Cost and profit driven cloud-P2P interaction

Abstract

I consider two scenarios of prospective P2P-Cloud interaction. In the first one, client peers are interested in sharing video content with the help of the cloud. Due to a limited monetary budget, only a small fraction of the clients can have the content delivered directly via the cloud servers. The rest need to engage in a mesh-pull P2P broadcast to exchange the content among them. I propose a novel algorithm for constructing an equicentric distribution overlay, where peer neighborhoods exhibit homogenous latencies relative to the cloud. I demonstrate that the resulting topology exhibits the small-world property, and leads to increased data sharing and reduced play-out latency of the content among the peers. The clients are further equipped with a novel utility-driven packet scheduling strategy, where the packet’s utility is driven by its importance for the video reconstruction quality at the destination client and its rarity within the respective peer neighborhood. My simulation results show that the proposed protocols enhance the performance of a reference P2P broadcast system. Significant improvement in terms of average video quality is demonstrated over conventional solutions due to the proposed packet scheduling. The mesh construction strategy enables additional benefits in terms of frame-freeze frequency and play-out latency reduction, relative to the common approach of random peer selection. These lead to corresponding gains in video quality due to the improved continuity of the playback experience. The second scenario I investigate considers hybrid P2P-Cloud operation where the clients can lease computing resources to the cloud in exchange forprofit. I design cooperative and noncooperative strategies that the cloud and the clients can follow in order to maximize their respective objective functions, independently or jointly.

Appendix A: Statistics of minimum latency spread neighborhood

For ease of presentation, I normalize the interval x _{m i n} , x _{m a x} to the unit range 0, 1. This restricts the support of the functions f(x) and F(x) to the latter interval, which in turn allows for further simplification. Specifically, the integral I(w _{r s} ) in Eq. 13 reduces to

$$\begin{array}{@{}rcl@{}} I(w_{rs}) & = & C_{rs} \int_{0}^{1} y^{r-1}(1-y)^{N-s} dy \\ & = & \frac{1}{B(s-r,N-s+r+1)} \, , \end{array} $$

(27)

where the constant B(a, b) is known as the Beta function [40]. Consequently, f(w _{r s} ) in Eq. 12 be comes the density of a beta β(s − r, N − s + 1 + 1) random variable. Given the above, the pdf of W _{r s(1)} obtains the following form:

$$ f_{W_{rs(1)}}(w){\kern-1.5pt}={\kern-1.5pt}\frac{1}{B(1,N)}(1{\kern-1.5pt}-{\kern-1.5pt}I_{w}(s{}-{}r,N{}-{}s+r+1))^{N-1} f(w_{rs}), $$

(28)

where I _x (a, b) in Eq. 28 denotes the incomplete beta function [40] that is defined as

$$ I_{x}(a,b) = \frac{1}{B(a,b)} \int_{0}^{x} t^{a-1}(1-t)^{b-1} dt \, . $$

The above integral can be solved, in the case of integer a and b, by using integration by parts. For completeness, I include the solution below

$$ I_{x}(a,b) = \sum_{j = a}^{a+b-1} \frac{(a + b - 1)!}{j! \, (a+b-1-j)!} \, x^{j} \, (1-x)^{a+b-1-j} . $$