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Multimedia cloud computing has emerged as a popular paradigm for the support of delay-intolerable immersive multimedia applications with high-end three-dimensional rendering. To that end, fog computing offers distributed computational offloading solutions, by positioning rendering servers in close proximity to end users promising in this way continuous service provision, that is otherwise not easily attainable under the strictly centralized cloud-only model. Yet, in order to alleviate the multimedia providers from unnecessary capital expenditure, a strategic placement approach of the servers at the fog layer must be implemented, that can effectively cope both with the network dynamics and the overall imposed deployment cost, and still adhere to the delay bounds set forth by the multimedia application. In this paper, we formally formulate the problem as a facility location problem using constrained optimization over a finite time horizon. We then theoretically analyze the minimum acceptable conditions necessary for a decentralized location of the servers, utilizing solely local information around their immediate neighborhood, that iteratively leads to better solutions. Based on the analysis, we propose a distributed algorithm, namely the Autonomous Renderer Placement Algorithm (ARPA), to address it. ARPA employs localized service relocation to shift the placement according to simple rules that designate elastic migration, replication, and complementary consolidation of the underlying renderers. Simulation results under diversified deployment scenarios, as well as trace-driven comparisons against other approaches, testify to ARPA's accountability in obeying the delay limits and fast converge in finite time slots to a placement solution that both outperforms the baseline alternatives and is close to the optimal one, rendering it suitable for scaling up and down to meet the current demands of the offered multimedia applications.

ARPA: An autonomous renderer placement algorithm in distributed multimedia fog networks with delay guarantees