Fairness-Aware Cooperative Caching Scheme for Mobile Social Networks

Transcription

1 Fairness-Aware Cooperative Caching Scheme for Mobile Social Networks Dongsheng Wei [, Konglin Zhu \, and Xin Wang [ [ School of Computer Science, Fudan University, Shanghai, China Engineering Research Center of Cyber Security Auditing and Monitoring, Ministry of Education, China \ Institute of Computer Science, University of Goettingen, Goettingen, Germany {222469, xinw}@fudan.edu.cn, zhu@cs.uni-goettingen.de Abstract Data access is an important and challenging issue in Mobile Social Networks (MSNs), and cooperative caching is an effective technique to improve the access performance. Most of current research efforts in data access of MSNs focus on improving the access performance while neglecting the fair treatment of users. Because fairness is considered as a major incentive for peer-to-peer service especially in infrastructure-less wireless networks, in this paper we propose a novel approach to support fairness aware cooperative caching scheme in MSNs. Through capturing close friend set of each node, we cache data prior at nodes which are overlapped by most nodes close friend sets. Then we derive the optimal cooperative scheme by using the minimum dominating set, which is an NP-Complete problem, and we design a heuristic algorithm to handle it. Experimental results show that our scheme can effectively improve data access fairness as well as maintain nearly the same access performance compared to existing cooperative caching schemes. I. INTRODUCTION Delay Tolerant Networks (DTNs) [] consist of mobile nodes which opportunistically contact each other. They facilitate the communication among people by short-range communication interfaces (e.g. WiFi or Bluetooth) without involving any infrastructure. DTNs have been prevailingly used in various scenarios, such as wildlife tracking, vehicular network, etc. Among many real life examples of DTNs, mobile social networks (MSNs) [2], where people can communicate with their friends nearby, are of growing significance as a result of rapid and wide spread usage of mobile devices (e.g., headsets, tablets) among people and their surroundings. In mobile social networks, data accessibility, as an important application, is exerted for many different purposes. For example, it is desirable that headset users find interesting contents from close peers, meanwhile interactively share their local data with their friends. However, due to the intermittent connectivity among mobile users, the data transmission from node to node is not guaranteed and always suffering massive delays. To enhance the chance of data access, cooperative data caching as an important technique has been applied in MSNs in recent years [3][4]. By caching data at nodes which are frequently contacted by others, so that queries in the future can be responded with less delay, and the average access performance (access ratio and access delay) of the whole network is efficiently improved. Although existing works [3][4] on cooperative caching efficiently improve data access performance of the network, they neglect the fairness of individuals, which each node can access the data with the same probability. Fig. shows an example with 6 users who are interconnected by solid lines (frequent encountering) or dotted lines (infrequent encountering) operating different cooperative caching schemes. Suppose it needs to select 2 caching nodes in the network. According to the literatures [3] and [4], node B and C, which are solid circle in Fig. (a), are chosen as caching nodes due to their high probabilities of being contacted by most of others (For instance, node C has 3 solid lines and dotted lines connect with others; node B connected with others with 2 solid lines and dotted lines). Under this caching strategy, the nodes contacting frequently to the caching nodes, such as node E and F, have much better access performance than others such as node A and D, which violates the fairness of individuals. Fairness, however, is particularly challenging and important because it is considered a major incentive for peer-to-peer service usage especially in infrastructure-less wireless networks [5]. Users participating in contents sharing networks want to equally have the same probability to access digital contents they are interested in. Still consider the example in Fig., instead of choosing node B and C, we select node A and C as caching nodes just as shown in Fig. (b). Although node A s contact probability is not higher than node B, all nodes in the network would have a favorable access performance, which achieves the fairness of individuals. Therefore, the problem of where to cache and how much to cache should be carefully determined. In this paper, we propose a heuristic solution to target the fairness of individuals and meanwhile maintain relatively high performance of data access. Particularly, we consider that each node maintains the information of its close friend set, and the caching nodes are selected from each node s close friend set. We develop an optimization procedure to restrict the scope of caching nodes to satisfy the condition that there is at least one common node between caching node set and each node s close friend set. By this mean, we minimize the number of caching nodes while ensuring the fairness of each node at the

2 A A B C D B C D E F E F (a) Caching strategy based on node s average contact probability (b) Caching strategy based on node s close friend set Fig.. Caching strategies based on different caching node selection schemes. The black point represents caching node and the white point is not. The solid line and dotted line between a pair of nodes indicate frequent encountering and infrequent encountering, respectively. same time. The contribution of this paper is summarized as follows: ) We develop a fairness-aware cooperative scheme in MSNs based on node close friend set information. 2) We design a heuristic algorithm to address the caching node selection problem, which is an NP-Complete problem. 3) We conduct experiments to show that our proposed method achieves relatively high data access performance and meanwhile ensures the fairness of individuals. The rest of the paper is organized as follows. In Sec. II, we review the existing work. We then analysis close friend set of node and present caching node selection strategy in Sec. III. In Sec. IV, we evaluate our scheme via trace-driven simulation, and Sec. V concludes the paper. II. RELATED WORK Recent research on cooperative caching in MSNs aims to improve average access performance by optimizing the resource (e.g., cache nodes) utilization. Gao et al. [3] propose to intentionally cache data at a pre-specified set of Network Central Locations (NCLs), which ensures that other nodes in the network can access data easily. They propose an effective scheme which ensures appropriate NCL selection based on a probabilistic selection metric, and then coordinate multiple caching nodes to leverage the tradeoff between data accessibility and caching overhead. However, their scheme requires to maintain shortest opportunistic paths information between each pair of nodes, which is complex and impractical since the topology of MSNs is rapidly changed. In [4], Zhuo et al. firstly identify the effects of the contact duration limitation on cooperative caching in MSNs. Their theoretical analysis shows that the marginal caching benefit that a caching node can provide diminishes when it caches more data. To fully utilize the storage space and the contact opportunities, they use network coding techniques in their cooperative caching scheme and design a contact Duration Aware Caching (DAC) protocol. Nevertheless, due to the coding operation both in source and destination nodes, it is energy dissipation for those battery limited mobile devices. Wang et al. [6] establish a mathematical model of mobile content sharing network based on file popularity distribution, user mobile and delay tolerance. They derive a strategy to achieve the optimal cache allocation. However, their model assumes the same node s mobility and does not consider the heterogeneous node s contact patterns and behaviors, which is unrealistic. The authors in [7] present a gossip-based cooperative caching to address cache placement problem by considering the sequential relation among data items. The main target of the work is to provide an uninterrupted data access service. In [8], the introduced cooperative caching policy aims to minimize electronic content provisioning cost in MSNs. However, all above existing cooperative caching schemes neglect the fairness of individual access performance. III. ALGORITHM DESIGN In this section, we describe the detail design of our proposed scheme. We first present an overview of the scheme and then show the selection of close friend set. Finally, the caching nodes strategy is proposed. A. Overview In our model of MSNs, we assume V is the set of mobile nodes, and F is the set of files being cached on the networks. Any file can be requested by mobile nodes whenever needed, and each node may become the requester at anytime. Different files own different lifetime, which means the file is out of date if the query delay exceeds the files lifetime. The intermittent contact between nodes in an MSN makes contact possible only in opportunistic manner. Each node in the network owns a close friend set which determined by the quality of the link. The cache nodes are selected from the dominate set of the union of all nodes close friend set to cover all nodes in the network. In such a manner, the fairness of each node is guaranteed. We use Fig. 2 to demonstrate how our algorithm works. Suppose we have a network as shown in the figure. There are 9 nodes in the network and each node should have a close friend set. To simply the structure of the figure, we only show

3 close friend set of N N close friend set of N4 N4 are p Xij (T k ) and p Xij (T k2 ) respectively, and p Xij (T k ) > p Xij (T k2 ) according to Eq. 2. If p Xij (T k ) > e P>p Xij (T k2 ), then to file k, node i and node j are close friends, while to file k 2, they are not. Thus, the close friend set of node i for file k, denoted by CF i,k, is restricted as: CF i,k = {j j 2 V,p Xij (T k ) e P },i2 V,k 2 F (3) close friend set of N2 N2 Normal node N3 close friend set of N3 Caching node Fig. 2. Overview of the algorithm the close friend sets of N, N2, N3 and N4. We can see that the close friend sets of these nodes have already covered all nodes in the network. Among these close friends sets, we find the minimal number of nodes that can reach all other nodes in the network, which is depicted as dashed circles in the figure. We consider them as the cache nodes of the network. By caching data on these two nodes, all other nodes have similar ability to access different pieces of data, which achieves the fairness of individuals. We will explain the detailed design on the algorithms in the following subsections. B. Close Friend Set According to recent studies [3][4][9], the inter-contact time X ij between node i and node j, as a random variable, follows an exponential distribution with probability density function (PDF), such that f Xij (x) = ij e ijx where ij is the average contact rate of i and j. From Eq., the contact probability among node i and node j within T is written as p Xij (T )= Z T f Xij (x)dx = e ijt To further excavate the relations among different pairs of nodes, we define node i s close friend set: CF i, constructed by a set of nodes that each node s contact probabilities with node i excess the threshold probability P e, which is a predefined parameter. For example, if node j can contact node i with probability p Xij (T ) > P e before the time constraint T, node j is in node i s close friend set: j 2 CF i. Thus without loss of generality, if a file is cached on node j and the file s lifetime is T, node i, one of the close friends of node j, can successfully access the file within the file s lifetime with at least the probability P e. However, considering the various lifetimes of different files, we cannot ensure the same low bound of access probability P e even to the same pair of nodes. For example, file k and file k 2 have their own lifetimes T k, T k2, and T k >T k2. For these two files, the successful contact probability of nodes i and j () (2) We set p Xii (T k ) =, which means a node is always a close friend to itself. C. Caching Node Selection To leverage the tradeoff between fairness and access performance, we assume a requester is satisfied with the situation when he can receive the file within the file s lifetime. As described in Sec. III-B, all nodes greedily desire the files they want to download could be cached in their corresponding close friend sets so that they can successfully access the files with at least the probability e P. In our caching node selection strategy, to effectively use the caching resource, we desire to use as less caching space and caching nodes as possible to support cooperative caching in MSNs. Our basic method is to extract caching nodes from each node s close friend set. That is, to ensure each node s satisfaction, it requires at least one caching node being selected from each node s close friend set. If the caching node set of file k is denoted as C k, then it can be represented as: C k = {i 8i 2 V,CF i,k \ C k 6=?},k 2 F (4) Due to the various lifetimes of files, each file may generate a caching set for nodes in the network. Thus, the overall caching node set should be the union of caching set of each file, it is denoted as: M[ C = C k (5) k= Hence, the formal definition of the optimal cooperative caching problem is given as: Definition : The cooperative caching problem is to determine the caching solution C k for 8k 2 F, which minimizes the total number of caching nodes C, subject to pre-defined lower bound of the probabilistic metric of friendship relation ep. min C (6) X s.t. q i,k s k apple B i (7) 8i2C,8k2F Here s k denotes the size of file k, B i is the caching space of node i and M is the total number of files. q i,k is the probability of cache node i has file k, which will be described in detail in Sec. III-C3.

4 ) Minimize Caching Nodes: If we view a node s close friend set as a vertex being adjacent to some other vertices in graph theory, the problem of determining optimal minimum number of caching nodes in Def. can reduce to standard minimum dominating set, which is an NP-Complete problem. Hence, we propose a heuristic algorithm shown in Alg. to approximately solve of this problem. We first select the node which appears most frequently in all nodes close friend sets as a caching node. Then we select node appearing most frequently (except for nodes already being selected as caching nodes) in all nodes close friend sets, and so on, until each node s close friend set has at least one node is chosen as caching node. This caching node selection algorithm operates in a centralized way because the input of the algorithm is all nodes close friend sets information, and the network administrator is responsible for assigning caching nodes after receiving the information of all nodes close friend sets and operating this algorithm. It can be extended to a distributed version by exchanging close friends set of each node. The detailed design of distributed algorithm will be studied in our future work. Algorithm File k s minimum caching node selection Input: CF,k,CF 2,k,...,CF n,k Output: C k : C k = ; 2: w be a n n zero metric 3: for each i 2 [,n] do 4: for each j 2 CF i,k do 5: w(i, j) =w(j, i) = 6: end for 7: end for 8: repeat 9: i max = arg max {D i D i = P n j= w(i, j)} S i2[,n] : C k = C k {imax } : for each j 2 [,n] and w(i, j) 6= do 2: w(i, j) =w(j, i) = 3: end for 4: until w is zero metric 2) Query Pattern & File Popularity : The query pattern and file popularity directly affect the cooperative caching strategy. Intuitively, if a file is more popular and requested by more nodes, it is more desirable to be cached on the network. And even when the file replacement happens due to full utilization of node s caching space, the popular file is more likely to be cached than unpopular files. It is well known that the popularity distribution of digital contents approximately follows Zipf distribution [3][6]. According to Zipf distribution, if among all files, a file is the kth most likely to be requested, then the probability of request, p k, approximately follows p k = k / P M i= i where is an exponent parameter. Therefore, in our model, we assume the query pattern and file popularity follow Zipf distribution. 3) Data Selection: Due to the limited caching space, some caching nodes may overflow due to many files being cached on them. The major reason is that, according to our network in Sec. III-C, every file independently select caching nodes, and some node(s) may be selected as caching node by many files. In this case, if the total volume of files supposed to be cached in the caching nodes exceeds the caching space, the caching nodes should be carefully selected which file should be cached on it. We used the same technique proposed in [3] as Probabilistic Data Selection, which operate the caching replacement strategy not only prioritizes popular files during cache replacement with higher utility, but also enable the files to have non-negligible chance to be cached on the network even though they are unpopular. The basic idea is probabilistically select files to cache when the more files should be cached on the same caching node, and such probabilistic selection, which is denoted as q i,k in Eq. 7, may be iteratively conducted multiple times to ensure that the caching buffer is fully utilized. IV. EVALUATION In this section, we evaluate the performance of our cooperative caching scheme through trace-driven simulations. A. Simulation Settings TABLE I SUMMARY OF REALISTIC TRACES Infocom5 Infocom6 Net. type Bluetooth Bluetooth # of devices 4 78 # of contacts 22,459 82,95 Duration(days) 3 4 Granularity(secs) 2 2 Avg. # of contacts(per day) Our performance evaluations are performed on Infocom5 trace and Infocom6 trace respectively, both of which are collected by the Haggle Project []. These two traces record contract history of users carrying on Bluetooth devices, which periodically detect their neighbors and record the contact information. The detailed characteristics of the two traces are summarized in Tab. I. Due to the coarse granularity of the two traces, there are a lot records whose contact duration is zero. In our simulation process, we remove these records because we think data cannot be transferred if the duration is zero. In the experiments, the first one third of the trace is used as the warm-up period for accumulating network information and forming each node s close friend set, and all the data queries are generated during the remaining two third of the traces. We adopt benchmark algorithm PROPHET [], which calculates a delivery predictability metric based on the contact histories and then relays the packet to the nodes with a higher metric, as the routing protocol for the caching nodes to send files to the requester. Although some recently work studies the impact of contact duration on caching scheme [4][2], we assume each file can be transmitted within one contact, and we

5 take the impact of contact duration on fairness as our future work. In communication networks, two general fairness indexes have been frequently used to measure the fairness of nodes in networks [3]: ) Gini index: I Gini = P P 2n 2 x i j x i y j. 2) Jain index: I Jain = P n i= xi 2 n P 2, where n is the total number i= x2 i of users, x i is the performance of user i, and x is the average performance of all users. Both of the indexes are in the range from to. The smaller Gini index, the more fair it is. While the smaller Jain index, the more unfair it is. In our work, we used these indexes to quantify fairness of cooperative caching scheme in MSNs. To evaluate the performance our cooperative caching scheme, we use and compare the following two metrics: ) Average access ratio, the average ratio of queries sent by all the requesters in the network being satisfied with the file within its lifetime. 2) Fairness, the difference of individual access ratio, which we will quantify this fairness by Gini and Jain index, respectively. To further understand the performance of our scheme, we compare our scheme to the following two caching strategies: ) Cache, in which files randomly cached on nodes without the consideration of file popularity ranking and node contact patterns. 2) Cache [3], which intentionally cache data at a pre-specified set of nodes which can be easily accessed by other nodes. Our scheme is denoted as (Fairness Aware cooperative Caching). B. Simulation Results In both traces, we set the number of file types as M = 5. Note that although there are 5 different types of files, to a specific kind of file, there are one or more replicas in the whole network. Each file has a finite lifetime uniformly distributed in range [.5T,.5T ], where T is the average lifetime of all files. Similarly, caching buffer is also uniformly distributed in range [.5B,.5B], B is the average caching space and can be adjusted to different node buffer conditions. In the same way, file size is in range[.5s,.5s] with average size s. We set T = 5 hours, B = 5Mb and s = Mb. By default, generate query pattern follows Zipf distribution with =. We evaluate the effectiveness of caching cost ratio, the ratio of the all nodes caching space occupied by files, of our caching strategy. Through adjusting e P in our scheme and changing number of NCLs in Cache, we set the range of caching cost ratio from. to.9. All the presented results are averaged over 5 runs with different random seeds. ) Fairness v.s. caching cost ratio: Fig. 3 shows the fairness metrics, Gini index and Jain index, for three schemes, as functions of the caching cost ratio in both traces. When the caching cost ratio changes from. to.9, the Gini index decreases and the Jain index increases accordingly, meaning all the three schemes become more and more fair. Compared with scheme and Cache scheme, our scheme performs more fair with the same caching cost ratio. This is because in Cache scheme, too many Gini index Gini index (a) Gini index - Infocom5 (c) Gini index - Infocom6 Fig. 3. Jain index Jain index (b) Jain index - Infocom5 (d) Jain index - Infocom6 Fairness v.s caching cost ratio packets are cached at some NCLs nodes with high probability been contacted by most other nodes, however, it is hard to ensure that every node has one or more caching nodes (NCLs nodes) he can frequently encounter. Thus, to these requesters whose close friend sets containing no caching nodes, they have poor accessibility performance than others. In this way, when there are not many NCLs nodes and the caching cost ratio is not large (less than.6), the fairness performance is not well maintained. In contrast, the caching node selection of is based on each node s close friend set, and thus the nodes overlapped by most close friend sets are selected as the caching nodes. In this way, the fairness is effectively improved. As can be seen from Fig. 3, when the caching cost ratio is below.6 more or less, the fairness performance of Cache scheme is sometime even better than. This is because in Cache scheme, all files are randomly cached on nodes without the consideration of node s contact patterns, thus the scheme s high performance of fairness is based on its low average delivery ratio, which would be shown in Fig. 4. 2) Average access ratio v.s. caching cost ratio: Fig. 4 shows the average delivery ratio of three schemes. As we can see that the performance of and Cache are almost the same, both of which outperform Cache. The reason is that to a caching node, it is more likely overlapped by most of other nodes close friend sets, as well as with high probability contacted by most of the others. Thus, for the caching node sets selected by the two schemes, the majority of both caching node sets are the same, which ensure that their average access performance are with little difference. However, the rest small portion of different caching nodes, caused by the different strategies of the two schemes, efficiently affects the fairness

6 Average access ratio (a) Delivery ratio - Infocom5 Average access ratio (b) Delivery ratio - Infocom6 Fig. 4. Average delivery ratio v.s. caching cost ratio of individual access satisfaction. On the other hand, without considering the contact patterns, it is obvious that the average delivery ratio of Cache scheme is lower than other two schemes. When the caching cost ratio is large, the performance gap is relatively small. This is because when more nodes become caching nodes, a lot of requests can be satisfied locally because the requester can find files what he want from his local cache space. Overall, maintains much better fairness and has similar access ratio with cache. Compared with cache, although sometimes maintains less fair than cache, it achieves much higher average access ratio. V. CONCLUSIONS &FUTURE WORK In this paper, we propose a novel approach to support cooperative caching in MSNs, which enables the fair sharing and coordination of cached data among multiple nodes. Specifically, through analysis each node s close friend set, we cache data prior at nodes which are overlapped by more node s close friend set. We derive the optimal caching node selection scheme and design a heuristic algorithm to solve it. Trace-driven simulation results show that our scheme can improve data access fairness as well as maintain nearly the same average access ratio compared to existing scheme. This work has the potential to be extended in some ways. In Alg., the caching node selection algorithm operates in a centralized way, it can be extended to a distributed version by exchanging close friends set of each node. Meanwhile, In this work, we assume each file can be transmitted within one contact, it may be of interest if we consider the impact of contact duration on fairness issue. [2] N. Kayastha, D. Niyato, P. Wang, and E. Hossain, Applications, architectures, and protocol design issues for mobile social networks: A survey, Proceedings of the IEEE, vol. 99, no. 2, pp , 2. [3] W. Gao, G. Cao, A. Iyengar, and M. Srivatsa, Supporting cooperative caching in disruption tolerant networks, in Proc. ICDCS, 2. [4] X. Zhuo, Q. Li, G. Cao, Y. Dai, B. Szymanski, and T. L. Porta, Social-Based Cooperative Caching in DTNs: A Contact Duration Aware Approach, in Proc. MASS, 2. [5] A. Mtibaa and K. A. Harras, Fairness-related challenges in mobile opportunistic networking, Computer Networks, 22. [6] T. Wang, P. Hui, S. R. Kulkarni, and P. Cuff, Cooperative Caching based on File Popularity Ranking in Delay Tolerant Networks, in Proc. ExtremeCom, Zürich, Switzerland, March 22. [7] X. Fan, J. Cao, H. Mao, and Y. Liu, Gossip-based cooperative caching for mobile applications in mobile wireless networks, Journal of Parallel and Distributed Computing, 23. [8] M. Taghizadeh, K. Micinski, and S. Biswas, Distributed cooperative caching in social wireless networks, Transactions on Mobile Computing, vol. 2, no. 6, June 23. [9] W. Gao, Q. Li, B. Zhao, and G. Cao, Multicasting in delay tolerant networks: A social network perspective, in Proc. of MOBIHOC, 29. [] J. Scott, J. Crowcroft, P. Hui, C. Diot et al., Haggle: A networking architecture designed around mobile users, in WONS 26, 26, pp [] A. Lindgren, A. Doria, and O. Schelén, Probabilistic routing in intermittently connected networks, ACM SIGMOBILE Mobile Computing and Communications Review, vol. 7, no. 3, pp. 9 2, 23. [2] X. Zhuo, Q. Li, W. Gao, G. Cao, and Y. Dai, Contact duration aware data replication in delay tolerant networks, in Network Protocols (ICNP), 2 9th IEEE International Conference on. IEEE, 2, pp [3] M. Dianati, X. Shen, and S. Naik, A new fairness index for radio resource allocation in wireless networks, in WCNC 5, vol. 2. IEEE, 25, pp VI. ACKNOWLEDGMENT This work was supported in part by the National Science Foundation of China under Grant 6774, Program for New Century Excellent Talents in University under Grant NCET- -3, Shanghai Municipal R&D Foundation under Grant No and the National S&T Major Project of China under Grant 2ZX Xin Wang is the corresponding author. REFERENCES [] K. Fall, A delay-tolerant network architecture for challenged internets, in Proc. SIGCOMM, 23, pp