Harish Madimangalam Ramesh, Yi Huang, Anup Kumar, Md Tanzil Hoque Chowdhury, Jayanta K. Debnath, Bin Xie
Controller Area Network (CAN) is a widely used in-vehicle communication protocol. However, CAN is vulnerable to a variety of attacks, including BUS-OFF attacks. BUS-OFF attacks can be launched by injecting malicious messages into the CAN bus, causing the target node to enter a BUS-OFF state. In a BUS-OFF state, the target node is unable to communicate with any other nodes on the CAN BUS. In this paper, we propose a reset-based recovery mechanism to mitigate BUS-OFF attacks. Our mechanism works by monitoring the entropy of the CAN bus. When the entropy of the CAN bus drops below a certain threshold, our mechanism triggers a reset of the target node. This reset causes the target node to reinitialize its CAN controller and rejoin the CAN bus.
We evaluated our mechanism through simulations and showed that it can effectively mitigate BUS-OFF attacks. Our mechanism can also be used to mitigate other types of attacks, such as Denial-of-Service (DoS) attacks.
Our approach is based on the following key ideas:
Our approach is a promising new direction for improving the security of CAN networks. It is proactive, lightweight, and generic, making it a valuable addition to the security toolkit for CAN networks.
CVSS-based Vulnerability and Risk Assessment for High Performance Computing Networks J. K. Debnath and D. Xie, "CVSS-based Vulnerability and Risk Assessment for High Performance Computing Networks," 2022 IEEE International Systems Conference (SysCon), Montreal, QC, Canada, 2022, pp. 1-8, doi: 10.1109/SysCon53536.2022.9773931.
Common Vulnerability Scoring System (CVSS) is intended to capture the key characteristics of a vulnerability and correspondingly produce a numerical score to indicate the severity. Important efforts are conducted for building a CVSS stochastic model in order to provide a high-level risk assessment to better support cybersecurity decision-making. However, these efforts consider nothing regarding HPC (High-Performance Computing) networks using a Science Demilitary Zone (DMZ) architecture that has special design principles to facilitate data transition, analysis, and store through in a broadband backbone. In this paper, an HPCvul (CVSS-based vulnerability and risk assessment) approach is proposed for HPC networks in order to provide an understanding of the ongoing awareness of the HPC security situation under a dynamic cybersecurity environment. For such a purpose, HPCvul advocates the standardization of the collected security-related data from the network to achieve data portability. HPCvul adopts an attack graph to model the likelihood of successful exploitation of a vulnerability. It is able to merge multiple attack graphs from different HPC subnets to yield a full picture of a large HPC network. Substantial results are presented in this work to demonstrate HPCvul design and its performance.
Antu, A.D., Kumar, A., Kelley, R., Xie, B. (2022). Comparative Analysis of Cloud Storage Options for Diverse Application Requirements. In: Ye, K., Zhang, LJ. (eds) Cloud Computing – CLOUD 2021. CLOUD 2021. Lecture Notes in Computer Science(), vol 12989. Springer, Cham.
Cloud Storage is the concept of combining and sharing of storage resources through the Internet. Each cloud service provider (CSP) offers universal data storage services using its geographically distributed datacenters. Businesses and consumers are increasingly reliant on cloud-based storage solutions instead of in-house, on-premises local storage hardware in order to save on initial expenditures to build and maintain the hardware infrastructures. Cloud Storage provides enormous levels of data protection and important data can be restored in case of missing local copies. Selecting the right public cloud provider has become critical to long term business success. Depending on the different business needs and requirements of these storage services, we compare a few of the storage services provided by three market giants like Amazon Web Services, Microsoft Windows Azure and Google Cloud Platform.
Read MoreNarikimilli, N.R.S., Kumar, A., Antu, A.D., Xie, B. (2020). Blockchain Applications in Healthcare – A Review and Future Perspective. In: Chen, Z., Cui, L., Palanisamy, B., Zhang, LJ. (eds) Blockchain – ICBC 2020. ICBC 2020. Lecture Notes in Computer Science(), vol 12404. Springer, Cham.
A digital transformation in health care is the positive impact of technology in health care. Wearable fitness technology, telemedicine, and AI-enabled medical devices are concrete examples of digital transformation in health care. And these are supposed to revolutionize the health care industry by improving patient care, streamline operations, and reducing costs but instead, it is facing significant challenges on cybersecurity and privacy of patient data, invoicing and payment processing, medical supply chain, drug integrity. Blockchain technology can absolve the healthcare industry from facing these challenges; it can establish a blockchain of medical records. Blockchain is considered to be a highly secure, transparent, and immune to hackers due to its digital encryption, it also plays a prominent role in reducing the intermediate fees as it is entirely decentralized. This review paper scrutinized the potential of blockchain technology to refine the security, privacy, and interoperability of healthcare data and after the detailed analysis of the current significant challenges in the healthcare sector, we proposed few advanced uses of blockchain in health care domain like Blockchain consortium, Smart contract-based health care intelligent claim processing and prior authorization and Wearable fitness device integration and monitoring health.
Read MoreR. Kelley, A. D. Antu, A. Kumar and B. Xie, "Choosing the Right Compute Resources in the Cloud: An analysis of the compute services offered by Amazon, Microsoft and Google," 2020 International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery (CyberC), Chongqing, China, 2020, pp. 214-223, doi: 10.1109/CyberC49757.2020.00042.
In this paper we present a comparison of the various compute resources offered Amazon Web Services, Microsoft Azure, and Google Cloud Platform. We further identify several platform features including geographic availability, security and compliance, operating system support, container support, and serverless computing support that are directly comparable and provide recommendations and guidance for choosing a platform. We found that overall, for compute resources, Microsoft Azure is the preferred provider for many of the features we identify. However, that differential is quite small; in reality it is difficult to find significant differences between the platforms since they are ever-changing.
Y. Huang, J. Debnath, M. Iorga, A. Kumar and B. Xie, "CSAT: A User-interactive Cyber Security Architecture Tool based on NIST-compliance Security Controls for Risk Management," 2019 IEEE 10th Annual Ubiquitous Computing, Electronics & Mobile Communication Conference (UEMCON), New York, NY, USA, 2019, pp. 0697-0707, doi: 10.1109/UEMCON47517.2019.8993090.
Security risk management is a vital part of any system development, including e-commerce and other information systems that need security. Notably, NIST has developed cyber security and privacy controls, such as SP-800-53, to facilitate risk management for federal information systems. By integrating such NIST-compliance security controls, our CSAT is innovative to offer a user-interactive software tool for effectively facilitating the robust and secure architecture development of information systems in the way of enhancing overall risk management. It specifically promotes the enhancement of risk management by composing reports/graphs in different NIST defined do-mains/controls/capabilities specification effectively. This helps to reduce development cost, time, and manpower by using the tool to quickly define information system security standards based on NIST's security and privacy guidelines. The development of such a tool is of importance for risk management, e.g., security evaluation, risk assessment, controls implementation, system security planning). It can be used to optimize the risk management in the information system architecture in the lowest cost, while increasing the security robustness by systemically providing NIST guideline and risk management in the information system development level.
W. Qi, Bin Xie, etc. "Real-time Distributed Graph Partition and Embedding of Large Network," CCgrid, IEEE, 2018, Submitted.
W. Qi, H. Li, S. Agarwal, K. Pham, Bin Xie, "Optimize the Spectrum Sensing and Decision Making Strategies under Uncertainty for SATCOM," MILCOM, IEEE, 2016.
The ability to provide accurate spectrum sensing and decision making under an uncertainty environment is proving useful for the military SATCOM to increases the spectrum utilization. Dynamic spectrum access(DSA) allows a secondary user to access the spectrum holes that are not occupied by the primary users. However, the spectrum sensing for DSA is normally performed in a complex SATCOM environment under uncertainty, caused by the high GEO/LEO mobility, weak signals after a long distance of propagation, the high interference and jamming in an adversarial environment, etc. The uncertainty results in a high error probability in the spectrum sensing. In such a case, DSA requires a decision-making process to optimally determine which channels to sense and access. In this paper, we propose an approach for optimal spectrum sensing and decision making that mathematically models the uncertainty in the SATCOM while the whole system throughput is maximized. Specifically, we model the DSA with decision making as a Partially Observable Markov Decision Process (POMDP) problem. Optimal DSA strategy has been discussed by an optimization process. Monte Carlo simulations are carried out and our simulation results demonstrate the efficiency of the proposed DSA strategy.
M. S. Khan, A. Kumar, Bin Xie "An Inverse Problem in Wireless Mesh Network," Accepted CyberC 2015, IEEE, 2015.
The wireless mesh network technology has been studied extensively over the last few years. It can be deployed to provide the broadband Internet services in rural and geographically disadvantaged areas, due to the ability to enable the extended coverage. It also provides an alternative to the last mile broadband access. In this paper, we present a network performance analysis using the network tomography paradigm to estimate the end-to-end link performance of the information flows over the mesh networks. A network tomography base routing scheme Expectation-Maximization (EM) routing approach is proposed to estimate the network flow performance such as delay, which again can be used for routing optimization over the network to achieve desirable performance. We then compare the estimated results with the NS-2 simulations.
Y. Ren, Y. Chen, J. Yang, and Bin Xie, "Privacy-preserving Ranked Multi- Keyword Search Leveraging Polynomial Function in Cloud Computing," In Pro- ceeding of Globecom, IEEE, 2014.
The rapid deployment of cloud computing provides users with the ability to outsource their data to public cloud for economic savings and flexibility. To protect data privacy, users have to encrypt the data before outsourcing to the cloud, which makes the data utilization, such as data retrieval, a challenging task. It is thus desirable to enable the search service over encrypted cloud data for supporting effective and efficient data retrieval over a large number of data users and documents in the cloud. Existing approaches on encrypted cloud data search either focus on single keyword search or become inefficient when a large amount of documents are present, and thus have little support for the efficient multi-keyword search. In this paper, we propose a light-weight search approach that supports efficient multi-keyword ranked search in cloud computing system. Specifically, we first propose a basic scheme using polynomial function to hide the encrypted keyword and search patterns for efficient multi-keyword ranked search. To enhance the search privacy, we propose a privacy-preserving scheme which utilizes the secure inner product method for protecting the privacy of the searched multi-keywords. We analyze the privacy guarantee of our proposed scheme and conduct extensive experiments based on the real-world dataset. The experiment results demonstrate that our scheme can enable the encrypted multi-keyword ranked search service with high efficiency in cloud computing.
A. Pandit, P. Polina, Anup Kumar, Bin Xie, "CAPPA: Context Aware Privacy Protecting Advertising - An Extension to CLOPRO Framework," IEEE Services computing conference (SCC-2014), Alaska, pages 805-812.
Advent of 4G networks, IPV6 and increased number of subscribers to these, has triggered many free applications that are easy to install on smart mobile devices, a primary computing device for many. The free application markets are sustainable as revenue model for most of these service providers is through profiling of users and pushing of the advertisements to the users. This imposes a serious threat to user's privacy. Most of the existing solutions starve the developers of their revenue by falsifying/altering the information of the users. In this paper, we attempt to bridge this gap by extending our integrated Context Cloaking Privacy Protection framework (CLOPRO) that achieves identity privacy, location privacy, and query privacy without depriving the service provider of sustainable revenue generated through the use of the Context Aware Privacy Preserving Advertising (CAPPA). The CLOPRO framework has been shown to provide privacy to the user while using location based services. In this paper we demonstrate how this framework can be extended to deliver the advertisements/coupons based on users interests, specified at the time of registration, and the current context of the user without revealing these details to the service provider. The original service requests of the registered users are modified by the CLOPRO framework using concepts of clustering and abstraction. The results are filtered to deliver the relevant information to the user. Since the advertisements received are relevant to the user, the click rate is likely to increase ensuring increased revenue for service provider. The proposed framework has O(n) complexity.
Tuan. T. Tran, Xiaolong Tang, Bin Xie, “Secure Wireless Multicast for Delay-Sensitive Prioritized Data Using Network Coding,” In Proceeding of Cyberc-2013, 2013.
Secure data multicast in wireless networks is challenging due to cyber-attacked vulnerabilities and high data loss of the wireless channels. Additionally, the receivers may have different characteristics (e.g., different memories, processing capabilities, etc.), thus, to be efficient, it is desirable to transmit a commensurate data to each receiver, depending on its need. The current approaches that divide the source information into packets for transmission result in a single transmission rate to all receivers. Such transmission methods not only overwhelm the receivers with less resources but also are unable to fully utilize the capabilities of receivers with higher performance. In this paper, we propose a network coding based encryption scheme for secure data transmission. The proposed scheme can achieve the same level of security with much less computational complexity at both transmitter and receivers. To achieve the maximum network transmission throughput, we then propose an optimal data transmission scheduling for delay-sensitive prioritized data. The transmissions are adaptively scheduled for each time slot based on the data importance and state of the network. The system performance is verified through both theoretical analysis and simulations. The results show that transmitted data is secure with much less computational complexity. In addition, high effective network throughput is obtained by using the proposed scheduling scheme.
Phani Polina, Tuan T. Tran, Bin Xie, and Anup Kumar, “SD2S: Social-based Distributed Data Storage,” In Proceeding of IEEE Local Computer Network (LCN), 2013.
Storing large amounts of data is challenging as it requires large reliable storage space. Currently, peer-to-peer(P2P) systems have been implemented for this purpose. However, these systems provide no guarantee of data retrieval as the data availability is determined by the interest of the users. On the other hand, cloud storage systems, built on top of a pool of powerful servers, can provide reliable data storage; however, they are costly and vulnerable to privacy leakage. This paper proposes a novel distributed data storage system based on the social networks. Particularly, our system utilizes the social information of the users to find the potential storage nodes. The storage nodes are then selected based on the social ties with the data owner. In order to quickly obtain the potential storage nodes, we provide an efficient algorithm to search and compute the social ties in the social networks. The system performance is verified through both theoretical analysis and simulations. The results show that data stored in our proposed system is reliable and stable given the random nature of storage nodes joining and leaving the system. A marginal performance gain is achieved in comparison to P2P systems.
Tuan T. Tran, P. Polina, X. Tang, Z. Jia, Y. Yang, A. Kumar, Bin Xie, “Showcase of a Fragment-based Distributed Cloud Storage System,” In Proceeding of IEEE Local Computer Network (LCN), 2013.
We propose to demonstrate a prototype of fragment-based distributed cloud storage system. The prototype is implemented by using efficient encoding/decoding, multiple-layer encryption and spatial data distribution for data efficiency and security. We will demonstrate that the proposed prototype offers significant improvement of data protection, compared with the file-based storage system, on both data reliability and security. For example, we will show that how fragment-based user data is processed and distributed over the cloud, or from security aspect, we will show how the system copes with the cybersecurity attacks during which some of the storage nodes are compromised (e.g., all stored data is lost and storage nodes are inaccessible.) The demonstration is performed via a web-based interface on several mobile devices which remotely connect to our prototype via the Internet.
Yanzhi Ren, Yingying Chen, Bin Xie, Willam J. Maxey, “Fuzzy Keyword Search in Cloud Computing,” In Proceeding of IEEE CNS, 2013.
As Cloud Computing becomes prevalent, more and more sensitive information are being centralized into the cloud. For the protection of data privacy, sensitive data usually have to be encrypted before outsourcing, which makes effective data utilization a very challenging task. Although traditional searchable encryption schemes allow a user to securely search over encrypted data through keywords and selectively retrieve files of interest, these techniques support only exact keyword search. That is, there is no tolerance of minor typos and format inconsistencies which, on the other hand, are typical user searching behavior and happen very frequently. This significant drawback makes existing techniques unsuitable in Cloud Computing as it greatly affects system usability, rendering user searching experiences very frustrating and system efficacy very low. In this paper, for the first time we formalize and solve the problem of effective fuzzy keyword search over encrypted cloud data while maintaining keyword privacy. Fuzzy keyword search greatly enhances system usability by returning the matching files when users' searching inputs exactly match the predefined keywords or the closest possible matching files based on keyword similarity semantics, when exact match fails. In our solution, we exploit edit distance to quantify keywords similarity and develop an advanced technique on constructing fuzzy keyword sets, which greatly reduces the storage and representation overheads. Through rigorous security analysis, we show that our proposed solution is secure and privacy-preserving, while correctly realizing the goal of fuzzy keyword search.
Mohammad S. Khan, Anup Kumar, and Bin Xie, “Stitching Algorithm: A Network Performance Analysis Tool for Dynamic Mobile Networks,” In Proceeding of CIIECC, 2012.
The performance analysis of the mobile ad-hoc network (MANET) is a challenging issue. In this paper, network tomography is studied to analyse the network performance in a dynamic MANET. For such a purpose, a network tomography analytical model is proposed for a dynamic network environment. Expected Maximization (EM) algorithm for network tomography is able to estimate the network performance parameter in accordance to network performance observations. Our study is different than current network tomography approaches where are applied for static wired network. Over the dynamic network, we proposed a new algorithm that is called Stitching algorithm to aggregate the dynamic performance. Specifically, the stitching algorithm concatenates the performance parameter i.e. link delay, from distinguish time periods. Therefore, the network behaviour as well as the corresponding performance in a mobile ad-hoc network can be derived over a continuous period.
G. Ru, H. Li, T. Tran, W. Lin, L. Liu, and H. Wu “Distributed Optimal Power Control for Multicarrier Cognitive Systems," IEEE GLOBECOM, 2012.
In this paper, the power optimization of the multicarrier cognitive system underlying the primary network is investigated. We consider the interference coupled cognitive network under individual secondary user's power constraint and primary user's rate constraint. A multicarrier discrete distributed (MCDD) algorithm based on Gibbs sampler is proposed. Although the problem is nonconcave, MCDD is proved to converge to the global optimal solution. To reduce the computational complexity and convergence time, the Gibbs sampler based Lagrangian algorithm (GSLA) is proposed to get a near optimal solution. We also provide simulation results to show the effectiveness of the proposed algorithms.
T. Tran, H. Li, W. Lin, L. Liu, and S. Khan “Adaptive Scheduling for Multicasting Hard Deadline Constrained Prioritized Data via Network Coding,” IEEE GLOBECOM, 2012.
Network coding offers a promising platform for multicast transmission by approaching its min-cut capacity. However, pushing the network throughput toward this upper bound comes with a sacrifice in delivery delay due to the decoding procedure that requires performing batch of coded packets. Further, in some transmission scenarios where the receivers experience deep fading or unable to collect a full set of the transmitted data, no useful information is recovered. The effect is more severe in the networks where the transmitted information has priority structure with hard deadline constraint due to the limited delivery time and data interdependencies. In this paper, we consider single-hop wireless networks where the transmitter wishes to multicast hard deadline constrained prioritized data to many receivers over lossy channels. We first study the network performance of a variety of transmission techniques, depending on how the transmitter schedules transmission in each time slot. We then propose an adaptive encoding and scheduling technique to maximize the network throughput. To find the optimal transmission scheduling at the presence of the network dynamics, we cast the problem in the framework of Markov Decision Processes (MDP) and use backward induction method to find an optimal solution. We further propose simulation-based algorithm and greedy scheduling technique that obtain high performance with much lower time complexity. Both analytical and simulation results have been provided to corroborate the effectiveness of the proposed techniques.
T. Tran, H. Li, L. Liu, and S. Khan “Secure Wireless Multicast for Delay- Sensitive Data via Network Coding and Adaptive Scheduling,” in IEEE International Conference on Communications (ICC) June, 2012.
Wireless multicast for delay-sensitive data is challenging because different receivers may experience different packet losses. Network coding offers significant advantages over the traditional Automatic Repeat-reQuest (ARQ) protocols in that it mitigates the need for retransmission and has the potential to approach the min-cut capacity. Network-coded multicast would be, however, vulnerable to false packet injection attacks, in which the adversary injects bogus packets to prevent receivers from correctly decoding the original data. Without a right defense in place, even a single bogus packet can completely change the decoding outcome. Existing solutions either incur high computation cost or cannot withstand high packet loss. In this paper, we propose a novel scheme to defend against false packet injection attacks on network-coded multicast for delay-sensitive data. Specifically, we propose an efficient authentication mechanism based on null space properties of coded packets, aiming to enable receivers to detect any bogus packets with high probability. We further design an adaptive scheduling algorithm based on Markov Decision Processes (MDP) to maximize the number of authenticated packets that can be received within a given time constraint. Both analytical and simulation results have been provided to demonstrate the efficacy and efficiency of our proposed scheme.
C. Thejaswi, T. Tran, and J. Zhang “When Compressive Sampling Meets Multicast: Outage Analysis and Subblock Network Coding,” INFOCOM, 2011.
This paper studies multicasting compressively sampled signals from a source to many receivers, over lossy wireless channels. Our focus is on the network outage from the perspective of signal distortion across all receivers, for both cases where the transmitter may or may not be capable of reconstructing the compressively sampled signals. Capitalizing on extreme value theory, we characterize the network outage in terms of key system parameters, including the erasure probability, the number of receivers and the sparse structure of the signal. We show that when the transmitter can reconstruct the compressively sensed signal, the strategy of using network coding to multicast the reconstructed signal coefficients can reduce the network outage significantly. We observe, however, that the traditional network coding could result in suboptimal performance with power-law decay signals. Thus motivated, we devise a new method, namely subblock network coding, which involves fragmenting the data into subblocks, and allocating time slots to different subblocks, based on its priority. We formulate the corresponding optimal allocation as an integer programming problem. Since integer programming is often intractable, we develop a heuristic algorithm that prioritizes the time slot allocation by exploiting the inherent priority structure of power-law decay signals. Numerical results show that the proposed schemes outperform the traditional methods with significant margins.
Robert Kelley, Anup Kumar, Bin Xie, and Xiangqian Liu, “Signal Strength Seeded Frequency Hopping: A Frequency Hopping Selection Scheme for Wireless Sensor Networks,” International Conference on Computer and Network Technology, 2010.
One approach to securing radio signals in wireless sensor networks is frequency hopping in which transmitters and receivers change frequencies at a predetermined interval using a pattern of frequencies that is programmed a priori or calculated dynamically via a shared seeding mechanism. For these systems, if an adversary can physically capture a node in the network and steal the seed or hopping set, it can compromise the network. To protect against this weakness, we propose Signal Strength Seed Frequency Hopping, a hopping set selection scheme in which the seed used to calculate a dynamic hopping set is generated using signal strength measurements collected after the network has been deployed. We show our scheme has sufficient stochasticity to produce hopping sets that cannot be easily reproduced by an adversary.
Bin Xie, Jingli Li, Sanjuli Agrawal, “Decentralized BDI-based Intelligent Multiagent for Optimizing Wireless Sensor Networks,” IEEE, IET International Symposium on Communication Systems, Networks and Digital Signal Processing, 2010.
Organized intelligent communications can effectively improve the surveillance quality for wireless sensor networks. In this paper, we propose a decentralized Belief-Desire-Intention (BDI) oriented system that adopts the BDI mental architecture for wireless sensor networks. It tunes the sensor operational parameters in order to reduce the power consumption upon the satisfactory of the situational awareness quality. In the BDI intelligent architecture, the agent behavior is composed of beliefs, desires, intentions, and actions. Various methods are used in the agents to optimize the initial sensing coverage, network connectivity, senor sleep schemes, and packet transmissions. Simulation results for a special situational awareness application demonstrate the effectiveness of the proposed system.
T. Tran and T. Nguyen “Adaptive Network Coding for Wireless Access Networks,” the 19th IEEE International Conference on Computer Communications and Networks (ICCCN), August, 2010 (runner-up for best paper award).
We propose a framework for optimizing the quality of service of multiple simultaneous flows in wireless access networks via network coding. Specifically, we consider the typical scenario in which multiple flows originate from multiple sources in the Internet and terminate at multiple users in a wireless network. In the current infrastructure, the wireless base station is responsible for relaying the packets from the Internet to the wireless users without any modification to the packet content. On the other hand, in the proposed approach, the wireless base station is allowed to perform network coding by appropriate linear mixing and channel coding of packets from different incoming flows before broadcasting a single flow of mixed or coded packets to all wireless users. Each user then uses an appropriate decoding method to recover its own packets from the set of coded packets that it receives. We show that in principle, for the given channel conditions and QoS requirements, appropriate mixing and channel coding of packets across different flows can lead to substantial quality improvement for both real-time and non-real time flows. On the other hand, blind mixing can be detrimental. We formulate this mixing problem as a combinatorial optimization problem, and propose a heuristic algorithm based on simulated-annealing method to approximate the optimal solution. Simulation results verify the performance improvement resulting from the proposed approach over the non-network coding and the state-of-the-art network coding approaches.
T. Tran and T. Nguyen “Prioritized Wireless Transmissions using Random Linear Codes,” the Fifth Network Coding Symposium (NetCod), June, 2010.
We investigate approximation algorithms for the problem of prioritized broadcast transmissions over independent erasure channels first described in Tran et al., 2009. In this work, the authors showed that under some settings, the achievable throughput regions for prioritized broadcast transmissions can be computed by a polynomial-time algorithm. In this paper, we study a class of approximate algorithms based on the Markov Chain Mote Carlo (MCMC) method, for obtaining the maximum sum of prioritized receiver's throughputs. Theoretical analysis and simulation results show the correctness and the convergence speed of the proposed algorithms.