Optimized bandwidth allocation for maximizing user's QoE in hybrid cloud P2P content distribution

The Journal of China Universities of Posts and Telecommunications June 2015, 22(3): 84–91 www.sciencedirect.com/science/journal/10058885

http://jcupt.xsw.bupt.cn

Optimized bandwidth allocation for maximizing user’s QoE in hybrid cloud P2P content distribution Zhang Yi (

), Guo Yuchun, Chen Yishuai

School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing 100044, China

Abstract Hybrid cloud peer to peer (P2P) system is widely used for content distribution by utilizing user’s capabilities to relieve the cloud bandwidth pressure. However, as demands for large-size files grow rapidly, it is a challenge to support high speed downloading experience simultaneously in different swarms with limited cloud bandwidth resource in such system. Therefore, it requires an optimized cloud bandwidth allocation to improve overall downloading experience of users. In this paper, we propose a system performance model which characterizes the relationship between cloud uploading bandwidth and user download speed. Based on the model, we study the cloud uploading bandwidth allocation, with the goal of optimizing user’s quality of experience (QoE) that mainly depends on downloading rate of desired contents. Furthermore, to decrease the computation complexity, we put forward a heuristic algorithm to approximate the optimized solution. Simulation results show that our heuristic algorithm can obtain higher user’s QoE as compared with two typical bandwidth allocation algorithms. Keywords bandwidth allocation, hybrid cloud P2P system, quality of experience (QoE)

1 Introduction It is reported that Internet traffic has already been dominated by large files like high definition (HD) videos [1]. High bandwidth requirement and fast growing demands for QoE impose significant pressure on the capacity of each content provider. It is a challenge for a content provider to maintain high QoE with limited cloud bandwidth resource to attract users and reduce system cost simultaneously. Therefore, most content providers have resorted to leasing more cloud upload bandwidth than they need to offer better service. For instance, Tencent cloud streaming system deploys large cloud uploading bandwidth to provide smooth watching experience and sufficient contents availability. In contrast, P2P based systems (e.g., BitTorrent) enable a group of users who need or process the same file, named a swarm, to share data with other peers in the same swarm. But in such systems, Received date: 13-10-2014 Corresponding author: Zhang Yi, E-mail: [email protected] DOI: 10.1016/S1005-8885(15)60656-2

performance is sensitive to high dynamics and heterogeneity of users, and the availability of unpopular content is not guaranteed. Hybrid cloud P2P systems [1] combine advantages of the cloud- and P2P- based systems. However, with the vast increasing rate of content and users in such systems, how to guarantee user QoE (specifying the downloading speed experience) requiring different content with limited cloud uploading bandwidth resource is not trivial, because great differences (e.g., swarm size and file size) exist among different swarms. Thus, it is urgent to design a bandwidth allocation scheme to optimize the user QoE, which mainly depends on the user’s downloading speed in such systems. So far, there has been some work on cloud uploading bandwidth allocation problem [2–3], but a basic system performance model is still needed to quantify the relationship between cloud upload bandwidth and user’s downloading speed. In this paper, we first model user’s QoE and cloud bandwidth as an optimization problem, after that, we obtain the optimal solution with linear interactive and

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general optimizer (LINGO). Finally, we present a heuristic algorithm to approximate the optimized solution for the high complexity of such an integer programming problem. The contributions of this paper are four folds. 1) We propose a new system performance model which describes the relationship between cloud upload bandwidth and user’s downloading speed. It is different from existing models on user’s downloading speed [1,4–5] which obtain theoretical bounds of maximum downloading speed or minimum download time, our system performance model quantifies user’s downloading speed as a function of the cloud bandwidth and other system parameters. 2) Based on the performance model, we study the cloud uploading bandwidth allocation problem to optimize user’s QoE in hybrid system. Simulations show that the optimized user’s QoE is about 13% and 17% better than that produced by existing algorithms proportional to the arrival rate of users’ or swarm demand (the product of arrival rate and file size) respectively. 3) We develop a heuristic algorithm to allocate cloud uploading bandwidth. Our experiment results show that the user QoE returned by this heuristic algorithm is about 4% better than that of the allocation proportional to user arrival rate. 4) We systematically analyze the effects of system parameters, including seeder uploading speed, seeder leaving probability and average uploading bandwidth utilization, finally, we find that leaving rate of seeders affects user’s QoE most. The remainder of this paper is structured as follows. Sect. 2 describes related work. Sect. 3 presents our fluid model. Sect. 4 analyzes the bandwidth allocation problem to maximize user’s QoE. Sect. 5 proposes and evaluates a heuristic algorithm. Section 6 lists the effects of system parameters on this heuristic. Sect. 7 concludes this work.

2 Related work Fluid model has been widely used in traditional P2P systems [6–8] to study the performance of BitTorrent systems and the efficiency of P2P systems. Research on cloud upload bandwidth allocation in hybrid cloud P2P systems becomes a focus in recent years. Ref. [1] investigate two service modes of cloud, i.e. helper mode and server mode based on a fluid model. They design a mode switch scheme adaptive to the change of

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movie popularity to minimize the average downloading time and figure out the worst downloading time in server mode and helper mode [1]. Ref. [9] propose a model, which focuses on the relationship between cloud uploading bandwidth and user downloading bandwidth unstable system, based on measurement in a cloud downloading system. However, none of these works takes the effects of peer and seed change process into consideration. For comparison, we analyze the peer and seeder change process in detail, and integrate it into the model. Server bandwidth allocation is a traditional work. Some proportional-allocation algorithms are used in real systems (UUSee web site. http://www.uusee.com), in which the cloud allocates bandwidth resource in proportional to the swarm size. Besides, the ration algorithm [3] dynamically assigns a minimal amount of server capacity to each channel to achieve a desired level of streaming quality in live system. But it is unsuitable in cloud P2P system for the importance of seeders. Ref. [2] propose a taxation-based incentive mechanism to stimulate user’s contribution of uploading capability and present a water-filling continuous algorithm to allocate system bandwidth to different swarms, but the seeder’s capacity contribution is neglected. For comparison, we comprehensively and systematically model the system. Aroussi et al. propose a model about the correlation of video of demand (VoD) flows between QoE and QoS [10]. Downloading speed is crucial for QoE and QoS, but we only consider QoE in this paper. Besides, the logarithmic nature has been reported both for the VoIP service [11] and the VoD service [2]. In this paper, we use the same model to present the relationship between user downloading rate and QoE. The model is still needed to elaborate on the relationship of the system performance with the peer arrival rate, the file size and the seeder departure rate for each swarm in a hybrid cloud P2P system. It is desired a practical bandwidth allocation to maximize QoE with given cloud uploading bandwidth.

3 System performance model In this section, after giving some assumptions and a notation table, we present our system performance model for a hybrid cloud P2P system which serves multiple swarms requesting different contents simultaneously.

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Assumptions and ntations Fig. 1

To keep the problem tractable, some assumptions are given for user behavior and system status. For simplicity, we suppose that arrival rate of peers in a swarm follows a Poisson process [12]. Peers stay in the system until they download the content completely and become seeders thereafter. Seeders would leave the system with the same probability. To focus on the cloud bandwidth allocation problem among swarms, the peer downloading speed and uploading speed in a swarm are both considered homogeneous, and differences between super peers and ordinary peers are neglected. Peers connect to each other completely. A swarm is assumed to become stable quickly after its birth in that the number of seeders and that of peers remain unchanged. Neither the peer selection nor bitmap interaction is considered. Effects of network congestion are also neglected. In Table 1, some notations used in the following analysis are listed for convenience of reference. Table 1 Symbol N Fk λk µ β αk C Sk Dk Uk Η V V0

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Some notations used In this paper

Definition Total number of different swarms. Size of the content in swarm k. Arrival rate of peers in swarm k. Leaving probability of seeders. Uploading capacity of seeders. Uploading capacity of peers in swarm k. Total cloud uploading bandwidth. Cloud uploading bandwidth of swarm k obtained. Downloading bandwidth of swarm k. Uploading capacity of swarm k. Effectiveness of file sharing in swarm k. Downloading speed of peers. Maximum downloading speed of peers.

Model

In this subsection, we will build a fluid model to characterize the relationship between cloud bandwidth and downloading speed. Firstly, we construct a fluid based model as shown in Fig. 1 to characterize the process of peer arrival, receiving service, becoming seeder and departure finally in a swarm. When a peer enters the system, he begins to download content from other peers, seeders and the cloud, meanwhile, he shares the content he owns with other peers. When the peer obtains the entire content, he becomes a seeder and continues to share his content until leaving the system.

A generic model for hybrid cloud P2P system

For the case that there is only one swarm in the system, at time t, λ(t) is the arrival rate of peers, µ means the seeder departure rate, and x(t) and y(t) are denoted by the number of peers and seeders, respectively. Thus for a swarm with file size F and average downloading speed V(t), we have x(t )V (t ) x ′(t ) = λ (t ) − (1) F x(t )V (t ) − µ y (t ) (2) y ′(t ) = F In Eq. (1), the first part is the arrival rate of peers, and the second one is the rate peers becomes seeders. It describes that the change rate of the number of peers equals to the peer arrival rate minus the rate of peers changing into seeders. Eq. (2) tells that the change rate of the number of seeders y(t) equals to the rate of peers changing into seeders minus the leaving rate of seeders. The value of x(t) in steady state can be determined by Little's law, i.e. (3) x (t ) = λT The above result indicates that the number of peers keeps constant, depending on the peer arrival rate and the time T to complete downloading of a file of size F at average downloading rate of V, i.e. F T= (4) V More specifically, when a swarm is newly formed, since x(t)V(t)/F ≤ λ, the number of peers increases with time and so is the number of seeders. From Fig. 1, the peer arrival rate must be no more than λ, so when x(t)V(t)/F = λ, the number of peers becomes λT. Then Eq. (2) will be change into (5) y ′(t ) = λ − µ y (t ) which means that the number of seeders still increases over time. Finally, because λ = µ y (t ) (6) the number of seeder stays constant, and the system enters steady state. To capture the supply and demand relationship between cloud and peers in cloud P2P hybrid systems, we plot the architecture in Fig. 2. It consists of cloud part and P2P part (surrounded by cycles). People who need or possess the same content form a swarm, namely a cycle in the figure. We can see that the cloud serves bandwidth (uploading bandwidth) to all the swarms, and people inside a swarm

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could share content with each other, meanwhile, download the content from the cloud.

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swarms have the same file size and peer uploading capacity of every peer is fully used. Proof If peers have the same downloading speed, from (9), the bandwidth obtained from the cloud meets S S1 S2 = =⋯= k (11)

λ1

λ2

λk

Property 2 For swarm k, if the arrival rate λk is invariable, the relationship between the downloading speed Vk and the cloud uploading bandwidth is convex from 0 to Sk as shown in Fig. 3, given the uploading bandwidth utilization ηk of swarm k has been fixed by the current number of swarm k. Property 2 can be easily proved as the second derivative of Eq. (9) is positive. Fig. 2

The architecture of cloud P2P hybrid system

As described above, for swarm k, the user downloading bandwidth Dk is the sum of the contribution of peers, seeders and the cloud, i.e. (7) Dk = U pk + U sk + S k where Upk is the uploading bandwidth of peers, Usk is the user uploading bandwidth and Sk is the cloud bandwidth allocated to swarm k. When swarm k becomes stable, denote the number of peers xk and the number of seeders yk. Then Eq. (7) becomes (8) Vk xk = α k xk + β yk + S k where Bk means the average downloading speed for users in swarm k in steady state. Therefore, we can obtain from Eqs. (3), (4), (6), (8) the relationship between Bk and Sk can be concluded as α k Fk (9) Vk = β S Fk − − k

µ

λk

Eq. (9) could be changed into α Fλ β Sk = Fk λk − k k k − λk Vk µ

(10)

which means that the cloud uploading bandwidth needed by the swarm k equals to the bandwidth demand Fkλk subtracting the sum of uploading capacity of peers and uploading capacity of seeders. Furthermore, we derive some system properties from the model. Property 1 To ensure the same downloading speed in different swarms, the cloud uploading bandwidth should be proportional to the peer arrival rate in each swarm if the

Fig. 3 Numerical result of the relationship between user downloading speed and cloud uploading bandwidth under the condition of the same arrival rate

4 Optimized bandwidth allocation for user’s QoE In this section, we introduce bandwidth allocation problem for user’s QoE, which is used to weigh user downloading satisfaction index of the system. In a Cloud-P2P VoD system, user’s QoE is the most important. We can use the expression log Vkl to represent the QoE [2] of peer l in swarm k. Then we have (12) Qkl = log Vkl where Vkl means the downloading speed of peer l in swarm k. And Qkl means the QoE of that peer. The log function reveals that for a peer with high downloading speed such as 200 kB/s, he thinks that speed such as 220 kB/s saves the downloading time little, however, for a poor peer with 10 kB/s, the downloading speed higher than 20 kB/s contributes too much. Given the cloud cannot satisfy all players in the system, that is to say, the cloud uploading bandwidth C is limited, the optimized allocation among swarms should maximize

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the user’s QoE, i.e. N

nk

Q = ∑∑ Qkl

(13)

k =1 l =1

where nk means the number of peers in swarm k. Since we assume the peers in a swarm could obtain the same service quality, we denote Vkl in Eq. (12) by Vk. Because peer arrival rate is λk in swarm k, the objective function should be converted into the following opt.

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12: end if 13: if(exp (k)>max e) 14: max e=expk 15: swarmno=k 16: end if 17: end for 18: allocate maxe to swarm swarmno, and delete k from Q 19: C=C − Sswarmno 20: end while

N

opt: max

∑λ

k

log Vk

(14)

k =1

s.t.

0≤Vk ≤V0 ; ∀k ∈ {1, 2,..., N }

(15)

N

C = ∑ S k ; Sk ≥0, ∀k ∈ {1, 2,..., N }

(16)

k =1

 α F β Sk =  Fk − k −  λk ; ∀k ∈ {1, 2,..., N } µ Vk 

(17)

5 Heuristic algorithm for bandwidth allocation To make the bandwidth allocation scheme practical, we develop a heuristic algorithm and compare it with the optimized solution returned by LINGO. But we have to wait 15 minutes to get a solution, which is impractical in real system. 5.1

Algorithm

From the analysis above, we can infer that, both peer arrival rate and file size are important to user’s QoE. We refer to water filling algorithm that swarm which produces the highest QoE should be given precedence, then we allocate the rest of bandwidth with the same rule. Here is our algorithm. Algorithm Heuristic bandwidth allocation algorithm (F , λ,α , β , µ, C) 1: put swarms into a queue Q 2: while (C > 0) 3: max e=0 4: swarmno=0 5: for each swarm k in the Q do 6: Sk=(Fk − αkFk/V0 − βk/µk)λk 7: exp(k) = λklog V0 8: if (C
Firstly, we try to allocate bandwidth B to each swarm as much as the cloud can till the swarms get full speed B0. Secondly, we figure out the user’s QoE, i.e., exp k, and find the swarm with maximum user’s QoE. Thirdly, allocating cloud uploading bandwidth to the swarm. Then repeat the three steps until the cloud uploading bandwidth C exhausts. The time complexity of the algorithm is O(n2). As a matter of fact, from Eq. (14), we could find that the user’s QoE of the system is dependent on the arrival rate and the file size among swarms. And the distribution of arrival rate and file size meet power law distribution in real systems [13]. We will discuss the effects of the two factors for user’s QoE of the system. We introduce the Pareto distribution [13], which is a commonly used but the simplest heavy tailed distribution. Its probability density function is described as p( x) = α K α x −α −1 (18) where α , K > 0, and x ≥ K. The probability of large x decreases with α , and vice versa. 5.2

Evaluation

In this subsection, we will provide our experiment settings, examine the optimized solution and compare it with solutions of existing common algorithms. We use α a to represent the tail index of arrival rate in a system, while αf denotes the tail index of file size. The minimum arrival rate K1 is set to 20, and the minimum file size K2 is 6 MB, that’s because, in real system, a file with too small file size will be transferred through TCP totally, as the P2P component does not have enough time to run. All the settings are listed in Table 2. Table 2

Experiment setting

Parameter αa

Value 1.01 − 1.99

Parameter Α

Value 20 kB/s

αf K1 K2 V

1.01 − 1.99 20 6 MB 40 kB/s

C N V0

12 GB 100 200 kB/s

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To simplify our experiment, we assume the files could be distributed efficiently, which means the uploading bandwidth utilization of peers is 1. Thus the optimized allocation problem could be considered as an integer programming problem. Fig. 3 plots the total user’s QoE given different αa and αf .

(a) The optimal QoE result calculated by LINGO

Fig. 4

QoE results in optimal solutions for different α a and α f

(b) The rate calculated by our algorithm

From Fig. 4, we could find that the user’s QoE decreases with αa and increases with α f , respectively, which is consistent with Eq. (9) and Eq. (14). The results reveal that both arrival rate and file size are critical for the user’s QoE of the system. We compare our algorithm with the result of the other two algorithms and LINGO result. 2 500 experiments are provided for αa and αf change from 1.01 to 1.99, and both increase with the step 0.02. Fig. 5 compares the QoE result calculated by LINGO with which produced by the other three algorithms, i.e., allocations by arrival rate, demand and our algorithm, respectively. Fig. 5(a) plots the variation of QoE with αa (x-axis) and αf. Others plot the ratio of users’ QoE calculated by the other three algorithms to the results in Fig. 5(a). The points over a fixed α a value represent

(c) The rate calculated by the algorithm proportional to user arrival

results produced by different αf under the condition of the same α a , and the trend lines are the average value of these results. The result of our algorithm approximates to optimized result, the mean of the ratio is 0.910 7, and the variance is 0.000 14. For algorithm proportional to arrival rate, the mean is 0.878 4 and the variance is 1.312 0 × 10 −4 , and for algorithm proportional to demand the mean ratio is 0.833 2, the variance is 1.932 7 × 10 −3 . The consequence above shows that, our heuristic algorithm is about 4% better can the algorithm proportional to arrival rate.

(d) The rate calculated by the algorithm proportional to user demand Fig. 5 The ratio of the total user QoE of our algorithm and existing algorithms to that of LINGO result

6 Parameter effects on system performance In this section, we study impacts of uploading speed of seeders, the leaving probability of seeders, and the effectiveness of file sharing. We use the experiment setting

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as follows. Table 3

Experiment Setting

Parameter αa

Value 1.23

Value 20 kB/s

1.23

Parameter α C

αf K1 K2

20 6 MB

N V0

100 200 kB/s

6.1

with the situation in real world. But improving seeder uploading speed is difficulty, for users are sensitive to that. And the result of our algorithm is the closest one to the optimal result.

12 GB

The power law factors are set to 1.23, because Ref. [13] says the regular value ranges from 1.1 to 2.0 in normal system. The setting of arrival rate and file size is shown in Fig. 6.

Fig. 6

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Leaving rate of seeders

We set seeder uploading speed to 40 kB/s, and the leaving rate of seeders ranges from 0.01 to 0.05. Fig. 7 plots the result of user’s QoE produced by the four algorithms under our experiment setting. Fig. 8 indicates that the user’s QoE is strongly influenced by the seeder leaving rate, content providers should try their best to attract seeders, because the power law like curve, slight increase of leaving rate damages user QoE seriously.

The arrival rate and file size setting

Uploading speed of seeders

We set the uploading speed of seeders between 20 and 80 kB/s. The leaving probability is 0.02 and uploading bandwidth utilization is 1. Fig. 7 plots the result of user’s QoE produced by the four algorithms under our experiment setting.

Fig. 8 rate

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Fig. 7 The relationship between user QoE and uploading speed (kB/s) of seeders

From the Fig. 6, we can see that user’s QoE augments with seeder uploading speed. Intuitively, it is coincident

The relationship between user QoE and seeder leaving

Uploading bandwidth utilization of peers

To meets the requirement of Ref. [14], we define an uploading bandwidth utilization function 1 − e − px ; x≥0, p > 0 η= (19) 0; x < 0, p > 0 where p means the utilization factor. From Eq. (19) we can see that the value of uploading bandwidth utilization increases with p. We set the range of uploading bandwidth utilization factor from 0.01 to 0.05. Fig. 8 plots the result of user QoE produced by the four algorithms under our experiment setting. Fig. 9 tells that uploading bandwidth utilization is an important factor. So far, there have been some excellent neighbor selection mechanisms [15–16] which make full

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use of peers’ share capacity, and our result verifies the validity.

3.

4. 5.

6.

Fig. 9 The relationship between user QoE and peer uploading bandwidth utilization

7.

7 Conclusions & future work 8.

This paper focuses on cloud uploading bandwidth allocation in hybrid cloud P2P system. We first derive a model which features the relationship between cloud uploading bandwidth and user downloading speed. Then, we study the problem of bandwidth allocation for QoE maximization. We solve it with off-shelf optimization software, and through the optimized results, we find that both file size and user arrival rate are crucial to the performance of the system. To decrease the computation complexity, we further develop a heuristic algorithm to approximate the optimal solution. Simulation results show that our heuristic algorithm can obtain higher user’s QoE compared with two popular allocation algorithms. We also find that leaving rate affects global QoE most. We will consider the situation of heterogeneous peers and fair allocation between swarms in the future. Acknowledgements

9.

10.

11.

12.

13.

14.

This work was supported by the National Natural Science Foundation of China (61271199, 61301082), and the Fundamental

15.

Research Funds for the Central Universities (W14JB00500).

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(Editor: Lu Junqiang)