Energy-Efficient Edge-Facilitated Wireless Collaborative Computing using Map-Reduce

Abstract

In this work, a heterogeneous set of wireless devices sharing a common access point (AP) or base station (BS) collaborates to complete a set of computing tasks within a given deadline in the most energy-efficient way. This pool of devices somehow acts like a distributed mobile edge computing (MEC) server to augment the computing capabilities of individual devices while reducing their total energy consumption. Using the Map-Reduce distributed computing framework -which involves both local computing at devices and communications between them -the tasks are optimally distributed amongst the nodes, taking into account their diversity in term of computing and communications capabilities.In addition to optimizing the computing load distribution, local parameters of the nodes such as CPU frequency and RF transmit power are also optimized for energy-efficiency. The corresponding optimization problem can be shown to be convex and optimality conditions offering insights into the structure of the solutions can be obtained through Lagrange duality theory. A waterfilling-like interpretation for the size of the computing task assigned to each node is given. Numerical experiments demonstrate the benefits of the proposed optimal collaborative-computing scheme over various other schemes in several respects.Most notably, the proposed scheme exhibits increased probability of successfully dealing with larger computing loads and/or smaller latency and energy-efficiency gains of up to two orders of magnitude.Both improvements come from the scheme ability to optimally leverage devices diversity.

Leveraging User-Diversity in Energy-Efficient Edge-Facilitated Collaborative Fog Computing

“…In this case, the variable t MAP n is set to c n l n /f max n for each device n while t RED n (now different for each device) is set to c n βL/f max n . This scheme is close to the one proposed in our previous work [22].…”

“…This paper extends our previous work [22], primarily with more realistic energy consumption models, both for devices local computations and for communications between devices. Although this change might appear subtle at first, it more than doubles the number of degrees of freedom in the collaborative-computing scheme, making it both more challenging to optimize and more interesting.…”

“…Although this change might appear subtle at first, it more than doubles the number of degrees of freedom in the collaborative-computing scheme, making it both more challenging to optimize and more interesting. While the optimization problem in [22] was relatively easy to solve and even admitted a semi-closed form solution, it only offered little insights into the structure of the optimal solution. At the opposite, the optimization problem in this work is more challenging and doesn't admit a closed-form solution.…”

“…• we propose an N -devices edge-facilitated collaborative fog computing scheme based on the Map-Reduce distributed computing framework [29] and formulate a joint computation and communication resources optimization problem with energy-efficiency as objective ; • we gain engineering insights into the structure of the optimal solution by leveraging Lagrange duality theory and offer a waterfilling-like interpretation for the size of the computing load assigned to each device ; • through numerical experiments, we compare the performance of the proposed scheme with various other schemes using less degrees-of-freedom in the optimization (such as the one proposed in [22]) to analyze the relative benefits of each set of variables being optimized and to show that the proposed scheme advantageously exploits devices diversity.…”

“…The number of CPU cycles needed to process one bit of input data at device n is assumed to be given by a constant c n . At the opposite of our previous work [22], devices are now assumed to be able to perform dynamic frequency scaling (DFS), i.e., a device can adjust its CPU frequency on the fly depending on the needs. Then, noting κ n the effective capacitance coefficient (that depends on the chip architecture of each device), the energy needed for computation during the Map phase can be modeled as [11], [12], [33]…”