Optimal Allocation of Tasks and Price of Anarchy of Distributed Optimization in Networked Computing Facilities

TL;DR

This work addresses task allocation across heterogeneous edge and cloud servers by integrating fixed network delays with server-side sojourn times into a convex latency framework. It characterizes the centralized optimum and the Nash equilibrium under selfish user behavior, provides exact polynomial-time algorithms (notably the Exact Probability Mapping) to compute both allocations, and derives the price of anarchy as a function of system load. The analysis includes M/M/1 and M/G/1 special cases, along with asymptotic results, and is validated through a real, distributed experiment spanning multiple countries. The findings show that fixed delays materially affect optimal decisions and PoA is generally small except near saturation, implying distributed strategies can perform well in practice while remaining tractable to analyze and implement.

Abstract

The allocation of computing tasks for networked distributed services poses a question to service providers on whether centralized allocation management be worth its cost. Existing analytical models were conceived for users accessing computing resources with practically indistinguishable (hence irrelevant for the allocation decision) delays, which is typical of services located in the same distant data center. However, with the rise of the edge-cloud continuum, a simple analysis of the sojourn time that computing tasks observe at the server misses the impact of diverse latency values imposed by server locations. We therefore study the optimization of computing task allocation with a new model that considers both distance of servers and sojourn time in servers. We derive exact algorithms to optimize the system and we show, through numerical analysis and real experiments, that differences in server location in the edge-cloud continuum cannot be neglected. By means of algorithmic game theory, we study the price of anarchy of a distributed implementation of the computing task allocation problem and unveil important practical properties such as the fact that the price of anarchy tends to be small -- except when the system is overloaded -- and its maximum can be computed with low complexity.

Figures (10)

• Figure 1: Reference scenario: a group of users on a single network slice with computing resources in the edge-cloud continuum
• Figure 2: Validation in Scenario 0
• Figure 3: Latency vs offered load in Scenario 1
• Figure 4: Price of anarchy vs load in Scenario 1. The marked point indicates the value computed with \ref{['eq:poa_mm1_asymptotic']}.
• Figure 5: Price of anarchy vs load in Scenario 2. The marked point indicates the value computed with \ref{['eq:poa_mm1_asymptotic']}.

Theorems & Definitions (16)

• Theorem 1
• proof
• Theorem 2
• proof
• Theorem 3
• proof
• Lemma 1
• proof
• Theorem 4
• proof