-ofservice requirements of different types of traffic while maximize throughput.

The non-collision packet reservation multiple access (NC-PRMA) protocol was proposed by Wen and Wang to eliminate the unstable phenomenon in the PRMA protocol under heavy load conditions by allocating dedicated control mini-slots to mobile terminals (MTs). However, this does not utilise the channel resource efficiently. A dynamic non-collision PRMA (DNC-PRMA) protocol has been proposed to dynamically allocate control mini-slots to MTs such that the channel resource can be utilised efficiently. Using simulation, the proposed DNC-PRMA protocol is shown to yield significantly higher channel utilisation, lower packet dropping probability and lower channel access delay than a protocol that allocates a dedicated mini-slot to each MT.