Redundancy Management for Fast Service (Rates) in Edge Computing Systems

TL;DR

This paper uses the average system computing time and blocking probability to evaluate edge system performance and analyzes the optimal resource allocation accordingly and proposes blocking probability and average system time optimization algorithms.

Abstract

Edge computing operates between the cloud and end users and strives to provide low-latency computing services for simultaneous users. Redundant use of multiple edge nodes can reduce latency, as edge systems often operate in uncertain environments. However, since edge systems have limited computing and storage resources, directing more resources to some computing jobs will either block the execution of others or pass their execution to the cloud, thus increasing latency. This paper uses the average system computing time and blocking probability to evaluate edge system performance and analyzes the optimal resource allocation accordingly. We also propose blocking probability and average system time optimization algorithms. Simulation results show that both algorithms significantly outperform the benchmark for different service time distributions and show how the optimal replication factor changes with varying parameters of the system.

Figures (7)

• Figure 1: Edge computing system deployed between the users and the cloud processes the jobs sent by the users. New service requests get sent to the cloud when all edge workers are busy.
• Figure 2: An Edge Computing System: Controller node $M$ processes jobs $J_i$, possibly generates redundant tasks and dispatches them to workers $W_1, W_2 , W_3, W_4$. $W_1$ and $W_2$ work as a group to process $J_1$, where the shaded job of $J_1$ indicates a redundant job. $W_3$ and $W_4$ also work as a group; each worker processes $1/2$ part of $J_2$.
• Figure 3: The expected job-computing time $\mathop{\mathrm{\mathbb{E}}}\nolimits[T_{\text{job}}]$ and the job-blocking probability $P_b$ as a function of $m$. The number of workers is $N=24$. The service time distribution are $\mathop{\mathrm{S-Exp}}\nolimits(1,1)$ (upper) and $\mathop{\mathrm{Pareto}}\nolimits(1,1.2)$ (lower).
• Figure 4: The average system time $\mathop{\mathrm{\mathbb{E}}}\nolimits[T_{sys}]$ versus the arrival rate $\lambda$ for different algorithms. The parameter settings are $N=24$ and $T_{cl}=15$. The service time distribution are $\mathop{\mathrm{S-Exp}}\nolimits(3,0.2)$ (upper) and $\mathop{\mathrm{Pareto}}\nolimits(1.5,1.2)$ (lower).
• Figure 5: The average system time $\mathop{\mathrm{\mathbb{E}}}\nolimits[T_{sys}]$ versus the arrival rate $\lambda$ for different values of $\lambda\in \{0.1,1,5\}$. The parameter settings are $N=24$ and $T_{cl}=8$. The service time distribution are $\mathop{\mathrm{S-Exp}}\nolimits(3,0.2)$ (left) and $\mathop{\mathrm{Pareto}}\nolimits(1.5,1.2)$ (right). Increasing the replication factor properly leads to a smaller average system time when $\lambda$ is small.

Theorems & Definitions (12)

• Theorem 1
• proof
• Lemma 1
• proof
• Theorem 2
• proof
• Lemma 2
• proof
• Theorem 3
• proof