| Summary: | Fog computing has become the primary infrastructure on the Internet for improving the quality of service. We consider a fog queueing system with limited infrastructure resources to accommodate real-time tasks with heterogeneities in task types and execution deadlines. Owing to the uncertain execution duration, such a fog system should jointly consider fog resource allocation and a task offloading to satisfy the deadline requirements. To consider the task heterogeneity, a parallel virtual queue model is applied to buffer each type of task in a separate queue. Subsequently, we use a framework, including three parallel algorithms, namely, offloading, buffering, and resource allocation, to improve resource allocation balance, throughput, and task completion ratio. The task offloading is decided according to the task urgencies in terms of the laxity times, which accounts for the deadline, estimated execution time, and transmission delay to the cloud. The buffering process rearranges the arriving tasks based on their laxity time and the estimated task execution time at the fog tier. The resource allocation uses an adaptive queue weight based on the Lyapunov drift to avoid task starvation that may lead to a long queueing delay for tasks with long execution time. The simulation results indicate that our proposed policies can avoid task starvation and yields a tradeoff between high throughput and a high task completion ratio.
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