- Email: [email protected]
Stability of ALM Tree with selfish receivers: A simulation study
Computer Communications 29 (2006) 2895–2903 www.elsevier.com/locate/comcom
Stability of ALM Tree with selfish receivers: A simulation study
q
Jianping Wu, Dan Li *, Yong Cui Department of Computer Science and Technology, Tsinghua University, Beijing 100084, PR China Available online 27 April 2006
Abstract Application Layer Multicast (ALM) is an effective supplement to IP Multicast. However, unlike the multicast tree in IP Multicast which is constructed on routers, the multicast tree in ALM is composed of host receivers. As selfish entities which have their own interests, the host receivers may cheat about their private information. Receiver cheating may transform the multicast tree, and lead to its instability. We establish the cheating model of selfish ALM receivers, and study the stability of ALM tree with selfish receivers through simulations. Simulation results show that receiver cheating has considerably negative effects on the stability of ALM tree. This discovery brings forward a new issue in ALM study, that is, we should take receiver cheating into consideration to maintain a stable ALM tree when designing ALM protocols. Ó 2006 Elsevier B.V. All rights reserved. Keywords: ALM; Stability; Cheating; Selfish receivers
1. Introduction Multicast is a communication technology which allows one host to send a single copy of data to many receivers [1]. It is an important part of many next-generation network applications [2]. Currently, there are two kinds of multicast technologies. One is realized in the network layer, named as IP Multicast; the other is realized in the application layer, named as Application Layer Multicast (ALM). IP Multicast makes use of the replicating and forwarding functions of routers to achieve the goal of saving network bandwidth and reducing server load. Since the multicast tree is composed of routers, IP Multicast has high scalability and high efficiency. However, IP Multicast changes the ‘‘unicast’’ principle of the traditional Internet, and a lot of problems in it, such as multicast management, congestion control, and pricing model, have not yet been solved well,
q This work is supported by the National Natural Science Foundation of China (Nos. 60303006 and 60403035) and the National Major Basic Research Program of China (No. 2003CB314801). * Corresponding author. Tel.: +86 10 62795818 6864. E-mail addresses: [email protected] (J. Wu), [email protected]. tsinghua.edu.cn (D. Li), [email protected] (Y. Cui).
0140-3664/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.comcom.2006.03.014
which results in its unwidely deployment in Internet. Later, researchers came up with ALM. Unlike IP Multicast, ALM relies on end systems to replicate and forward data in the application layer, and does not make any change in the network layer. Compared with IP Multicast, ALM is obviously lower in efficiency, but much more deployable. ALM exemplifies a trade-off between the efficiency of IP Multicast and the ease of deployment of group communication [3]. In addition to the ease of deployment, ALM also has some other advantages. ALM is more flexible, because it does not depend on bottom layers, and end systems in the application layer can provide more semantics. We can design suitable multicast models and algorithms for different multicast applications. Therefore, ALM is an efficient supplement to IP Multicast. Even when IP Multicast is ubiquitously deployed, ALM is still a useful tool for group communication. In ALM, the multicast tree is composed of the data source and multicast receivers. In order to receive data, multicast receivers should participate in constructing the multicast tree as well as replicating and forwarding data. In other words, multicast receivers pay costs for obtaining services. However, the costs they pay differ according to the
2896
J. Wu et al. / Computer Communications 29 (2006) 2895–2903
numbers of children they have in the multicast tree. The fewer children a receiver has, the less cost it will pay for maintaining the children list as well as replicating and forwarding data. Meanwhile, receivers at different depths of the multicast tree observe different propagation delays. The closer the receiver is to the source, the less propagation delay it observes. Therefore, there is an intrinsic imbalance of roles in a multicast tree. Multicast receivers at different positions of the multicast tree differ much in the cost they have to pay and the service they can obtain. Most of the current ALM protocols require each receiver to measure its distances to other receivers and sources in the ALM tree and report these distance measurements to other nodes or use these measurements for decision-making. Thus, there exists a serious hidden trouble of trust on receivers during the construction of ALM tree. A selfish receiver may cheat outright about its distance measurements, in order to try to improve its position in the tree. By cheating, the receiver may get closer to the source node to observe less propagation delay, or may have fewer children to reduce replication and forwarding burdens. As most ALM protocols allow the multicast tree to be dynamically updated to suit the real-time change of the network topology, there are a lot of chances for selfish ALM receivers to cheat. Selfish receivers may cause the structure change and thus the instability of the ALM tree. An unstable ALM tree means the oscillation of multicast routing, which affects the normal propagation of multicast data, and also means more control overhead of computation, storage and communication. Application-layer cheating has often been discussed, but as far as we know, there is no research on the impact of receiver cheating on the stability of ALM Tree until now. We establish the cheating model of selfish ALM receivers in this paper, and analyze the stability of ALM tree with selfish receivers through simulation study. The rest of this paper is organized as follows. In Section 2 related work is discussed. The cheating model of selfish ALM receivers is established in Section 3. We discuss ALM tree’s stability problem with selfish receivers in Section 4. Section 5 focuses on the simulation study. Further discussions are made in Section 6. Finally, conclusions are presented in Section 7. 2. Related work Since ALM was born, there are many protocols proposed. All ALM protocols organize the group members into two topologies, namely control topology and data topology [4]. Members that are peers on the control topology exchange the reachability and distance information between them. The data topology is usually a subset of the control topology and identifies the data path for a multicast packet in the ALM. In fact, the data topology is a tree, called ALM tree, while the control topology has greater connectivity between members. Changes in control topology may cause the changes in data topology. Most ALM protocols primarily concern the construction of the data topology. According
to the construction sequence of the control topology and the data topology, we can classify the current proposed ALM protocols into three different categories – mesh-first, treefirst and implicit approaches [4]. In the mesh-first approach, multicast members first organize themselves into an overlay mesh topology and then compute the forwarding tree based on the mesh. Examples of this category of ALM protocols include End-System Multicast [5], Scattercast [6], Kudos [7], etc. In contrast, protocols based on the tree-first approach first construct a shared data delivery tree, and subsequently each member discovers a few other members of the multicast group that are not its neighbors on the overlay tree, then establishes and maintains additional control links to these members. The data delivery tree and the additional control links form the control topology. Representations of this category of ALM protocols include Yoid [8], Host Multicast [9], ALMI [10], Switch Tree [11], Overcast [12], TBCP [13], TAG [14], etc. Protocols using the implicit approach create a control topology with some specific properties. The data delivery path is implicitly defined on this control topology by some packet forwarding rule which leverages the specific properties of the control topology to create loop-free multicast paths. ALM protocols belonging to this category include NICE [15], Delauary Triangulations [16], CAN-Multicast [17], Scribe [18], Bayeux [19], and so on. Lately, researchers are turning to other problems in ALM, such as reliability [20–22], scalability [21,23,24], host heterogeneity [25], and peer trust [3,30–34]. As for the problem of peer trust, L. Mathy studied the impact of receiver cheating on the link stress and stretch in ALM [3]. There are also some approaches to this problem [30–34]. However, current approaches are far from satisfactory. Before the thorough solution to the problem, the influence of selfish peers may need to be further considered, for example, its impact on the stability of ALM tree, which was not studied before. Stability of the multicast tree is an important issue in the multicast researches. Although researchers have designed a lot of ALM protocols as mentioned above, there are few approaches aimed to ensure the ALM tree’s stability. The problems with the stability of ALM tree can be divided into two types. One is caused by the dynamic changes of multicast members, and the other is due to the changes of the network topology, receiver cheating or other causes when multicast members do not change at all. For IP multicast where the deployment of routers is comparatively stable, the stability problem of multicast tree primarily belongs to the first type [26–28]. However in ALM, because application-level nodes are unstable and the construction and maintenance of the ALM tree are dependent on these nodes, the ALM tree might be unstable even when multicast members do not change. In this case, the causes for the instability of ALM tree probably include node movement, node performance change, receiver cheating, etc. As a matter of fact, with the occurrence of receiver cheat-
J. Wu et al. / Computer Communications 29 (2006) 2895–2903
ing, the stability of ALM tree becomes an important issue because structure change of the ALM tree may cause additional control overhead and impede the normal propagation of multicast data.
r
In most ALM protocols, when a receiver i joins the multicast session, it is bootstrapped with a random set of neighboring nodes that are already in the ALM tree. Receiver i then selects one neighboring node as its parent. In link-weighted ALM, the parent node selected is usually the neighboring node from which receiver i could observe the shortest propagation delay, according to the distances declared by the neighboring nodes. Neighboring nodes in the ALM tree periodically advertise the connectivity information and link distances between each other to suite the dynamical change of network topology. Based on the dynamical information, each receiver periodically reselects its parent node from its neighboring nodes. To get the benefit of receiving multicast data, each receiver in ALM also pays the cost of forwarding data to its children nodes in the multicast tree. But the cost they pay varies with different children number. The fewer children a receiver has, the less cost it pays for maintaining the children list as well as replicating and forwarding data. Therefore, there is motivation as well as chance for a selfish multicast receiver to cheat. In different ALM protocols, multicast receivers may cheat in different ways. We here discuss a general cheating approach for ALM receivers that can be frequently used in ALM protocols. When reporting its measurement distances to the source node, the receiver reduces the distances by some degree, so as to appear as closer to the source node in the ALM tree and to observe less propagation delay. Similarly, when reporting its measurement distances to other receivers, the receiver increases the distances by some degree, so as to reduce the probability of becoming the father node of other receivers and have less replicating and forwarding burden. The degree of distance reduction from the cheating receiver to the source node and the degree of distance increase from the cheating receiver to other receivers are both reflections of the cheating degree. Since ALM receivers periodically reselect their parent nodes, there are a lot of chances for them to cheat, and the cheating degree may vary within a wide range. When ALM protocols discover the change of the control topology, the ALM tree may be transformed. Fig. 1 shows an example where receiver a cheats about its distance to receiver c from 1 to 3, receiver c cheats about its distance to receiver f from 2 to 6, and receiver d cheats about its distance to receiver g from 2 to 6. The resulting ALM tree changes subsequently. The propagation delay receiver c observes changes from 4 to 5, that of receiver f changes from 6 to 8, and that of receiver g changes from 7 to 8. To establish the receiver cheating model, here we define some cheating parameters.
r 2
3
5
b
c
3 3 3
2
f
d
2
2 4
2
3
a 1
3. Cheating model of selfish ALM receivers
2897
Receiver cheating
1
a
b 3
e
c
5
5
g
3
3 3
6
f
d
2
6 4
1
e 5
g
Data link Control link
Fig. 1. Cheating example.
Definition 1. Source Cheating Degree When an ALM receiver reports its distance to the source node, the proportion of the reduced value to the actual value is defined as the Source Cheating Degree, which is denoted by s. Definition 2. Receiver Cheating Degree When an ALM receiver reports its distance to another ALM receiver, the proportion of the increased value to the actual value is defined as the Receiver Cheating Degree, which is denoted by o. In most cases, the beneficiary nodes after receiver cheating are the cheating receivers, while the victims are the honest receivers as well as the source node. Therefore, different percentages of cheating receivers out of all receivers will lead to different impacts on the ALM tree. ALM nodes measure their distances to other nodes, which forms the ALM control topology. A receiver can only cheat about the distances to its reachable nodes. Thus, the number of reachable nodes for cheating receivers in the control topology directly affects their cheating chances. We define Measurement Degree to describe this issue. Definition 3. Measurement Degree In ALM, the proportion of the number of links of the control topology to the number of links when nodes are all-connected is defined as Measurement Degree. It is denoted by d. According to the definition, it is apparent that the maximum value of d is 1. Assuming that the total number of nodes of ALM tree is n, to ensure the connectivity of the control topology, the minimum number of links should be n 1, while the number of links is n (n 1)/2 when nodes are all-connected, so the minimum value of d is 2/n. Based on the above descriptions, we can establish the cheating model of ALM receivers. Assuming that a single-source ALM session has n receivers (total number of nodes is n + 1), a measurement degree of d, a cheating receiver percentage of p, and all cheating receivers cheat as follows: when reporting their distances to the source node, they reduce the actual distances by the source cheating degree of s; and when reporting their distances to other receivers, they increase the actual distances by the receiver
2898
J. Wu et al. / Computer Communications 29 (2006) 2895–2903
cheating degree of o. We denote this receiver cheating as Cn (d, p, s, o), where 2/(n + 1) 6 d 6 1, 0 6 p 6 100%, 0 6 s < 1, and o P 0. 4. Stability of ALM tree with selfish receivers Since the multicast tree is built on end systems in ALM, there are many causes that can lead to instability of the multicast tree, including the change of topology, the change of multicast members, the change of location or performance of end systems, receiver cheating, etc. To discuss the stability of ALM tree under the condition of receiver cheating, we assume that there are no other factors to cause the structure change of ALM tree. The model of receiver cheating is described in Section 3. The impact of receiver cheating Cn (d, p, s, o) on the stability of ALM tree can be reviewed on two aspects. One is the structure change of the whole ALM tree caused by the cheating, and the other is the position change of receivers after the cheating. The former aspect describes the tree switch from a global view. We define the Link Jitter Index of ALM Tree to quantify the switch extent. The latter aspect concerns the position change of each receiver, which also means the benefit or damage each receiver gets or suffers from receiver cheating. We define the Benefit Index of Source Node, Benefit Index of Honest Receivers, and Benefit Index of Cheating Receivers to quantify the change extent. Definition 4. Link Jitter Index of ALM Tree In a receiver cheating Cn (d, p, s, o), if a directed link L in the ALM tree Tn does not exist any longer after the cheating, L is regarded as changed. Assuming the total number of changed directed links in Tn after receiver cheating Cn (d, p, s, o) is Dn (d, p, s, o), we define the Link Jitter Index of ALM Tree in the receiver cheating Cn (d, p, s, o) as Jn (d, p, s, o) = 1 Dn (d, p, s, o)/n.1 It can be inferred from definition 4 that the less Jn (d, p, s, o) is, the greater impact Cn (d, p, s, o) will be on the link change of ALM tree. Definition 5. Benefit Index of Source Node In a receiver cheating Cn (d, p, s, o), the proportion of the children number of the source node after cheating to that of before is defined as the Benefit Index of Source Node in the receiver cheating Cn (d, p, s, o). It is denoted by Sn (d, p, s, o). Definition 6. Benefit Index of Honest Receivers In a receiver cheating Cn (d, p, s, o), the proportion of the total children number of all the honest receivers after cheating to that of before is defined as the Benefit Index of Honest Receivers in the receiver cheating Cn (d, p, s, o). It is denoted by Hn (d, p, s, o).
1 The number of nodes of ALM is n + 1, so the total number of links of the ALM tree is n.
Definition 7. Benefit Index of Cheating Receivers In a receiver cheating Cn (d, p, s, o), the proportion of the total children number of all the cheating receivers after cheating to that of before is defined as the Benefit Index of Cheating Receivers in the receiver cheating Cn (d, p, s, o). It is denoted by Fn (d, p, s, o). Based on definition 5, Sn (d, p, s, o) > 1 shows that the source node is a victim in the receiver cheating Cn (d, p, s, o), and the more Sn (d, p, s, o) is, the more damage the source node suffers. On the contrary, Sn (d, p, s, o) < 1 means that the source node gets benefit from the receiver cheating Cn (d, p, s, o), and the less Sn (d, p, s, o) is, the more it benefits. It is also the same for Hn (d, p, s, o) and Fn (d, p, s, o). 5. Simulation study By use of GT-ITM [29], we have simulated 50 groups of multicast sessions sized of 50 receivers and 50 groups of multicast sessions sized of 200 receivers, each with a single source. The results are all average values of the 50 groups. To study the impact of cheating behaviors of selfish receivers on the stability of ALM tree under different cheating parameters, we try each group with a measurement degree d of 10%, 30%, 50%, 70%, and 90%, respectively, a source cheating degree s of 10%, 50%, and 90%, respectively, a receiver cheating degree o of 25%, 50%, 100%, and 200%, respectively, and a cheating receiver percentage p of 5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, and 95%, respectively. Let us see the values of Link Jitter Index of ALM Tree Jn (d, p, s, o), Benefit Index of Source Node Sn (d, p, s, o), Benefit Index of Honest Receivers Hn (d, p, s, o), and Benefit Index of Cheating Receivers Fn (d, p, s, o), against different receiver cheating parameters. 5.1. Link Jitter Index of ALM Tree Jn (d, p, s, o) The value of Link Jitter Index of ALM Tree Jn (d, p, s, o) against p and d when s = 50% and o = 100% is illustrated in Fig. 2A, its value against p and o when d = 50% and s = 50% is illustrated in Fig. 2B, and its value against p and s when d = 50% and o = 100% is illustrated in Fig. 2C. As shown in Fig. 2A, the bigger d is, the smaller Jn (d, p, s, o) will be. The reason is that when the measurement degree gets higher, the cheating chances of the cheating receivers will go up, as a result, the link change of ALM tree is greater and the Link Jitter Index of ALM Tree is smaller. From Figs. 2B and C, we can see that Jn (d, p, s, o) decreases with the growth of s or o. It is because that when the source cheating degree or receiver cheating degree is higher, the change of ALM control topology will be greater, which leads to a bigger link change number in the reconstructed data topology and a smaller Link Jitter Index of ALM Tree. These three figures also show that with the growth of p, Jn (d, p, s, o) first decreases, and then increases. This
J. Wu et al. / Computer Communications 29 (2006) 2895–2903
A
1
B
1
0.9 Link Jitter Index of ALM Tree
Link Jitter Index of ALM Tree
0.9
2899
0.8
0.7 n=50, d=10% n=50, d=30% n=50, d=50% n=50, d=70% n=50, d=90% n=200, d=10% n=200, d=30% n=200, d=50% n=200, d=70% n=200, d=90%
0.6
0.5
0.4 0
20
0.8
0.7 n=50, o=25% n=50, o=50% n=50, o=100% n=50, o=200% n=200, o=25% n=200, o=50% n=200, o=100% n=200, o=200%
0.6
0.5
0.4
40 60 % of Cheating Receivers
C
80
100
0
20
40 60 % of Cheating Receivers
80
100
1
Link Jitter Index of ALM Tree
0.9
0.8
0.7
0.6 n=50, s=10% n=50, s=50% n=50, s=90% n=200, s=10% n=200, s=50% n=200, s=90%
0.5
0.4
0
20
40 60 % of Cheating Receivers
80
100
Fig. 2. Link Jitter Index of ALM Tree. (A) s = 50%, o = 100%. (B) d = 50%, s = 50%. (C) d = 50%, o = 100%.
can be explained as follows. When the cheating receiver percentage is small, more cheating receivers mean greater influence on the reconstruction of the ALM tree. However, when most of the receivers cheat, the control topology after cheating is merely the former distances shifted by a constant (of course the distances to the source are excluded), which results in the decrease of the link change number. As a whole, we conclude that the structure change extent of ALM tree is large under receiver cheating, especially when the measurement degree is great, the cheating degree is high, and the cheating receiver percentage is medium. Receiver cheating will cause much additional overhead for reconstructing the ALM tree. 5.2. Benefit Index of Source Node Sn (d, p, s, o) The value of Benefit Index of Source Node Sn (d, p, s, o) against p and d when s = 50% and o = 100% is illustrated in Fig. 3A, its value against p and o when d = 50% and s = 50% is illustrated in Fig. 3B, and its value against p and s when d = 50% and o = 100% is illustrated in Fig. 3C.
The bigger d is, the bigger Sn (d, p, s, o) will be. This is illustrated in Fig. 3A. It is similar to Fig. 2A. When the measurement degree is higher, the cheating chances of cheating receivers will be greater, as a result the ALM tree will be transformed by a greater extent, and there will be more receivers to be the children of the source node. As shown in Figs. 3B and C, with the increasing of s or o, Sn (d, p, s, o) increases. This is also because that when the cheating degree is higher, the transformation of ALM control topology is greater, and subsequently the children number of the source node is more after reconstructing the ALM tree. Also from these three figures, Sn (d, p, s, o) increases as p grows. This conclusion may be somewhat obvious. Due to the existences of more cheating receivers, more receivers will be further from each other, as a result of which more receivers will become the children of the source node. On all occasions, the value of Benefit Index of Source node is more than 1, sometimes even around 50. Therefore, receiver cheating will add considerable burdens to the source node. However, one of the most important original goals of ALM is to reduce the server load. For this reason,
2900
J. Wu et al. / Computer Communications 29 (2006) 2895–2903 40 35 Benefit Index of Source Node
B
n=50, d=10% n=50, d=30% n=50, d=50% n=50, d=70% n=50, d=90% n=200, d=10% n=200, d=30% n=200, d=50% n=200, d=70% n=200, d=90%
30 25 20
25 n=50, o=25% n=50, o=50% n=50, o=100% n=50, o=200% n=200, o=25% n=200, o=50% n=200, o=100% n=200, o=200%
20 Benefit Index of Source Node
A
15 10
15
10
5 5 0
0
20
40 60 % of Cheating Receivers
C
100
0
0
20
40 60 % of Cheating Receivers
80
100
60 n=50, s=10% n=50, s=50% n=50, s=90% n=200, s=10% n=200, s=50% n=200, s=90%
50 Benefit Index of Source Node
80
40
30
20
10
0
0
20
40 60 % of Cheating Receivers
80
100
Fig. 3. Benefit Index of Source Node. (A) s = 50%, o = 100%. (B) d = 50%, s = 50%. (C) d = 50%, o = 100%.
we claim that receiver cheating has severe negative impact on ALM. 5.3. Benefit index of Honest Receivers Hn (d, p, s, o) The value of Benefit Index of Honest Receivers Hn (d, p, s, o) against p and d when s = 50% and o = 100% is illustrated in Fig. 4A, its value against p and o when d = 50% and s = 50% is illustrated in Fig. 4B, and its value against p and s when d = 50% and o = 100% is illustrated in Fig. 4C. As illustrated in Fig. 4A, Hn (d, p, s, o) grows with the increase of d, which means an increase of damage the honest receivers suffer from receiver cheating. This is because the cheating chances for cheating receivers will go up when measurement degree increases, leading to more children of honest receivers. From Figs. 4B and C, the growth of s or o will cause the increase of Hn (d, p, s, o). The higher the cheating degree is, the more change will take place in the control topology, as well as the chance of honest receivers to be the father nodes of other receivers when reconstructing the ALM tree.
Moreover, these three figures show that Hn (d, p, s, o) increases with the growth of p. Since cheating receivers claim to be further from other receivers than they actually are, more cheating receivers will enhance the probability of honest receivers to become the father nodes of other receivers. Under most situations, the value of Benefit Index of Honest Receivers is more than 1, which means that honest receivers are also the victims of receiver cheating. But it should be noted that when the cheating degree is much too large, the value of Benefit Index of Honest Receivers may be less than 1, which means that honest receivers also get benefits from receiver cheating. The reason is that when this happens, most receivers will become the children of the source node, and the total children number of honest receivers will relatively decrease. In this case, the burden added to the source node is especially high. 5.4. Benefit index of Cheating Receivers Fn (d, p, s, o) The value of Benefit Index of Cheating Receivers Fn (d, p, s, o) against p and d when s = 50% and o = 100%
J. Wu et al. / Computer Communications 29 (2006) 2895–2903
A
3.5
3
2.5
2
1.5
1
n=50, o=25% n=50, o=50% n=50, o=100% n=50, o=200% n=200, o=25% n=200, o=50% n=200, o=100% n=200, o=200%
5
Benefit Index of Honest Receivers
4 Benefit Index of Honest Receivers
B
n=50, d=10% n=50, d=30% n=50, d=50% n=50, d=70% n=50, d=90% n=200, d=10% n=200, d=30% n=200, d=50% n=200, d=70% n=200, d=90%
2901
4.5 4 3.5 3 2.5 2 1.5
0
20
40 60 % of Cheating Receivers
C
100
1
0
20
40 60 % of Cheating Receivers
80
100
5 n=50, s=10% n=50, s=50% n=50, s=90% n=200, s=10% n=200, s=50% n=200, s=90%
4.5 Benefit Index of Honest Receivers
80
4 3.5 3 2.5 2 1.5 1
0
20
40 60 % of Cheating Receivers
80
100
Fig. 4. Benefit Index of Honest Receivers. (A) s = 50%, o = 100%. (B) d = 50%, s = 50%. (C) d = 50%, o = 100%.
is illustrated in Fig. 5A, its value against p and o when d = 50% and s = 50% is illustrated in Fig. 5B, and its value against p and s when d = 50% and o = 100% is illustrated in Fig. 5C. As shown in Fig. 5A, Fn (d, p, s, o) decreases with the increase of d, which means that the benefit the cheating receivers get from the cheating behaviors increases. In fact, it is consistent with Figs. 3A and 4A. When the measurement degree is higher, the cheating chances of the cheating receivers are greater; as a result, the probability is less for cheating receivers to become other receivers’ father nodes. We can see from Figs. 5A and B that if s or o is bigger, Fn (d, p, s, o) will be less. This is also because the change of control topology will be greater when the cheating degree is higher, causing the cheating receivers to have even less children. Also illustrated in these figures, Fn (d, p, s, o) increases when p grows, which means that the average benefit each cheating receiver gets decreases. The reason is when there are more cheating receivers, the probability of cheating behavior between cheating receivers will go up, which will counteract the cheating effects to some extent.
In general, the value of Benefit Index of Cheating Receivers is always less than 1. It means that when receiver cheating happens, cheating receivers will always be benefited. The benefit they get is especially apparent with great measurement degree, high cheating degree, and low cheating receiver percentage. Therefore, cheating receivers always have the motivation to cheat more, so as to benefit more, which will lead to significant impact on the stability of ALM tree. 6. Discussions In order to construct an optimal ALM tree, it relies on the multicast receivers to tell their actual private information. Existing ALM protocols always assume that all multicast receivers will behave as the protocols demand. However, as an entity which has its own interests, each ALM receiver is selfish. To obtain more benefits for itself, a selfish receiver may cheat about its distances to other nodes. This cheating behavior will not only result in a sub-optimal ALM tree, but will also lead the ALM tree to instability, as we study by simulations in the above section.
2902
J. Wu et al. / Computer Communications 29 (2006) 2895–2903
B
1 n=50, d=10% n=50, d=30% n=50, d=50% n=50, d=70% n=50, d=90% n=200, d=10% n=200, d=30% n=200, d=50% n=200, d=70% n=200, d=90%
Benefit Index of Cheating Receivers
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
n=50, o=25% n=50, o=50% n=50, o=100% n=50, o=200% n=200, o=25% n=200, o=50% n=200, o=100% n=200, o=200%
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
0.1 0
1 0.9
Benefit Index of Cheating Receivers
A
0
20
40 60 % of Cheating Receivers
C
100
0
0
20
40 60 % of Cheating Receivers
80
100
1 n=50, s=10% n=50, s=50% n=50, s=90% n=200, s=10% n=200, s=50% n=200, s=90%
0.9 Benefit Index of Cheating Receivers
80
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
20
40 60 % of Cheating Receivers
80
100
Fig. 5. Benefit Index of Cheating Receivers. (A) s = 50%, o = 100%. (B) d = 50%, s = 50%. (C) d = 50%, o = 100%.
In fact, the position of a receiver in the ALM tree depends on two factors: the competence and the intent. If a receiver is closer to the source node and closer to other receivers, it is regarded as more competent because it has more chance to forward data to other receivers. If a receiver is more willing to be the parent node of other receivers, it is viewed as more intent. To construct an optimal and stable ALM tree given each receiver’s competence, it is needed to encourage receivers to heighten their intentions. In some literatures, an extra payment is introduced to each ALM receiver to encourage them to tell the actual private information. Wang studied how to design strategyproof multicast protocols in non-cooperative networks and designed distributed payment computation algorithms [30]. Yuen proposed strategyproof mechanisms for the dynamic formation of an optimal ALM tree, and also designed distributed algorithms [31]. However, an important assumption of their works is that the distributed incentive algorithms they design will be carried out truthfully by the selfish receivers. In fact, just as the receivers cheat when carrying out the ALM protocols, they may also cheat when they fulfill the incentive algorithms. To thoroughly solve the problem of cheating behaviors of selfish receivers in ALM, it is needed
to design an incentive algorithm that can not only encourage selfish receivers to tell their actual private information, but also encourage them to truthfully fulfill the algorithm itself. 7. Conclusion We study the stability of ALM tree with selfish receivers in this paper, which is not addressed in prior works. The cheating model of ALM receivers is established and the stability issue of ALM tree when receiver cheating occurs is discussed through simulations. According to the simulation results, receiver cheating will not only cause much additional overhead for ALM to reconstruct the multicast tree, but also add more burdens to honest receivers, and especially the source node, which is against the original aims of ALM. In other words, receiver cheating has considerably negative effect on the stability of ALM tree. Therefore, we should take receiver cheating into consideration to maintain a stable ALM tree when designing ALM protocols. As we discussed in the above section, a trustworthy incentive mechanism may be needed to thoroughly solve the problem of selfish receivers in ALM. This will also be the aim of our future work.
J. Wu et al. / Computer Communications 29 (2006) 2895–2903
References [1] S. E. Deering, Multicast routing in Internetworks and extended LANs, SIGCOMM 1988, Stanford, CA, 1988. [2] S.Y. Shi, J.S. Turner, Multicast routing and bandwidth dimensioning in overlay networks, IEEE J. Select. Areas Commun. 20 (8) (2002). [3] L. Mathy, N. Blundell, Impact of simple cheating in application-level multicast, in: IEEE INFOCOM, 2004. [4] S. Banerjee, B. Bhattacharjee, A comparative study of application layer multicast protocols, http://www.cs.wisc.edu/~suman/pubs.html. [5] Y.-H. Chu, S. G. Rao, H. Zhang, A case for end system multicast, in: Proceedings of ACM Sigmetrics, 2000. [6] Y. Chawathe, Scattercast: an architecture for Internet broadcast distribution as an infrastructure service, Ph.D. Thesis, University of California, Berkeley, December, 2000. [7] S. Jain, R. Mahajan, D. Wetherall, G. Borriello, Scalable selforganizing overlays, Technical report, Washington University, 2000. [8] P. Francis, Yoid: extending the Internet multicast architecture, White Paper, http://www.icir.org/yoid. [9] B. Zhang,S. Jamin,L. Zhang,Hostmulticast:aframeworkfordelivering multicast to end users, in: Proceeding of IEEE INFOCOM, 2002. [10] D. Pendarakis, S. Shi, D. Verma, M. Waldvogel, ALMI: an application level multicast infrastructure, in: Proceedings of USENIX Symposium on Internet Technologies and Systems, 2001. [11] D. A. Helder, S. Jamin, End-host multicast communication using Switch-trees protocols, in: Proceedings of Workshop on Global and Peer-to-Peer Computing on Large Scale Distributed Systems, 2002. [12] J. Jannotti, D. K. Gifford, K. L. Johnson, M. F. Kaashoek, Overcast: reliablemulticastwithanoverlaynetwork,in:ProceedingsofOSDI,2000. [13] L. Mathy, R. Canonico, D. Hutchison, An overlay tree building control protocol, in: Proceedings of the Third International Workshop on Networked Group Communication, 2001. [14] M. Kwon, S. Fahmy, Topology-aware overlay networks for group communication, in: Proceedings of International Workshop on Network and Operating Systems Support for Digital Audio and Video, 2002. [15] S. Banerjee, B. Bhattacharjee, C. Kommareddy, Scalable application layer multicast, in: Proceedings of ACM SIGCOMM, 2002. [16] J. Liebeherr, M. Nahas, Application-layer multicast with delaunay triangulations, in: Proceedings of IEEE GlobeCom, 2001. [17] S. Ratnasamy, M. Handley, R. Karp, S. Shenker, Application-level Multicast using Content-Addressable Networks, in: Proceedings of the Third International Workshop on Networked Group Communication, 2001. [18] M. Castro, P. Druschel, A. Kermarrec, A. Rowstron, SCRIBE: a large-scale and decentralized application-level multicast infrastructure, IEEE J. Select. Areas Commun. (2002). [19] S. Q. Zhuang, B. Y. Zhao, A. D. Joseph, R. H. Katz, Bayeux: an architecture for scalable and fault-tolerant wide-area data dissemination, in: Proceedings of International Workshop on Network and Operating Systems Support for Digital Audio and Video, 2001. [20] G. Kwon, J. W. Byers, ROMA: reliable overlay multicast with loosely coupled tcp connections, in: Proceedings of IEEE INFOCOM 2004, Hong Kong, China, March 2004. [21] F. Baccelli, A. Chaintreau, Z. Liu, A. Riabov, The one-to-many TCP overlay: a scalable and reliable multicast architecture, in: Proceedings of IEEE INFOCOM 2005, Miami, Florida, USA, March 2005. [22] R. Tian, Q. Zhang, Z. Xiang, Y. Xiong, X. Li, W. Zhu, Robust and efficient path diversity in application-layer multicast for video streaming, IEEE Trans. Circuits Syst. Video Technol. 15 (8) (2005) 961–972. [23] K. Sripanidkulchai, A. Ganjam, B. Maggs, H. Zhang, The feasibility of supporting large-scale live streaming applications with dynamic application end-points, in: Proceedings of ACM SICOMM, August 2004. [24] B. Knutsson, H. Lu, W. Xu, B. Hopkins, Peer-to-Peer Support for Massively Multiplayer Games, in: Proceedings of IEEE INFOCOM 2004, Hong Kong, China, March 2004.
2903
[25] Z. Zhang, S. Chen, Y. Ling, R. Chow, Resilient capacity-aware multicast based on overlay networks, in: Proceedings of ICDCS 2005, June 2005. [26] P.V. Mieghem, M. Janic, Stability of a multicast tree, in: IEEE INFOCOM, 2002. [27] F. Shi, J. Wu, K. Xu, Stability of a multicast tree in cumulative layered multicast congestion control, IPCCC (2003). [28] F. Shi, J. Wu, K. Xu, Impact of congestion on the stability of a multicast tree in cumulative layered multicast, IEE (2003). [29] E. Zegura, K. Calvert, S. Bhattacharjee, ‘‘how to model an internetwork, in: IEEE INFOCOM 1996. [30] W. Wang, X. Li, Z. Suny, Y. Wang, Design multicast protocols for non-cooperative networks, in: Proceedings of IEEE INFOCOM 2005, Miami, Florida, USA, March 2005. [31] S. Yuen, B. Li, Strategyproof mechanisms for dynamic multicast tree formation in overlay networks, in: Proceedings of IEEE INFOCOM 2005, Miami, Florida, USA, March 2005. [32] J. Shneidman, D. C. Parkes, Rationality and self-interest in peer to peer networks, in: Proceedings of IPTPS 2003, Berkeley, CA, USA, 2003. [33] R. Ma, S. Lee, J. Lui, D. Yau, A game theoretic approach to provide incentive and service differentiation in P2P networks, in: Proceedings of ACM SIGMETRICS 2004, New York, NY, USA, 2004. [34] A. Habib J. Chuang, Incentive mechanism for peer-to-peer media streaming, in: Proceedings of IWQOS 2004, Montreal, Canada, 2004.
Jianping Wu, male, born in 1953, master and doctor from Tsinghua University. He is a full professor in the Department of Computer Science, Tsinghua University, PR China from 1993. In the research areas of the network architecture, high performance routing and switching, protocol testing and formal methods, he has published more than 200 technical papers in the academic journals and proceedings of international conferences.
Dan Li, male, born in 1981, Ph.D. candidate at Department of Computer Science in Tsinghua University, PR China. He received his BS (2003) in Computer Science from Beijing Normal University. His current research interests lie in the architecture of computer networks, P2P and overlay network, and multicast. He is an IEEE student member.
Yong Cui, male, born in 1976, received the Ph.D. degree in 2004 from Tsinghua University, PR China. He is now an assistant professor at the Department of Computer Science in Tsinghua University. During his Ph.D. course, he published 20 technical papers in journals and international conferences. He has also applied for several patents in China. He has participated in many research projects. His major research interests include computer network architecture, distributed routing protocols, QoS routing and core routers.
Stability of ALM Tree with selfish receivers: A simulation study
q
Jianping Wu, Dan Li *, Yong Cui Department of Computer Science and Technology, Tsinghua University, Beijing 100084, PR China Available online 27 April 2006
Abstract Application Layer Multicast (ALM) is an effective supplement to IP Multicast. However, unlike the multicast tree in IP Multicast which is constructed on routers, the multicast tree in ALM is composed of host receivers. As selfish entities which have their own interests, the host receivers may cheat about their private information. Receiver cheating may transform the multicast tree, and lead to its instability. We establish the cheating model of selfish ALM receivers, and study the stability of ALM tree with selfish receivers through simulations. Simulation results show that receiver cheating has considerably negative effects on the stability of ALM tree. This discovery brings forward a new issue in ALM study, that is, we should take receiver cheating into consideration to maintain a stable ALM tree when designing ALM protocols. Ó 2006 Elsevier B.V. All rights reserved. Keywords: ALM; Stability; Cheating; Selfish receivers
1. Introduction Multicast is a communication technology which allows one host to send a single copy of data to many receivers [1]. It is an important part of many next-generation network applications [2]. Currently, there are two kinds of multicast technologies. One is realized in the network layer, named as IP Multicast; the other is realized in the application layer, named as Application Layer Multicast (ALM). IP Multicast makes use of the replicating and forwarding functions of routers to achieve the goal of saving network bandwidth and reducing server load. Since the multicast tree is composed of routers, IP Multicast has high scalability and high efficiency. However, IP Multicast changes the ‘‘unicast’’ principle of the traditional Internet, and a lot of problems in it, such as multicast management, congestion control, and pricing model, have not yet been solved well,
q This work is supported by the National Natural Science Foundation of China (Nos. 60303006 and 60403035) and the National Major Basic Research Program of China (No. 2003CB314801). * Corresponding author. Tel.: +86 10 62795818 6864. E-mail addresses: [email protected] (J. Wu), [email protected]. tsinghua.edu.cn (D. Li), [email protected] (Y. Cui).
0140-3664/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.comcom.2006.03.014
which results in its unwidely deployment in Internet. Later, researchers came up with ALM. Unlike IP Multicast, ALM relies on end systems to replicate and forward data in the application layer, and does not make any change in the network layer. Compared with IP Multicast, ALM is obviously lower in efficiency, but much more deployable. ALM exemplifies a trade-off between the efficiency of IP Multicast and the ease of deployment of group communication [3]. In addition to the ease of deployment, ALM also has some other advantages. ALM is more flexible, because it does not depend on bottom layers, and end systems in the application layer can provide more semantics. We can design suitable multicast models and algorithms for different multicast applications. Therefore, ALM is an efficient supplement to IP Multicast. Even when IP Multicast is ubiquitously deployed, ALM is still a useful tool for group communication. In ALM, the multicast tree is composed of the data source and multicast receivers. In order to receive data, multicast receivers should participate in constructing the multicast tree as well as replicating and forwarding data. In other words, multicast receivers pay costs for obtaining services. However, the costs they pay differ according to the
2896
J. Wu et al. / Computer Communications 29 (2006) 2895–2903
numbers of children they have in the multicast tree. The fewer children a receiver has, the less cost it will pay for maintaining the children list as well as replicating and forwarding data. Meanwhile, receivers at different depths of the multicast tree observe different propagation delays. The closer the receiver is to the source, the less propagation delay it observes. Therefore, there is an intrinsic imbalance of roles in a multicast tree. Multicast receivers at different positions of the multicast tree differ much in the cost they have to pay and the service they can obtain. Most of the current ALM protocols require each receiver to measure its distances to other receivers and sources in the ALM tree and report these distance measurements to other nodes or use these measurements for decision-making. Thus, there exists a serious hidden trouble of trust on receivers during the construction of ALM tree. A selfish receiver may cheat outright about its distance measurements, in order to try to improve its position in the tree. By cheating, the receiver may get closer to the source node to observe less propagation delay, or may have fewer children to reduce replication and forwarding burdens. As most ALM protocols allow the multicast tree to be dynamically updated to suit the real-time change of the network topology, there are a lot of chances for selfish ALM receivers to cheat. Selfish receivers may cause the structure change and thus the instability of the ALM tree. An unstable ALM tree means the oscillation of multicast routing, which affects the normal propagation of multicast data, and also means more control overhead of computation, storage and communication. Application-layer cheating has often been discussed, but as far as we know, there is no research on the impact of receiver cheating on the stability of ALM Tree until now. We establish the cheating model of selfish ALM receivers in this paper, and analyze the stability of ALM tree with selfish receivers through simulation study. The rest of this paper is organized as follows. In Section 2 related work is discussed. The cheating model of selfish ALM receivers is established in Section 3. We discuss ALM tree’s stability problem with selfish receivers in Section 4. Section 5 focuses on the simulation study. Further discussions are made in Section 6. Finally, conclusions are presented in Section 7. 2. Related work Since ALM was born, there are many protocols proposed. All ALM protocols organize the group members into two topologies, namely control topology and data topology [4]. Members that are peers on the control topology exchange the reachability and distance information between them. The data topology is usually a subset of the control topology and identifies the data path for a multicast packet in the ALM. In fact, the data topology is a tree, called ALM tree, while the control topology has greater connectivity between members. Changes in control topology may cause the changes in data topology. Most ALM protocols primarily concern the construction of the data topology. According
to the construction sequence of the control topology and the data topology, we can classify the current proposed ALM protocols into three different categories – mesh-first, treefirst and implicit approaches [4]. In the mesh-first approach, multicast members first organize themselves into an overlay mesh topology and then compute the forwarding tree based on the mesh. Examples of this category of ALM protocols include End-System Multicast [5], Scattercast [6], Kudos [7], etc. In contrast, protocols based on the tree-first approach first construct a shared data delivery tree, and subsequently each member discovers a few other members of the multicast group that are not its neighbors on the overlay tree, then establishes and maintains additional control links to these members. The data delivery tree and the additional control links form the control topology. Representations of this category of ALM protocols include Yoid [8], Host Multicast [9], ALMI [10], Switch Tree [11], Overcast [12], TBCP [13], TAG [14], etc. Protocols using the implicit approach create a control topology with some specific properties. The data delivery path is implicitly defined on this control topology by some packet forwarding rule which leverages the specific properties of the control topology to create loop-free multicast paths. ALM protocols belonging to this category include NICE [15], Delauary Triangulations [16], CAN-Multicast [17], Scribe [18], Bayeux [19], and so on. Lately, researchers are turning to other problems in ALM, such as reliability [20–22], scalability [21,23,24], host heterogeneity [25], and peer trust [3,30–34]. As for the problem of peer trust, L. Mathy studied the impact of receiver cheating on the link stress and stretch in ALM [3]. There are also some approaches to this problem [30–34]. However, current approaches are far from satisfactory. Before the thorough solution to the problem, the influence of selfish peers may need to be further considered, for example, its impact on the stability of ALM tree, which was not studied before. Stability of the multicast tree is an important issue in the multicast researches. Although researchers have designed a lot of ALM protocols as mentioned above, there are few approaches aimed to ensure the ALM tree’s stability. The problems with the stability of ALM tree can be divided into two types. One is caused by the dynamic changes of multicast members, and the other is due to the changes of the network topology, receiver cheating or other causes when multicast members do not change at all. For IP multicast where the deployment of routers is comparatively stable, the stability problem of multicast tree primarily belongs to the first type [26–28]. However in ALM, because application-level nodes are unstable and the construction and maintenance of the ALM tree are dependent on these nodes, the ALM tree might be unstable even when multicast members do not change. In this case, the causes for the instability of ALM tree probably include node movement, node performance change, receiver cheating, etc. As a matter of fact, with the occurrence of receiver cheat-
J. Wu et al. / Computer Communications 29 (2006) 2895–2903
ing, the stability of ALM tree becomes an important issue because structure change of the ALM tree may cause additional control overhead and impede the normal propagation of multicast data.
r
In most ALM protocols, when a receiver i joins the multicast session, it is bootstrapped with a random set of neighboring nodes that are already in the ALM tree. Receiver i then selects one neighboring node as its parent. In link-weighted ALM, the parent node selected is usually the neighboring node from which receiver i could observe the shortest propagation delay, according to the distances declared by the neighboring nodes. Neighboring nodes in the ALM tree periodically advertise the connectivity information and link distances between each other to suite the dynamical change of network topology. Based on the dynamical information, each receiver periodically reselects its parent node from its neighboring nodes. To get the benefit of receiving multicast data, each receiver in ALM also pays the cost of forwarding data to its children nodes in the multicast tree. But the cost they pay varies with different children number. The fewer children a receiver has, the less cost it pays for maintaining the children list as well as replicating and forwarding data. Therefore, there is motivation as well as chance for a selfish multicast receiver to cheat. In different ALM protocols, multicast receivers may cheat in different ways. We here discuss a general cheating approach for ALM receivers that can be frequently used in ALM protocols. When reporting its measurement distances to the source node, the receiver reduces the distances by some degree, so as to appear as closer to the source node in the ALM tree and to observe less propagation delay. Similarly, when reporting its measurement distances to other receivers, the receiver increases the distances by some degree, so as to reduce the probability of becoming the father node of other receivers and have less replicating and forwarding burden. The degree of distance reduction from the cheating receiver to the source node and the degree of distance increase from the cheating receiver to other receivers are both reflections of the cheating degree. Since ALM receivers periodically reselect their parent nodes, there are a lot of chances for them to cheat, and the cheating degree may vary within a wide range. When ALM protocols discover the change of the control topology, the ALM tree may be transformed. Fig. 1 shows an example where receiver a cheats about its distance to receiver c from 1 to 3, receiver c cheats about its distance to receiver f from 2 to 6, and receiver d cheats about its distance to receiver g from 2 to 6. The resulting ALM tree changes subsequently. The propagation delay receiver c observes changes from 4 to 5, that of receiver f changes from 6 to 8, and that of receiver g changes from 7 to 8. To establish the receiver cheating model, here we define some cheating parameters.
r 2
3
5
b
c
3 3 3
2
f
d
2
2 4
2
3
a 1
3. Cheating model of selfish ALM receivers
2897
Receiver cheating
1
a
b 3
e
c
5
5
g
3
3 3
6
f
d
2
6 4
1
e 5
g
Data link Control link
Fig. 1. Cheating example.
Definition 1. Source Cheating Degree When an ALM receiver reports its distance to the source node, the proportion of the reduced value to the actual value is defined as the Source Cheating Degree, which is denoted by s. Definition 2. Receiver Cheating Degree When an ALM receiver reports its distance to another ALM receiver, the proportion of the increased value to the actual value is defined as the Receiver Cheating Degree, which is denoted by o. In most cases, the beneficiary nodes after receiver cheating are the cheating receivers, while the victims are the honest receivers as well as the source node. Therefore, different percentages of cheating receivers out of all receivers will lead to different impacts on the ALM tree. ALM nodes measure their distances to other nodes, which forms the ALM control topology. A receiver can only cheat about the distances to its reachable nodes. Thus, the number of reachable nodes for cheating receivers in the control topology directly affects their cheating chances. We define Measurement Degree to describe this issue. Definition 3. Measurement Degree In ALM, the proportion of the number of links of the control topology to the number of links when nodes are all-connected is defined as Measurement Degree. It is denoted by d. According to the definition, it is apparent that the maximum value of d is 1. Assuming that the total number of nodes of ALM tree is n, to ensure the connectivity of the control topology, the minimum number of links should be n 1, while the number of links is n (n 1)/2 when nodes are all-connected, so the minimum value of d is 2/n. Based on the above descriptions, we can establish the cheating model of ALM receivers. Assuming that a single-source ALM session has n receivers (total number of nodes is n + 1), a measurement degree of d, a cheating receiver percentage of p, and all cheating receivers cheat as follows: when reporting their distances to the source node, they reduce the actual distances by the source cheating degree of s; and when reporting their distances to other receivers, they increase the actual distances by the receiver
2898
J. Wu et al. / Computer Communications 29 (2006) 2895–2903
cheating degree of o. We denote this receiver cheating as Cn (d, p, s, o), where 2/(n + 1) 6 d 6 1, 0 6 p 6 100%, 0 6 s < 1, and o P 0. 4. Stability of ALM tree with selfish receivers Since the multicast tree is built on end systems in ALM, there are many causes that can lead to instability of the multicast tree, including the change of topology, the change of multicast members, the change of location or performance of end systems, receiver cheating, etc. To discuss the stability of ALM tree under the condition of receiver cheating, we assume that there are no other factors to cause the structure change of ALM tree. The model of receiver cheating is described in Section 3. The impact of receiver cheating Cn (d, p, s, o) on the stability of ALM tree can be reviewed on two aspects. One is the structure change of the whole ALM tree caused by the cheating, and the other is the position change of receivers after the cheating. The former aspect describes the tree switch from a global view. We define the Link Jitter Index of ALM Tree to quantify the switch extent. The latter aspect concerns the position change of each receiver, which also means the benefit or damage each receiver gets or suffers from receiver cheating. We define the Benefit Index of Source Node, Benefit Index of Honest Receivers, and Benefit Index of Cheating Receivers to quantify the change extent. Definition 4. Link Jitter Index of ALM Tree In a receiver cheating Cn (d, p, s, o), if a directed link L in the ALM tree Tn does not exist any longer after the cheating, L is regarded as changed. Assuming the total number of changed directed links in Tn after receiver cheating Cn (d, p, s, o) is Dn (d, p, s, o), we define the Link Jitter Index of ALM Tree in the receiver cheating Cn (d, p, s, o) as Jn (d, p, s, o) = 1 Dn (d, p, s, o)/n.1 It can be inferred from definition 4 that the less Jn (d, p, s, o) is, the greater impact Cn (d, p, s, o) will be on the link change of ALM tree. Definition 5. Benefit Index of Source Node In a receiver cheating Cn (d, p, s, o), the proportion of the children number of the source node after cheating to that of before is defined as the Benefit Index of Source Node in the receiver cheating Cn (d, p, s, o). It is denoted by Sn (d, p, s, o). Definition 6. Benefit Index of Honest Receivers In a receiver cheating Cn (d, p, s, o), the proportion of the total children number of all the honest receivers after cheating to that of before is defined as the Benefit Index of Honest Receivers in the receiver cheating Cn (d, p, s, o). It is denoted by Hn (d, p, s, o).
1 The number of nodes of ALM is n + 1, so the total number of links of the ALM tree is n.
Definition 7. Benefit Index of Cheating Receivers In a receiver cheating Cn (d, p, s, o), the proportion of the total children number of all the cheating receivers after cheating to that of before is defined as the Benefit Index of Cheating Receivers in the receiver cheating Cn (d, p, s, o). It is denoted by Fn (d, p, s, o). Based on definition 5, Sn (d, p, s, o) > 1 shows that the source node is a victim in the receiver cheating Cn (d, p, s, o), and the more Sn (d, p, s, o) is, the more damage the source node suffers. On the contrary, Sn (d, p, s, o) < 1 means that the source node gets benefit from the receiver cheating Cn (d, p, s, o), and the less Sn (d, p, s, o) is, the more it benefits. It is also the same for Hn (d, p, s, o) and Fn (d, p, s, o). 5. Simulation study By use of GT-ITM [29], we have simulated 50 groups of multicast sessions sized of 50 receivers and 50 groups of multicast sessions sized of 200 receivers, each with a single source. The results are all average values of the 50 groups. To study the impact of cheating behaviors of selfish receivers on the stability of ALM tree under different cheating parameters, we try each group with a measurement degree d of 10%, 30%, 50%, 70%, and 90%, respectively, a source cheating degree s of 10%, 50%, and 90%, respectively, a receiver cheating degree o of 25%, 50%, 100%, and 200%, respectively, and a cheating receiver percentage p of 5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, and 95%, respectively. Let us see the values of Link Jitter Index of ALM Tree Jn (d, p, s, o), Benefit Index of Source Node Sn (d, p, s, o), Benefit Index of Honest Receivers Hn (d, p, s, o), and Benefit Index of Cheating Receivers Fn (d, p, s, o), against different receiver cheating parameters. 5.1. Link Jitter Index of ALM Tree Jn (d, p, s, o) The value of Link Jitter Index of ALM Tree Jn (d, p, s, o) against p and d when s = 50% and o = 100% is illustrated in Fig. 2A, its value against p and o when d = 50% and s = 50% is illustrated in Fig. 2B, and its value against p and s when d = 50% and o = 100% is illustrated in Fig. 2C. As shown in Fig. 2A, the bigger d is, the smaller Jn (d, p, s, o) will be. The reason is that when the measurement degree gets higher, the cheating chances of the cheating receivers will go up, as a result, the link change of ALM tree is greater and the Link Jitter Index of ALM Tree is smaller. From Figs. 2B and C, we can see that Jn (d, p, s, o) decreases with the growth of s or o. It is because that when the source cheating degree or receiver cheating degree is higher, the change of ALM control topology will be greater, which leads to a bigger link change number in the reconstructed data topology and a smaller Link Jitter Index of ALM Tree. These three figures also show that with the growth of p, Jn (d, p, s, o) first decreases, and then increases. This
J. Wu et al. / Computer Communications 29 (2006) 2895–2903
A
1
B
1
0.9 Link Jitter Index of ALM Tree
Link Jitter Index of ALM Tree
0.9
2899
0.8
0.7 n=50, d=10% n=50, d=30% n=50, d=50% n=50, d=70% n=50, d=90% n=200, d=10% n=200, d=30% n=200, d=50% n=200, d=70% n=200, d=90%
0.6
0.5
0.4 0
20
0.8
0.7 n=50, o=25% n=50, o=50% n=50, o=100% n=50, o=200% n=200, o=25% n=200, o=50% n=200, o=100% n=200, o=200%
0.6
0.5
0.4
40 60 % of Cheating Receivers
C
80
100
0
20
40 60 % of Cheating Receivers
80
100
1
Link Jitter Index of ALM Tree
0.9
0.8
0.7
0.6 n=50, s=10% n=50, s=50% n=50, s=90% n=200, s=10% n=200, s=50% n=200, s=90%
0.5
0.4
0
20
40 60 % of Cheating Receivers
80
100
Fig. 2. Link Jitter Index of ALM Tree. (A) s = 50%, o = 100%. (B) d = 50%, s = 50%. (C) d = 50%, o = 100%.
can be explained as follows. When the cheating receiver percentage is small, more cheating receivers mean greater influence on the reconstruction of the ALM tree. However, when most of the receivers cheat, the control topology after cheating is merely the former distances shifted by a constant (of course the distances to the source are excluded), which results in the decrease of the link change number. As a whole, we conclude that the structure change extent of ALM tree is large under receiver cheating, especially when the measurement degree is great, the cheating degree is high, and the cheating receiver percentage is medium. Receiver cheating will cause much additional overhead for reconstructing the ALM tree. 5.2. Benefit Index of Source Node Sn (d, p, s, o) The value of Benefit Index of Source Node Sn (d, p, s, o) against p and d when s = 50% and o = 100% is illustrated in Fig. 3A, its value against p and o when d = 50% and s = 50% is illustrated in Fig. 3B, and its value against p and s when d = 50% and o = 100% is illustrated in Fig. 3C.
The bigger d is, the bigger Sn (d, p, s, o) will be. This is illustrated in Fig. 3A. It is similar to Fig. 2A. When the measurement degree is higher, the cheating chances of cheating receivers will be greater, as a result the ALM tree will be transformed by a greater extent, and there will be more receivers to be the children of the source node. As shown in Figs. 3B and C, with the increasing of s or o, Sn (d, p, s, o) increases. This is also because that when the cheating degree is higher, the transformation of ALM control topology is greater, and subsequently the children number of the source node is more after reconstructing the ALM tree. Also from these three figures, Sn (d, p, s, o) increases as p grows. This conclusion may be somewhat obvious. Due to the existences of more cheating receivers, more receivers will be further from each other, as a result of which more receivers will become the children of the source node. On all occasions, the value of Benefit Index of Source node is more than 1, sometimes even around 50. Therefore, receiver cheating will add considerable burdens to the source node. However, one of the most important original goals of ALM is to reduce the server load. For this reason,
2900
J. Wu et al. / Computer Communications 29 (2006) 2895–2903 40 35 Benefit Index of Source Node
B
n=50, d=10% n=50, d=30% n=50, d=50% n=50, d=70% n=50, d=90% n=200, d=10% n=200, d=30% n=200, d=50% n=200, d=70% n=200, d=90%
30 25 20
25 n=50, o=25% n=50, o=50% n=50, o=100% n=50, o=200% n=200, o=25% n=200, o=50% n=200, o=100% n=200, o=200%
20 Benefit Index of Source Node
A
15 10
15
10
5 5 0
0
20
40 60 % of Cheating Receivers
C
100
0
0
20
40 60 % of Cheating Receivers
80
100
60 n=50, s=10% n=50, s=50% n=50, s=90% n=200, s=10% n=200, s=50% n=200, s=90%
50 Benefit Index of Source Node
80
40
30
20
10
0
0
20
40 60 % of Cheating Receivers
80
100
Fig. 3. Benefit Index of Source Node. (A) s = 50%, o = 100%. (B) d = 50%, s = 50%. (C) d = 50%, o = 100%.
we claim that receiver cheating has severe negative impact on ALM. 5.3. Benefit index of Honest Receivers Hn (d, p, s, o) The value of Benefit Index of Honest Receivers Hn (d, p, s, o) against p and d when s = 50% and o = 100% is illustrated in Fig. 4A, its value against p and o when d = 50% and s = 50% is illustrated in Fig. 4B, and its value against p and s when d = 50% and o = 100% is illustrated in Fig. 4C. As illustrated in Fig. 4A, Hn (d, p, s, o) grows with the increase of d, which means an increase of damage the honest receivers suffer from receiver cheating. This is because the cheating chances for cheating receivers will go up when measurement degree increases, leading to more children of honest receivers. From Figs. 4B and C, the growth of s or o will cause the increase of Hn (d, p, s, o). The higher the cheating degree is, the more change will take place in the control topology, as well as the chance of honest receivers to be the father nodes of other receivers when reconstructing the ALM tree.
Moreover, these three figures show that Hn (d, p, s, o) increases with the growth of p. Since cheating receivers claim to be further from other receivers than they actually are, more cheating receivers will enhance the probability of honest receivers to become the father nodes of other receivers. Under most situations, the value of Benefit Index of Honest Receivers is more than 1, which means that honest receivers are also the victims of receiver cheating. But it should be noted that when the cheating degree is much too large, the value of Benefit Index of Honest Receivers may be less than 1, which means that honest receivers also get benefits from receiver cheating. The reason is that when this happens, most receivers will become the children of the source node, and the total children number of honest receivers will relatively decrease. In this case, the burden added to the source node is especially high. 5.4. Benefit index of Cheating Receivers Fn (d, p, s, o) The value of Benefit Index of Cheating Receivers Fn (d, p, s, o) against p and d when s = 50% and o = 100%
J. Wu et al. / Computer Communications 29 (2006) 2895–2903
A
3.5
3
2.5
2
1.5
1
n=50, o=25% n=50, o=50% n=50, o=100% n=50, o=200% n=200, o=25% n=200, o=50% n=200, o=100% n=200, o=200%
5
Benefit Index of Honest Receivers
4 Benefit Index of Honest Receivers
B
n=50, d=10% n=50, d=30% n=50, d=50% n=50, d=70% n=50, d=90% n=200, d=10% n=200, d=30% n=200, d=50% n=200, d=70% n=200, d=90%
2901
4.5 4 3.5 3 2.5 2 1.5
0
20
40 60 % of Cheating Receivers
C
100
1
0
20
40 60 % of Cheating Receivers
80
100
5 n=50, s=10% n=50, s=50% n=50, s=90% n=200, s=10% n=200, s=50% n=200, s=90%
4.5 Benefit Index of Honest Receivers
80
4 3.5 3 2.5 2 1.5 1
0
20
40 60 % of Cheating Receivers
80
100
Fig. 4. Benefit Index of Honest Receivers. (A) s = 50%, o = 100%. (B) d = 50%, s = 50%. (C) d = 50%, o = 100%.
is illustrated in Fig. 5A, its value against p and o when d = 50% and s = 50% is illustrated in Fig. 5B, and its value against p and s when d = 50% and o = 100% is illustrated in Fig. 5C. As shown in Fig. 5A, Fn (d, p, s, o) decreases with the increase of d, which means that the benefit the cheating receivers get from the cheating behaviors increases. In fact, it is consistent with Figs. 3A and 4A. When the measurement degree is higher, the cheating chances of the cheating receivers are greater; as a result, the probability is less for cheating receivers to become other receivers’ father nodes. We can see from Figs. 5A and B that if s or o is bigger, Fn (d, p, s, o) will be less. This is also because the change of control topology will be greater when the cheating degree is higher, causing the cheating receivers to have even less children. Also illustrated in these figures, Fn (d, p, s, o) increases when p grows, which means that the average benefit each cheating receiver gets decreases. The reason is when there are more cheating receivers, the probability of cheating behavior between cheating receivers will go up, which will counteract the cheating effects to some extent.
In general, the value of Benefit Index of Cheating Receivers is always less than 1. It means that when receiver cheating happens, cheating receivers will always be benefited. The benefit they get is especially apparent with great measurement degree, high cheating degree, and low cheating receiver percentage. Therefore, cheating receivers always have the motivation to cheat more, so as to benefit more, which will lead to significant impact on the stability of ALM tree. 6. Discussions In order to construct an optimal ALM tree, it relies on the multicast receivers to tell their actual private information. Existing ALM protocols always assume that all multicast receivers will behave as the protocols demand. However, as an entity which has its own interests, each ALM receiver is selfish. To obtain more benefits for itself, a selfish receiver may cheat about its distances to other nodes. This cheating behavior will not only result in a sub-optimal ALM tree, but will also lead the ALM tree to instability, as we study by simulations in the above section.
2902
J. Wu et al. / Computer Communications 29 (2006) 2895–2903
B
1 n=50, d=10% n=50, d=30% n=50, d=50% n=50, d=70% n=50, d=90% n=200, d=10% n=200, d=30% n=200, d=50% n=200, d=70% n=200, d=90%
Benefit Index of Cheating Receivers
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2
n=50, o=25% n=50, o=50% n=50, o=100% n=50, o=200% n=200, o=25% n=200, o=50% n=200, o=100% n=200, o=200%
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
0.1 0
1 0.9
Benefit Index of Cheating Receivers
A
0
20
40 60 % of Cheating Receivers
C
100
0
0
20
40 60 % of Cheating Receivers
80
100
1 n=50, s=10% n=50, s=50% n=50, s=90% n=200, s=10% n=200, s=50% n=200, s=90%
0.9 Benefit Index of Cheating Receivers
80
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0
20
40 60 % of Cheating Receivers
80
100
Fig. 5. Benefit Index of Cheating Receivers. (A) s = 50%, o = 100%. (B) d = 50%, s = 50%. (C) d = 50%, o = 100%.
In fact, the position of a receiver in the ALM tree depends on two factors: the competence and the intent. If a receiver is closer to the source node and closer to other receivers, it is regarded as more competent because it has more chance to forward data to other receivers. If a receiver is more willing to be the parent node of other receivers, it is viewed as more intent. To construct an optimal and stable ALM tree given each receiver’s competence, it is needed to encourage receivers to heighten their intentions. In some literatures, an extra payment is introduced to each ALM receiver to encourage them to tell the actual private information. Wang studied how to design strategyproof multicast protocols in non-cooperative networks and designed distributed payment computation algorithms [30]. Yuen proposed strategyproof mechanisms for the dynamic formation of an optimal ALM tree, and also designed distributed algorithms [31]. However, an important assumption of their works is that the distributed incentive algorithms they design will be carried out truthfully by the selfish receivers. In fact, just as the receivers cheat when carrying out the ALM protocols, they may also cheat when they fulfill the incentive algorithms. To thoroughly solve the problem of cheating behaviors of selfish receivers in ALM, it is needed
to design an incentive algorithm that can not only encourage selfish receivers to tell their actual private information, but also encourage them to truthfully fulfill the algorithm itself. 7. Conclusion We study the stability of ALM tree with selfish receivers in this paper, which is not addressed in prior works. The cheating model of ALM receivers is established and the stability issue of ALM tree when receiver cheating occurs is discussed through simulations. According to the simulation results, receiver cheating will not only cause much additional overhead for ALM to reconstruct the multicast tree, but also add more burdens to honest receivers, and especially the source node, which is against the original aims of ALM. In other words, receiver cheating has considerably negative effect on the stability of ALM tree. Therefore, we should take receiver cheating into consideration to maintain a stable ALM tree when designing ALM protocols. As we discussed in the above section, a trustworthy incentive mechanism may be needed to thoroughly solve the problem of selfish receivers in ALM. This will also be the aim of our future work.
J. Wu et al. / Computer Communications 29 (2006) 2895–2903
References [1] S. E. Deering, Multicast routing in Internetworks and extended LANs, SIGCOMM 1988, Stanford, CA, 1988. [2] S.Y. Shi, J.S. Turner, Multicast routing and bandwidth dimensioning in overlay networks, IEEE J. Select. Areas Commun. 20 (8) (2002). [3] L. Mathy, N. Blundell, Impact of simple cheating in application-level multicast, in: IEEE INFOCOM, 2004. [4] S. Banerjee, B. Bhattacharjee, A comparative study of application layer multicast protocols, http://www.cs.wisc.edu/~suman/pubs.html. [5] Y.-H. Chu, S. G. Rao, H. Zhang, A case for end system multicast, in: Proceedings of ACM Sigmetrics, 2000. [6] Y. Chawathe, Scattercast: an architecture for Internet broadcast distribution as an infrastructure service, Ph.D. Thesis, University of California, Berkeley, December, 2000. [7] S. Jain, R. Mahajan, D. Wetherall, G. Borriello, Scalable selforganizing overlays, Technical report, Washington University, 2000. [8] P. Francis, Yoid: extending the Internet multicast architecture, White Paper, http://www.icir.org/yoid. [9] B. Zhang,S. Jamin,L. Zhang,Hostmulticast:aframeworkfordelivering multicast to end users, in: Proceeding of IEEE INFOCOM, 2002. [10] D. Pendarakis, S. Shi, D. Verma, M. Waldvogel, ALMI: an application level multicast infrastructure, in: Proceedings of USENIX Symposium on Internet Technologies and Systems, 2001. [11] D. A. Helder, S. Jamin, End-host multicast communication using Switch-trees protocols, in: Proceedings of Workshop on Global and Peer-to-Peer Computing on Large Scale Distributed Systems, 2002. [12] J. Jannotti, D. K. Gifford, K. L. Johnson, M. F. Kaashoek, Overcast: reliablemulticastwithanoverlaynetwork,in:ProceedingsofOSDI,2000. [13] L. Mathy, R. Canonico, D. Hutchison, An overlay tree building control protocol, in: Proceedings of the Third International Workshop on Networked Group Communication, 2001. [14] M. Kwon, S. Fahmy, Topology-aware overlay networks for group communication, in: Proceedings of International Workshop on Network and Operating Systems Support for Digital Audio and Video, 2002. [15] S. Banerjee, B. Bhattacharjee, C. Kommareddy, Scalable application layer multicast, in: Proceedings of ACM SIGCOMM, 2002. [16] J. Liebeherr, M. Nahas, Application-layer multicast with delaunay triangulations, in: Proceedings of IEEE GlobeCom, 2001. [17] S. Ratnasamy, M. Handley, R. Karp, S. Shenker, Application-level Multicast using Content-Addressable Networks, in: Proceedings of the Third International Workshop on Networked Group Communication, 2001. [18] M. Castro, P. Druschel, A. Kermarrec, A. Rowstron, SCRIBE: a large-scale and decentralized application-level multicast infrastructure, IEEE J. Select. Areas Commun. (2002). [19] S. Q. Zhuang, B. Y. Zhao, A. D. Joseph, R. H. Katz, Bayeux: an architecture for scalable and fault-tolerant wide-area data dissemination, in: Proceedings of International Workshop on Network and Operating Systems Support for Digital Audio and Video, 2001. [20] G. Kwon, J. W. Byers, ROMA: reliable overlay multicast with loosely coupled tcp connections, in: Proceedings of IEEE INFOCOM 2004, Hong Kong, China, March 2004. [21] F. Baccelli, A. Chaintreau, Z. Liu, A. Riabov, The one-to-many TCP overlay: a scalable and reliable multicast architecture, in: Proceedings of IEEE INFOCOM 2005, Miami, Florida, USA, March 2005. [22] R. Tian, Q. Zhang, Z. Xiang, Y. Xiong, X. Li, W. Zhu, Robust and efficient path diversity in application-layer multicast for video streaming, IEEE Trans. Circuits Syst. Video Technol. 15 (8) (2005) 961–972. [23] K. Sripanidkulchai, A. Ganjam, B. Maggs, H. Zhang, The feasibility of supporting large-scale live streaming applications with dynamic application end-points, in: Proceedings of ACM SICOMM, August 2004. [24] B. Knutsson, H. Lu, W. Xu, B. Hopkins, Peer-to-Peer Support for Massively Multiplayer Games, in: Proceedings of IEEE INFOCOM 2004, Hong Kong, China, March 2004.
2903
[25] Z. Zhang, S. Chen, Y. Ling, R. Chow, Resilient capacity-aware multicast based on overlay networks, in: Proceedings of ICDCS 2005, June 2005. [26] P.V. Mieghem, M. Janic, Stability of a multicast tree, in: IEEE INFOCOM, 2002. [27] F. Shi, J. Wu, K. Xu, Stability of a multicast tree in cumulative layered multicast congestion control, IPCCC (2003). [28] F. Shi, J. Wu, K. Xu, Impact of congestion on the stability of a multicast tree in cumulative layered multicast, IEE (2003). [29] E. Zegura, K. Calvert, S. Bhattacharjee, ‘‘how to model an internetwork, in: IEEE INFOCOM 1996. [30] W. Wang, X. Li, Z. Suny, Y. Wang, Design multicast protocols for non-cooperative networks, in: Proceedings of IEEE INFOCOM 2005, Miami, Florida, USA, March 2005. [31] S. Yuen, B. Li, Strategyproof mechanisms for dynamic multicast tree formation in overlay networks, in: Proceedings of IEEE INFOCOM 2005, Miami, Florida, USA, March 2005. [32] J. Shneidman, D. C. Parkes, Rationality and self-interest in peer to peer networks, in: Proceedings of IPTPS 2003, Berkeley, CA, USA, 2003. [33] R. Ma, S. Lee, J. Lui, D. Yau, A game theoretic approach to provide incentive and service differentiation in P2P networks, in: Proceedings of ACM SIGMETRICS 2004, New York, NY, USA, 2004. [34] A. Habib J. Chuang, Incentive mechanism for peer-to-peer media streaming, in: Proceedings of IWQOS 2004, Montreal, Canada, 2004.
Jianping Wu, male, born in 1953, master and doctor from Tsinghua University. He is a full professor in the Department of Computer Science, Tsinghua University, PR China from 1993. In the research areas of the network architecture, high performance routing and switching, protocol testing and formal methods, he has published more than 200 technical papers in the academic journals and proceedings of international conferences.
Dan Li, male, born in 1981, Ph.D. candidate at Department of Computer Science in Tsinghua University, PR China. He received his BS (2003) in Computer Science from Beijing Normal University. His current research interests lie in the architecture of computer networks, P2P and overlay network, and multicast. He is an IEEE student member.
Yong Cui, male, born in 1976, received the Ph.D. degree in 2004 from Tsinghua University, PR China. He is now an assistant professor at the Department of Computer Science in Tsinghua University. During his Ph.D. course, he published 20 technical papers in journals and international conferences. He has also applied for several patents in China. He has participated in many research projects. His major research interests include computer network architecture, distributed routing protocols, QoS routing and core routers.