On File Delay Minimization for Content Uploading
to Media Cloud via Collaborative Wireless Network
Ge Zhang and Yonggang Wen
School of Computer Engineering Nanyang Technological UniversitySingapore
Email:{zh0001ge, ygwen}@ntu.edu.sg
Jiang Zhu
Department of Electrical and Computer Engineering Carnegie Mellon University, USAEmail: [email protected]
Qinghua Chen
Yangtze Delta Institute ofTsinghua University Zhejiang, China
Email: [email protected]
Abstract—This paper investigates the problem of uploading user-generated content files (e.g., video captured on mobile devices) to a media cloud via a cooperative wireless network. The multi-path opportunity inherent to the cooperative network provides a new dimension by optimally allocating all the packets into different paths to improve the user experience. Specifically, we aim to minimize the end-to-end file delay, resulting in a better experience for end users. We first show that the file delay is penalized by a path-starvation effect, which results from poor packet allocation among different paths. Secondly, our in-depth analysis of the canonical two-path case indicates that it could hurt in some cases to use more paths. Especially, when the delay variance of assigning one packet to the slower path is on the same order of that of assigning all the packets to the faster path, using one path is better than using both paths. Finally, based on this insight, we propose an iterative algorithm to assign packets into a set of chosen paths to alleviate the path starvation problem, with an objective to reducing the end-to-end file delay. Numerical simulations demonstrate its near-optimal performance. The insights from our theoretical analysis could provide guidelines for platform and application development.
Index Terms—File delay, media cloud, collaborative wireless network, content uploading.
I. INTRODUCTION
Growing popularity of smart phones and ubiquitous wireless Internet access are fueling an exponential growth of mobile media. Many mobile devices nowadays are capable of cap-turing high-quality photos and videos. These user-generated contents are then directly uploaded to the cloud via wireless connections. Such emerging usage pattern has contributed significantly to the growth of mobile data traffic. According to a recent study by Cisco [1], mobile data traffic will increase by a factor of 40 between 2009 and 2014; by 2015, two-thirds of world’s mobile data will be video.
However, the user experience of content uploading has been hampered by the resource constraint on mobile devices [2]. The performance is further degraded by the signal fading phe-nomenon in wireless links. At the same time, the application usually needs to squeeze the duration of an uploading session, either to fit the time frame or available network connections, or to avoid user impatience. As a result, a critical design objective is to minimize the file uploading delay, under the bandwidth constraint of wireless links.
The emergence of cooperative wireless networks [3], [4] provides a novel paradigm for the resource-constrained mobile device. Due to technology advancements, mobile devices with multiple wireless network interfaces (e.g., 3G, WiFi, Blue-tooth, etc) can overcome the limitation of a single wireless link, by strategically relaying data transfer via machine-to-machine (M2M) communications. The cooperation among wireless devices opens up a new research area to enhance the performance of wireless communication. As such, cooperative wireless networks provided provably a lot of advantages, such as, increasing the network throughput [5], extending the network coverage[6], decreasing the energy cost [7], [8], and reducing the file downloading delay [9], to name a few. Nevertheless, exploiting multi-path opportunity also comes with challenges, such as, the complexity of managing mul-tiple simultaneous connections and the heterogeneity among different paths.
In this paper, we aim to minimize the file delay for con-tent uploading to the media cloud via multiple connections over cooperative wireless networks. Our high-level strategy to tackle this problem follows a three-step process. First, we identify the path-starvation effect as the main pain point in transferring content files through multi-path connections; second, our thorough analysis of the canonical 2-path case suggests that, in some cases, using more paths is not always necessary to reduce the file delay. Finally, we propose an iterative algorithm to allocate all the packets across different paths. Our numerical results suggest that a rate-based packet allocation policy, when applied to a set of optimally-chosen connections, is near-optimal. The insights obtained from our theoretical investigation, when properly applied, can provide practical guidelines for software design in CDN platform and application development.
The rest of the paper is organized as follows. Section II presents a system model and a problem formulation for ana-lytical purpose. Section III identifies a path-starvation effect as the main bottleneck in the design. Section IV analyzes a fundamental building block for our analysis, i.e., the canonical 2-path case. The insights from this simplest example suggest an iterative packet allocation policy, included in Section V. Its near-optimal performance is verified through numerical results. Section IV concludes this paper.
Fig. 1. Collaborative wireless network for uploading user-generated content files to media cloud: mobile device communicates with the media cloud via multiple paths including direct connection to base station or access point and indirect connections via machine-to-machine cooperation.
II. SYSTEMMODEL ANDPROBLEMFORMULATION
In this section, we present an analytical model for file-based content distribution over multiple connections and a problem formulation to minimize the file delay.
A. Network Model
In this paper, we consider a collaborative wireless network for content uploading in cloud media network, as illustrated in Figure 1. We assume that a mobile device is equipped with multiple network interfaces, supporting different wireless protocols (e.g., 3G, WiFi and Bluetooth, etc). The mobile device can communicate with a media cloud via multiple routing paths, including direct connections to a base station and/or an access point, and indirect connections via machine-to-machine (M2M) communication over peer mobile devices. The application of interest is for the mobile device to upload user-generated content files to the media cloud, by leveraging the multi-path opportunity enabled by the collaborative wire-less network. Due to physical limitations (e.g., finite time of Internet access while the user is on motion) or user preference, the critical performance metric is the file delay, defined as the time duration between the moment when the mobile device starts to transmit the content packets and the moment when all the packets arrive at the media cloud. In this case, our design objective is to minimize the end-to-end file delay for content uploading.
B. Mathematical Model
We model the content uploading via multiple paths in Figure 2. Our proposed model consists of three parts: the source, the destination, and a set of network paths.
On the source side, a content file of𝑘 packets, is dispersed into 𝑝disjoint paths through the network. Path 𝑖 is assumed to carry 𝑘𝑖 packets, and we assume that ∑𝑝𝑖=1 ≥𝑘 for load conservation.
Fig. 2. Multi-path transmission model for content uploading: a content file of𝑘packets is dispersed into𝑝parallel paths, each of which is modeled as a FIFO queue with service rate of𝜇𝑖.
On the network side, path𝑖 is modeled as an independent FIFO queue. Following the widely adopted exponential delay model [10], the delay of packet𝑗along routing path𝑖, denoted as 𝜈𝑗𝑖 , is modeled as an exponential random variable with rate of 𝜇𝑖. In addition, we assume that delays experienced by different packets on the same path are identically and independently distributed, and delays experienced by different packets on different paths are independent. Therefore, the delay of transferring 𝑘𝑖 packets, denoted as 𝜏𝑖 , can be expressed as, 𝜏𝑖= 𝑘𝑖 ∑ 𝑗=1 𝜈𝑖 𝑗, (1)
which is an Erlang random variable with order𝑘𝑖 .
On the destination side, the file can be reconstructed upon receiving𝑘packets. The end-to-end file delay,𝜏, is defined as the max of all the path delays, i.e.,
𝜏 = max{𝜏𝑖, 𝑖= 1,2,⋅ ⋅ ⋅, 𝑝}. (2) C. Problem Formulation
Under this system model, the research problem can be stated as follows: given a content file of 𝑘 packets, how to transfer it through𝑝parallel connections to its destination so that the file delay is minimized? Specifically, we are seeking an lightweight algorithm on the mobile device to allocate content packets across different paths. Mathematically, it can be modeled as the following non-linear programming problem,
min
⃗𝑘 𝔼{𝜏}, (3)
s.t. 𝑘1+𝑘2+⋅ ⋅ ⋅+𝑘𝑝=𝐾.
where ⃗𝑘 = (𝑘1, 𝑘2,⋅ ⋅ ⋅ , 𝑘𝑝) denotes a packet application vector.
III. PAINPOINT: PATH-STARVATIONPHENOMENON
In this section, we first illustrate one crucial factor that penalizes the end-to-end file delay in content uploading to the media cloud over multiple connections, and then outline two possible approaches to mitigate such a factor. This paper will focus on one mitigation approach.
Let us first consider an example as in Figure 3a, where the source uploads a content file (e.g., a picture taken on the road)
(a) Two-Path Example (b) Ill-Allocated Case (c) Well-Allocated Case Fig. 3. An illustration of the path-starvation phenomenon: (a) two-path example, (b) ill-allocated case, and (c) well-allocated case
of 4 packets. The mobile device transfers the file through two parallel connections: path 1 and path 2. If three packets are sent to path 1 and one packet is sent to path 2 (see Figure 3b), there is a positive probability with which packet 2 arrives much earlier than packet 3. In this case, path 2 is starved while path 1 has two packets to complete. This phenomenon is called apath starvation.
Mathematically, the path-starvation phenomenon results from the delay variance of each path. Even if all the packets are allocated to align the average arrival times of the last packet in each path, there is a positive probability that packet will not arrive at the expected time. As a result, there will be a vacant period in some path, which could penalize the end-to-end file delay.
To minimize the file delay, one should allocate all the packets such that the possible path vacant period is minimized. For the same example in Figure 3, we can look at two extreme cases. On one hand, if both paths are equally good, one can assign two packets to each path (see Figure 3c). With a high probability, the difference between arrival times of packet 3 and 4 will be small and the path-starvation effect is minimized. On the other hand, if one path is much faster than the other one, one should assign all 4 packets to the faster path. Otherwise, the faster path is starved in waiting for the last packet on the slower path. In this paper, extending this example to a generic multi-path case, we focus on the problem of minimizing the end-to-end file delay by optimally allocating all the packets in a content file across all possible network connections.
An alternative strategy to reduce the end-to-end file delay is to introduce redundant packets to suppress potential path-starvation effect. The intuition is to truncate the long tail of the packet delay distribution, resulting in a shorter delay mean. It is beyond the scope of this paper. Interesting readers could refer to [11] for further details.
IV. CANONICALCASE: 2-PATHPROBLEM
The solution to the general optimization problem in (3) can be derived from an in-depth understanding of the canonical 2-path case. Our previous work in [12] has addressed that problem in depth. In this section, for the sake of completeness, we recapture the essential results of the canonical 2-path case, as presented in [12]. The insights obtained from this 2-path case allow us to develop a near-optimal packet allocation policy for the generic multi-path case.
Fig. 4. Illustration of optimal packet allocation policies for the canonical 2-path case, adopted from [12].
A. End-to-End File-Delay Analysis
Consider the simplest 2-path case with a content file of𝑘 packets. Using a Chernoff bound approach, we have obtained in [12] an upper bound for the average file delay for any packet allocation policy of(𝑘1, 𝑘2), given as follows,
𝔼{𝜏} ≤max{𝜇𝑘1 1, 𝑘2 𝜇2}+ √ 2𝜋( √ 𝑘1 𝜇2 1 + √ 𝑘1 𝜇2 1). (4) Notice that the upper bound consists of contributions from two components: the first term from the delay mean and the second term from the delay variance of individual path. This observation dictates the system behavior, as explained next.
Let us first understand how the average file delay varies under different packet allocation policies. In Figure 4, we plot the average delay for content file uploading as a function of number of packets allocated to path 1, for a content file of 100 packets. For each set of path service rates, two lines are plot: a solid one for the delay bound as in (4) and a dotted one for the simulation-based delay. In all cases, we observe an optimal packet allocation policy to minimize the file delay. Specifically, for some sets of service rates, both paths are used and the number of packets allocated to each path is proportional to its service rate (i.e., a proportion-to-rate policy); and for some other sets of service rates, only the faster path is used and allocate all the packets to that path (i.e., a winner-takes-all
Fig. 5. The optimality condition for the canonical 2-path case as a function of the content file size,𝑘.
policy). This observation can be generalized into the 2-path case with any file size and any path serving rate, as presented in next sub-section.
B. Optimal Packet Allocation Policies
In general, as proved in [12], to minimize the average delay of uploading a content file of𝑘packets via two disjointed paths with service rates of 𝜇1 ≥𝜇2 , the optimal allocation policy is one of the following two candidates:
∙ proportion-to-rate policy:(𝜇1𝜇1+𝜇2,𝜇1𝜇2+𝜇2)𝑘 ;
∙ winner-takes-all policy: (1,0)𝑘.
The optimality condition for both policies has been charac-terized and can be summarized in Figure 5. On one hand, when the winner-takes-all policy performs better, the condition is given by 𝑘≤𝜋(𝜇1/𝜇2)2. One can rewrite this condition with the big-o notation, as 𝑘/𝜇21 =O(1/𝜇22) , where 𝑘/𝜇21 is the delay variance of sending 𝑘 packets through the faster path, and1/𝜇22is the delay variance of sending one packet through the slower path. This suggests that, when the delay variance of sending one packet through the slower path is comparable to the delay variance of sending all the packets to the faster path, it is advantageous to send all the packets through the faster path. On the other hand, when the proportion-to-rate policy outperforms, the threshold is given by 𝑘 ≥4𝜋𝜇31/𝜇32. In between these two regions, one can simple compare these two policies and choose the winner.
This analysis provides us with a simple heuristics to allocate packets to a 2-path cases, as given by the following rule
Eliminating Path 2, if (𝜇1
𝜇2) 2≥ 𝑘
𝜋 (5)
In the rest of this paper, we call this procedure the 2-path optimality test. It is the basis for our proposed packet allocation algorithm in Section V.
V. ITERATIVEPACKETALLOCATIONALGORITHM
Insights from our understanding of the canonical 2-path case can be applied to develop efficient packet allocation algorithms for the generic multi-path case. In this section, we first propose an iterative packet allocation algorithm based on the 2-path optimality test and then investigate how to select paths to allocate content packets under two special cases of path parameters.
A. An Iterative Packet Allocation Algorithm
Using the 2-path optimality test, we develop a general principle for efficient packet allocation algorithms for the generic multi-path case; therefore, the rule is modified as below Eliminating Path p, if (𝜇1 𝜇𝑝) 2≥ 𝑘 𝜋 𝜇1+𝜇𝑝 ∑𝑝 𝑖=1𝜇𝑖. (6)
In the rest of this paper, we call this procedure the 2-path optimality test. It is the basis for our proposed packet allocation algorithm in Section V.
The key idea is to group the fastest path and the slowest path into the canonical 2-path case. We assert that the optimality test in (6) will not be satisfied for any two paths, if it is not satisfied for the fastest and the slowest paths.
Proof: Let 𝜇1 ≥𝜇𝑚 ≥𝜇𝑛 ≥𝜇𝑝 for any two available paths m and n, having (𝜇1𝜇
𝑝)2 < 𝑘 𝜋∑𝜇1𝑝+𝜇𝑝 𝑖=1𝜇𝑖, we need to show that (𝜇𝑚 𝜇𝑛)2< 𝑘 𝜋∑𝜇𝑚+𝑝 𝜇𝑛 𝑖=1𝜇𝑖. Hence, we have, 𝜇1 𝜇𝑝 < 𝑘 𝜋 𝜇𝑝+𝜇 2 𝑝 𝜇1 ∑𝑝 𝑖=1𝜇𝑖. (7) (𝜇𝑚 𝜇𝑛) 2≤𝜇𝑚 𝜇𝑛 𝜇1 𝜇𝑝 < 𝑘 𝜋 𝜇𝑝𝜇𝑚 𝜇𝑛 + 𝜇2 𝑝𝜇𝑚 𝜇1𝜇𝑛 ∑𝑝 𝑖=1𝜇𝑖 ≤ 𝑘 𝜋 𝜇∑𝑚+𝜇𝑛 𝑝 𝑖=1𝜇𝑖. (8)
An efficient packet allocation strategy for the original multi-path problem should go through the 2-multi-path optimality test to iteratively eliminate paths from the set of available paths such that the resulting packet allocation policy has no conflict with the 2-path optimality test.
Using this general principle, we propose an iterative packet allocation algorithm as follows. Without loss of generality, we sort all the available paths from the fastest to the slowest according their service rates. We denote a set of 𝒜, denoted as the active path set, which contains all the paths that are not eliminated in the procedure. Initially, set 𝒜 contains all the available paths. A proportion-to-rate packet allocation is conduct over the set𝒜. Then, the fastest and the lowest paths in the set𝒜is grouped into a 2-path case. If the optimality test in (6) is satisfied, the slowest path is eliminated from the set 𝒜and the algorithm repeats above steps for the updated set of active paths. Otherwise, the algorithm terminates with the set 𝒜 of active paths and a proportion-to-rate packet allocation among the set𝒜.
Note that each iteration takes constant time and the algo-rithm will terminate within𝑝−1iterations; therefore, the time complexity of the proposed algorithm is bounded by𝑂(𝑝).
We illustrate the logic flow of this proposed algorithm in Figure 6. Let us consider an example of allocating 200 packets into 4 paths, with service rates of (64, 16, 4, 1) packets per unit time. After the first round of proportional allocation (packets allocated into each path are 151, 38, 9 and 2), path 1 and path 4 are grouped together. Path 4 is then eliminated because the two-path test is satisfied. The same procedure continues and
Fig. 6. The logic flow of our proposed iterative packet allocation algorithm.
terminates after 3 rounds of proportional allocation with path elimination, resulting in a packet allocation vector as (160, 40) for the first two paths.
B. Path Selection Analysis
In this subsection, we will investigate how paths should be selected under the aforementioned iterative packet allocation algorithms, for two alternative path parameter settings.
1) Linearly Degraded Paths: In this case, we assume that the service rates of all the paths increases linearly as the path index increase. Specifically, the service rate of path 𝑖is given by
𝜇𝑖 =𝛿(𝑝+ 1−𝑖), 𝑖= 1,2, . . . , 𝑝. (9)
Applying the iterative packet allocation algorithm, we no-tice that the path elimination process would continue if the following condition is met,
(𝜇𝜇1 𝑝) 2≥ 𝑘 𝜋 𝜇1+𝜇𝑝 ∑𝑝 𝑖=1𝜇𝑖. (10)
Plugging (9) into (10), we obtain
𝑝≥ 3 √
2𝑘
𝜋. (11)
As a result, the algorithm will stop when the number of paths left in the active set is
𝑝∗ 𝑙 = ⌊ 3 √ 2𝑘 𝜋 ⌋ . (12) All the packets are proportionally allocated to the set of active paths from path 1 to path 𝑝∗.
2) Exponentially Degraded Paths : In this case, we assume that the service rates of all the paths increases linearly as the path index increase. Specifically, the service rate of path 𝑖 is given by 𝜇𝑖=𝛼𝑒−𝛽𝑖, 𝑖= 1,2, . . . , 𝑝. (13) 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 2 4 6 8 10 12 14 16 18 20 File Size, k
Number of Active Path, p
*
Linearly−Degraded Path Exponentially−Degraded Path
Fig. 7. The number of active paths is plot as a function of the content file size,𝑘, for the two specific path settings.
Applying the iterative packet allocation algorithm, we no-tice that the path elimination process would continue if the following condition is met,
(𝜇𝜇1 𝑝) 2≥ 𝑘 𝜋 𝜇1+𝜇𝑝 ∑𝑝 𝑖=1𝜇𝑖. (14)
Plugging (13) into (14) and ignoring some tail terms, we obtain
𝑝≥ 1 2𝛽 ln [ (1−𝑒−𝛽)𝑘 𝜋 ] + 1. (15)
As a result, the algorithm will stop when the number of paths left in the active set is
𝑝∗ 𝑒= ⌊ 1 2𝛽ln [ (1−𝑒−𝛽)𝑘 𝜋 ] + 1 ⌋ . (16) All the packets are proportionally allocated to the set of active paths from path 1 to path 𝑝∗.
In Figure 7, we compare the resulted number of active paths, from our proposed iterative packet allocation algorithm, for the aforementioned two path settings. As shown in (15), for a set of linearly-degraded paths, the number of active paths scales in a cubic root of the content file size; while for a set of exponentially-degraded paths, the number of active paths scales logarithmically with the content file size. Therefore, the number of active paths for exponentially-degraded paths is much less than the number of active paths for linearly-degraded paths.
VI. NUMERICALPERFORMANCEANALYSIS
In this section, we investigate the performance penalty, re-sulted from our proposed iterative path application algorithm. Specifically, let us consider a case in which 3 paths are available between the mobile device and the media cloud. In our simulation, we obtain two packet allocation policies with its corresponding file delays: the optimal one through an exhaustive searching algorithm and the efficient one through our iterative algorithm.
Fig. 8. The normalized delay diversion, between the packet allocation vector resulted from our proposed iterative algorithm and the one resulted from the exhaustive searching algorithm, is plotted as a function of the content file size (i.e.,𝑘), for four different sets of exponentially-degraded paths.
To quantify the performance penalty of our proposed algo-rithm compared to the optimal packet allocation, we define a performance metric as the normalized delay diversion between the efficient policy and the optimal policy, given by the following formula,
𝒟= 𝜏†𝜏−∗𝜏∗, (17)
where 𝜏† and𝜏∗ are the average file delay resulted from our proposed algorithm and the optimal one.
In Figure 8, we plot the normalized delay diversion as the function of the content file size for four different sets of exponentially-degraded paths. There are a few observations from this result. First, the normalized delay diversion is bounded and the upper limit is normally small. In our case, it is less than 5%. As a result, the file delay of our efficient packet allocation policy is quite close to that of the optimal one. Second, when the degradation coefficient is small(i.e., the service rates degrades slowly), our proposed algorithm always generates an optimal packet allocation policy. For example, our algorithm results in optimal packet allocation policies for path service rate vectors (128, 128, 128) and (128, 64, 32). However, for a set of paths with wildly varying path service rates, our algorithm often results in a sub-optimal packet allocation policy. Finally, for a set of paths degrading fast, the performance penalty increases with a larger file size, in a concave fashion. This numerical investigation suggests that our proposed iterative algorithm will generates a near-optimal packet allocation vector, and will result in an optimal packet allocation vector for a set of comparable paths.
VII. CONCLUSION
In this paper, we investigated the problem of minimizing the average file delay of uploading user-generated content files of
finite size to the media cloud through multiple connections in cooperative wireless networks. The objective is to provide an improved user experience for emerging video traffic and mobile applications. Using a simplified queue model, we first identified the path starvation as a major bottleneck. Our proposed solution is to reduce possible path starvation by optimally allocating all the packets into possible paths. We then proposed an iterative packet allocation algorithm by leveraging insights obtained from our previous research in the canonical 2-path case. Numerical simulations indicated that the delay performance of the packet allocation policy from our proposed algorithms is very close to that of the optimal packet allocation policy from an exhaustive search algorithm. In term of additional research, we are looking at the strategy of applying inter-path packet coding technique to further reduce the average file delay. In order to make the research practical, we are also exploiting the interaction with TCP/IP protocols.
ACKNOWLEDGMENT
The authors would like to thank Singapore Nanyang Tech-nological University for the start-up grant support of this re-search as well as the grant support from China NSF 61170256.
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