Modelling and performance analysis of content sharing and distribution in community networks with infrastructure support

Abstract

We consider the problem of sharing a viral file between users in a local community network (e.g., college and office campuses). Community computing is computer networking among and between users in a geographically bounded setting for local purposes and activities. Due to the community-oriented nature of such networks, it is likely that users of a community network would like to share content. Peer-to-Peer (P2P) networks have turned out to be one of the most innovative paradigms for sharing content on the Internet. In this paper, we analyze the performance of P2P content sharing in community networks and investigate the role that infrastructure nodes (helpers) can play to enhance the performance of content sharing and distribution. We model the evolution of content demand in a community network. The use of this demand prediction model allows us to design a delicate P2P-with-helpers content distribution system. Our insights that we obtain using fluid-flow model increase our understanding of how helper provisioning affects the performance of content sharing and distribution. The derived results show that significant reduction in both the cost of distributing content and the average content download time can be realized when only few infrastructure nodes in the community network play the role helpers and cache P2P objects.

Appendix

In this section, we show that enabling few infrastructure nodes in the community network to participate in P2P content distribution results in significant reduction in the network power consumption.

The energy consumption of communication systems is becoming a fundamental issue. In fact, the information and communication technology sector is responsible for 2 to 2.5 % of the GHG annual emission [32, 33], and the wireless access networks are largely responsible for the increase in energy consumption. It follows that being able to minimize the base station energy consumption in a wireless network represents an important green networking objective.

We assume, without loss of generality, a wireless community network consisting of wireless routers that are connected in the form of wireless mesh network (WMN) [1, 2]. We assume a large wireless mesh network consisting of many stationary mesh routers (M) uniformly deployed in a 2-dimensional squared area (grid-like topology) (Fig. 9). Any two nodes that can communicate directly with each other are connected by an edge in the graph. Within the mesh network, data is communicated over wireless links. Nodes may communicate directly over a wireless link or over multiple hops with intermediate nodes forwarding data. Mesh clients (peers) are usually with much less upload bandwidth compared to the mesh routers. We assume that the routing algorithm employs a minimum hop routing metric such as AODV and DSR.

Fig. 9

Network model

Although the assumptions about community network being a wireless mesh network with grid-like topology may be restrictive, we use these assumptions in our analysis for the purpose of explaining our model and verifying the effectiveness of our approach in reducing the energy consumption. However, the results that we derive can be extended to any community network topology no matter wired or wireless. However, the problem is more difficult due to the complexity of the wired network topology.

We compare the power consumption in two content distribution schemes in WMN. The first scheme is content distribution using a centralized server that is physically located in the center of the network with upload bandwidth of μ _s . The second scheme is the P2P content distribution using the proactive helpers scheme (Section 4.1).

Let the transmission power, that is required at each mesh router in order to relay a data packet of content i to the next router towards the destination be P _MR (assuming all content packets are with the same size). To reduce the network power consumption that results from accessing P2P objects from peers and helpers using the P2P with proactive helper scheme, we consider the following content retrieval scheme: a peer j which downloads object i retrieves segments of i from the nearest helper y, which caches a replica of i, and from all the served peers.

Let us suppose that object i has only one replica at one of the helpers at time t, and is placed as shown in Fig. 10a. Let the maximum power that is consumed in the network as a result of accessing object i at that helper from any peer in the network at time t be P _h (t). We can see that P _h is the power that is consumed when peer x accesses the replica of content i at that helper. We can further see that $P_{h}(t) = \frac{\sqrt{M}}{2} \cdot P_{MR}$, where M is the total number of mesh routers in the WMN. Suppose object i has 4 replicas at the helpers at time t, and those replicas are placed as shown in Fig. 10b. Then, the maximum power consumed in accessing a replica of object i at the helpers becomes $P_{h}(t)=\frac{\sqrt{M}}{2} \cdot P_{MR} (\frac{1}{2})$. Similarly, we can compute the maximum access cost when the number of replicas at helpers is 16 (Fig. 10c). The computation of the maximum power consumption in accessing a replica of object i at the helpers for varied number of replicas stored at the helpers are shown in Table 1. We note here that the computation of power consumption is based upon our assumption of the placement of the replicas of object i at the helpers.

Fig. 10

Average power consumption

Table 1 Summary of network power consumption for varied number of replicas at the helpers

Recall that $Y_{h_{i}}(t)$ is the number of replicas of object i that are stored at the helpers at time t. Hence, we can see that for a WMN that is deployed in a two-dimensional space, when $Y_{h_{i}}$ is increased by a factor of 4, P _h is reduced by half. Hence, we can write

$$ P_{h}(t) \approx \frac{\sqrt{M}}{2} \cdot \frac{P_{MR}}{\sqrt{Y_{h_{i}}(t)}}. $$

This approximation is feasible especially when we assume a large-scale WMN with many helpers.

The total power consumption of object i with size L (packets) using the P2P-with-helpers system ($P_{\rm Helpers-System_{\it i}}$) can be written as $P_{\rm Helpers-System_{\it i}} = P_{\rm Peers-and-Helpers_{\it i}} + P_{\rm Peers-to-Helpers_{\it i}}$, where $P_{\rm Peers-and-Helpers_{\it i}}$ accounts for the power consumed when uploading content i from the served peers and helpers to the interested peers during time 0 ≤ t ≤ t ₂, while $P_{\rm Peers-to-Helpers_{\it i}}$ accounts for the power that is consumed when uploading content i from the served peers to the helpers during time 0 ≤ t ≤ t ₁. Hence, we can write

$$ \begin{array}{rll} \label{eqn:power_cons} P_{\rm Helpers-System_{\it i}} &=& L \cdot \int_{0}^{t_{2}} \left ( \mu_{p} \cdot \eta_{P2H} \cdot S_{i}(t) \cdot E[P_{p}(t)]\right. \\ && \left.+\ \mu_{h_{i}} \cdot Y_{h_{i}}(t) \cdot P_{h}(t) \right ) dt \\ &&+ \ L \cdot \int_{0}^{t_{1}} \varepsilon \cdot \mu_{p} \cdot S_{i}(t) \cdot E[P_{p}(t)] dt , \end{array} $$

where η _P2H  = 1 − ε when t ≤ t ₁, and 0 when t > t ₁, and E[P _p (t)] is the expected value of the maximum power that is consumed in the network as a result of accessing object i from the served peers. If we assume that the requests for content is generated at peers uniformly at random, it is easy to see that $E[P_{p}(t)] = \frac{\sqrt{M}}{2} \cdot P_{MR}$.

To compute the saving in network power consumption as compared to the case of centralized server, we need to compute the total power consumption when using the centralized server ($P_{\rm Server_{\it i}}$). $P_{\rm Server_{\it i}}$ can be computed as $P_{\rm Server_{\it i}} = L \cdot N_T \cdot P_{s}$, where P _s is the power that is consumed in the network as a result of accessing object i of size L packets at the centralized server that is located in the center of the network, and $P_{s} = \frac{\sqrt{M}}{2} \cdot P_{MR}$ (again we assume first in first served scheme). Hence, $P_{\rm Server_{\it i}}$ can be written as $P_{\rm Server_{\it i}}= L \cdot N_T \cdot \frac{\sqrt{M}}{2} \cdot P_{MR}$, and the saving in network power consumption using the P2P-with-helpers schemes η _save can be computed as $\eta_{\rm save}~\text{\%} = \frac{P_{\rm Server_{\it i}}-P_{\rm Helpers-System_{\it i}}}{P_{\rm Server_{\it i}}}$.

1.1 Numerical results

We numerically evaluated the power consumption when the proactive helper scheme for the cases when μ _p  = 0.001, N = 10, p _i  = 0.00075, M = 1,000, P _MR  = 1 (μ w/packet), size of the file L = 1,000 (packet), N _T  = 750, and $\mu_{h_{i}}$ takes the values $\mu_{h_{1}} = 0.03$, $\mu_{h_{2}}=0.04$, and $\mu_{h_{3}}=0.06$. (Fig. 11a). We observe that the saving in power increases with increasing the upload rate at the helpers. This is because increasing upload rate at the helpers implies that a higher fraction of content i is accessed from the nearby helpers. Another observation is that the saving increase with increasing the number of replicas at the helpers. This is because having more replicas at the helpers reduces number of hops in a path between replicas and downloading peers.

Fig. 11

Fluid model results

We also computed the power consumption when the upload rate at the served peers takes the values $\mu_{p_{1}}= 0.001$ and $\mu_{p_{2}} =0.00075$, while $\mu_{h_{i}}$ was kept constant at 0.03 (Fig. 11b). We further computed the power consumption in the P2P-with-helper system for the case when μ _p  = 0.001, $\mu_{h_{i}} = 0.03$, and content popularity take the values p ₁ = 0.0007 and p ₂ = 0.00075 (Fig. 11c). We observe that the saving in power consumption is less when the upload rate of peers is higher and the content is more popular. This is because the fraction of content i that is accessed from served peers that are physically far from a downloading peer is higher. This results suggest some enhancement to the content retrieval scheme that we used in the P2P- with-helpers system. Specifically, the content retrieval scheme must enable interested peers to download content only from the peers which are physically close.

1.2 Simulation results

We simulated the P2P-with-helper as a stochastic system using Matlab. We simulated a WMN that consists of M = 1,000 mesh routers deployed in a grid topology. Total number of interested users who eventually download the file was N _T  = 750, and each user was connected to (N = 10) other users (friend) at any time unit. We considered a single file i that is generated at a random user, and popularity of file i was p _i  = 0.0075. The generator of content i was selected uniformly at random, and the request for content was generated at the peers uniformly at random. The size of the file is 10 Mbyte; while the size of a packet follows a normal distribution with mean 1,024 kbyte. Number of replicas at the helpers varied between 4 to 25. The upload rate of peers and helpers follow exponential distribution with means μ _p  = 10 kbps = 0.001 (file/sec) and $\mu_{h_{i}} = 300~{\rm kbps} = 0.03$ (file/sec), respectively. The power at mesh routers was set fixed at P _MR  = 1 (μ w/packet).

We carried out the simulation five times for each statistical data and computed the average total power consumption in the network using the P2P-with-helper scheme for varied number of replicas at helpers with confidence intervals. We compared the simulation results with the numerical results that was obtained using the fluid model (Fig. 12). The results show that the proposed fluid model provides a good approximation of the real system, and the fluid approximation does not impact the validity of our analytical results.

Fig. 12

Average total power consumption