Internet of Things (IoT) systems are expected to generate a massive amount of data that needs to be processed. Given the large scale and geo-distributed nature of such systems, fog computing along with publish/subscribe (pub/sub) messaging has been proposed as possible solutions for coping with processing at scale. However, it is still unclear how practitioners can leverage the benefits of fog computing, e.g., how to optimally place data processing operators and pub/sub brokers. Moreover, current IoT systems typically rely on pub/sub brokers at the cloud, which might diminish the benefits offered by edge or fog processing as the communication between IoT operators has to be mediated by the brokers located in the cloud. To address this shortcoming, we propose to place the IoT application operators and the pub/sub brokers jointly on a network of nodes spanning from edge to the cloud considering various factors such as network topology or the locations of the IoT sensors and the consumers of the IoT applications. Different than the prior works, we specifically consider pub/sub brokers and their unique characteristics in the placement decision. First, we formulate the placement of operators and brokers jointly across edge, fog, and the cloud as a cost minimization problem. Next, we design two low-complexity heuristics. Our simulation results corroborate the argument that a placement in the cloud is usually a good option for IoT use cases, but also reveal the gap to the optimal solution in scenarios with heavier clustering of producers and consumers of sensor data. Studying the optimality gap shows that in such a setting heuristic solutions usually stay under a stretch factor of 2, with a worst case factor of 2.5 for a tabu-based solution and 2.85 for a greedy and a fixed placement in the cloud.

物联网（IoT）系统有望生成大量需要处理的数据。考虑到这种系统的大规模和地理分布的性质，雾计算连同发布/订阅（pub / sub）消息传递已被提出作为应对大规模处理的可能解决方案。但是，还不清楚从业人员如何利用雾计算的好处，例如，如何最佳地放置数据处理运营商和发布/订阅经纪人。此外，当前的物联网系统通常依赖于云上的发布/订阅代理，这可能会削弱边缘或雾处理所提供的好处，因为物联网运营商之间的通信必须由位于云中的代理进行中介。为了解决这个缺点，考虑到各种因素，例如网络拓扑或IoT传感器的位置以及IoT应用程序的使用者，我们建议将IoT应用程序运营商和发布/订阅代理共同放置在从边缘到云的节点网络上。与先前的作品不同，我们在安置决策中特别考虑了发布/订阅经纪人及其独特特征。首先，我们将运营商和经纪人在边缘，迷雾和云环境中的共同安置公式化为成本最小化问题。接下来，我们设计两种低复杂度的启发式方法。我们的模拟结果证实了这样的论点，即在物联网用例中，通常将云放置在一个很好的选择中，但同时也揭示了在传感器数据的生产者和消费者聚集较多的情况下，最佳解决方案的差距。