Abstract-Network Function Virtualization (NFV) has the potential to significantly reduce the capital and operating expenses, shorten product release cycle, and improve service agility. In this paper, we focus on minimizing the total number of Virtual Network Function (VNF) instances to provide a specific service (possibly at different locations) to all the flows in a network. Certain network security and analytics applications may allow fractional processing of a flow at different nodes (corresponding to datacenters), giving an opportunity for greater optimization of resources. Through a reduction from the set cover problem, we show that this problem is NP-hard and cannot even be approximated within a factor of (1 − o(1)) ln m (where m is the number of flows) unless P=NP. Then, we design two simple greedy algorithms and prove that they achieve an approximation ratio of (1 − o(1)) ln m + 2, which is asymptotically optimal. For special cases where each node hosts multiple VNF instances (which is typically true in practice), we also show that our greedy algorithms have a constant approximation ratio. Further, for tree topologies we develop an optimal greedy algorithm by exploiting the inherent topological structure. Finally, we conduct extensive numerical experiments to evaluate the performance of our proposed algorithms in various scenarios.
The Age-of-Information (AoI) has recently been proposed as an important metric for investigating the timeliness performance in information-update systems. Prior studies on AoI optimization often consider a Push model, which is concerned about when and how to "push" (i.e., generate and transmit) the updated information to the user. In stark contrast, in this paper we introduce a new Pull model, which is more relevant for certain applications (such as the real-time stock quotes service), where a user sends requests to the servers to proactively "pull" the information of interest. Moreover, we propose to employ request replication to reduce the AoI. Interestingly, we find that under this new Pull model, replication schemes capture a novel tradeoff between different levels of information freshness and different response times across the servers, which can be exploited to minimize the expected AoI at the user's side. Specifically, assuming Poisson updating process at the servers and exponentially distributed response time, we derive a closedform formula for computing the expected AoI and obtain the optimal number of responses to wait for to minimize the expected AoI. Finally, we conduct numerical simulations to elucidate our theoretical results. Our findings show that waiting for more than one response can significantly reduce the AoI in most scenarios.
The internal structure of buildings is becoming increasingly complex. Providing a scientific and reasonable evacuation route for trapped persons in a complex indoor environment is important for reducing casualties and property losses. In emergency and disaster relief environments, indoor path planning has great uncertainty and higher safety requirements. Q-learning is a value-based reinforcement learning algorithm that can complete path planning tasks through autonomous learning without establishing mathematical models and environmental maps. Therefore, we propose an indoor emergency path planning method based on the Q-learning optimization algorithm. First, a grid environment model is established. The discount rate of the exploration factor is used to optimize the Q-learning algorithm, and the exploration factor in the ε-greedy strategy is dynamically adjusted before selecting random actions to accelerate the convergence of the Q-learning algorithm in a large-scale grid environment. An indoor emergency path planning experiment based on the Q-learning optimization algorithm was carried out using simulated data and real indoor environment data. The proposed Q-learning optimization algorithm basically converges after 500 iterative learning rounds, which is nearly 2000 rounds higher than the convergence rate of the Q-learning algorithm. The SASRA algorithm has no obvious convergence trend in 5000 iterations of learning. The results show that the proposed Q-learning optimization algorithm is superior to the SARSA algorithm and the classic Q-learning algorithm in terms of solving time and convergence speed when planning the shortest path in a grid environment. The convergence speed of the proposed Q- learning optimization algorithm is approximately five times faster than that of the classic Q- learning algorithm. The proposed Q-learning optimization algorithm in the grid environment can successfully plan the shortest path to avoid obstacle areas in a short time.
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