Mobility Weakens the Distinction between Multicast and Unicast Xinbing Wang Dept. of Electronic Engineering Shanghai Jiao Tong University Shanghai, China

2 Outline Introduction   Previous works & Motivation System model and main idea The impact of mobility on capacity for restricted mobility model The impact of mobility on delay for restricted mobility model Discussion Conclusion and future direction

Previous Works & Motivation What is multicast?   One source to m destinations 3 Data copy is necessary One copy may be sent to multiple destinations The number of flows is reduced comparing with unicast Xiangyang Li [1] [1] X. Li, “Multicast Capacity of Large Scale Wireless Ad Hoc Networks”, IEEE/ACM Trans. Networking, Vol.17, No. 3, pp , Jan (citation:234)

Previous Works & Motivation The multicast uses 4

Previous Works & Motivation The essential difference between multicast and unicast   The flow aggregation in multicast case (multiple flows with different destinations can be aggregated, and therefore only one flow is enough)   Due to the flow aggregation, the number of flows is reduced (11→5 in this example) by the multicast scheduling comparing with the multi-unicast case. 5

Previous Works & Motivation The mobility   Everything is going mobile   Currently, more than 70% of Facebook users access the service via a mobile device at least some of the time [2].   65% growth in mobile data traffic between Q and Q [3]. 6 [2] Christopher Penn, “State of Facebook: 70% use a mobile device to access Facebook”, [3] Ericsson, “Ericsson Mobility Report-June 2014”,

Previous Works & Motivation The study of mobility 7   A large number of studies focus on the mobility, including the modeling, measurement, scheduling design, performance analysis and etc. [4] P. Gupta and P. R. Kumar, "The capacity of wireless networks", IEEE Trans. Inform. Theory, vol. 46, no. 2, pp (citation:7678) [5] A. Gamal, J. Mammen, B. Prabhakar and D. Shah, “Optimal Throughput-Delay Scaling in Wireless Networks-Part I: The Fluid Model,” in IEEE Transactions on Information Theory, vol. 52, no. 6, pp , (citation:249) [6] Y. Tao, B. Ye, X. Wang, et al.,“Capacity and delay of heterogeneous wireless networks with correlated mobility,” in Wireless Communications and Networking Conference (WCNC) 2013, Shanghai, China, Apr [7] M. Garetto, E. Leonardi, “Restricted Mobility Improves DelayThroughput Tradeoffs in Mobile Ad Hoc Networks,” in IEEE Transactions on Information Theory, vol. 56, no. 10, pp , [8] C. Zhang, X. Zhu and Y. Fang, “On the improvement of scaling laws for large-scale MANETs with network coding,” in IEEE Journal on Selected Areas in Communications, vol. 27, no. 5, pp , 2009.

Previous Works & Motivation The impact of mobility(1)   The mobility helps deliver the packet 8

Previous Works & Motivation The impact of mobility(2)   The mobility may reduce the probability of flow aggregation 9

Previous Works & Motivation Our view on the impact of mobility   According to the mentioned impacts above, we can conclude that: The mobility helps deliver the packet → The mobility improves the capacity. The mobility may reduce the probability of flow aggregation → The mobility weakens the distinction between multicast and unicast. 10

Previous Works & Motivation Our view on the impact of mobility   The mobility improves the capacity 11 Static Random i.i.d. Mobility Static Random i.i.d. Mobility Unicast Multicast [9] Z. Wang, H. Sadjadpour, J.J. Garcia Luna Aceves, “A Unifying Perspective on the Capacity of Wireless Ad Hoc Networks,” in Proc. of IEEE INFOCOM 2008, Phoenix, AZ, USA, Apr [10] X. Wang, Q. Peng, Y. Li, “Cooperation Achieves Optimal Multicast Capacity-Delay Scaling in MANET,” in IEEE Transactions on Communications, vol. 60, no. 10, pp , [9] [10]

Previous Works & Motivation Our view on the impact of mobility   The mobility weakens the distinction between multicast and unicast 12 We verify this observation in our paper

13 Outline Introduction System model and main idea The impact of mobility on capacity for restricted mobility model The impact of mobility on delay for restricted mobility model Discussion Conclusion and future direction

System model The restricted mobility model 14 Each node i has a corresponding home point H i. Defining: The PDF of satisfies   This model includes many important mobility models such as static model, random i.i.d. mobility model etc.   The node speed is a decreasing function of α. Therefore, by adjusting the α, the impact of mobility on the network capacity can be well studied. where. Consequently, the can be further expressed as

System model The network model 15   Restricted mobility networks   Total number of nodes : n   Unicast, Multicast   Protocol model   Transmission range:   Bandwidth of each hop: constant   Destinations are randomly selected   Number of destinations is m

System model Capacity definition 16 Per-node Throughput: For a given scheme, we define the per-node throughput as the maximum achievable transmission rate. In t time slots, we assume that there are M(i,t) packets transmitted from node i to its destination(s). Firstly, the long term per-node throughput is defined as Afterwards, the per-node throughput of this model for a given scheme is defined by the maximum T(n) satisfying Per-node Capacity: For a given network, the per-node capacity of it is defined as where is a scheme for the network, is the set of all possible schemes, and is the per-node throughput of scheme.

System model Delay definition 17 Delay: For a given scheme, assuming that the source sends the packet to the network at time slot t s and the destination receives the packet at time slot t d, the delay is defined as the average value of t s - t d, i.e., It should be noted that the queuing delay at source is not considered here, which is the same as in many important works. Moreover, for wireless networks, we assume that the operation time spent in coding/decoding is negligible compared to the transmission time.

Main idea of this paper 18 Restricted mobility model Unicast Capacity, Delay Multicast Capacity, Delay Multicast gain (The capacity and delay gain of multicast comparing with unicast) More general case (The upper-bound and lower- bound of multicast gain)

Main contribution of this paper 19 [7] M. Garetto, E. Leonardi, “Restricted Mobility Improves DelayThroughput Tradeoffs in Mobile Ad Hoc Networks,” in IEEE Transactions on Information Theory, vol. 56, no. 10, pp , 2010.

20 Outline Introduction System model and main idea The impact of mobility on capacity for restricted mobility model   The capacity of unicast case   The capacity of multicast case   The multicast capacity gain The impact of mobility on delay for restricted mobility model Discussion Conclusion and future direction

21 The capacity of unicast case The throughput upper-bound In order to derive the per-node capacity, a contact graph is considered, in which the nodes are allocated at their home-points respectively. Moreover, we put an edge between any two-nodes, whose weight is defined as the probability that they happen to be within distance of each other. Considering a cut dividing the contact graph into two parts with the same size, there are nodes in each part in average. Therefore, the sum per-node throughput of these pairs is bounded by the sum weight of the edges across the cut.   Based on the contact graph

22 The capacity of unicast case The throughput upper-bound The sum weight of the edges across the cut can be expressed as where Further computation

23 The capacity of unicast case The throughput upper-bound After some mathematical manipulations, the throughput upper-bound can be obtained

24 The capacity of unicast case The optimal throughput achieving scheme The 2-hop relay scheme: the relay is selected from the nodes with home-point in the circle centered at the middle point of the source’s and destination’s home-points. The radius is 1/3 of the distance between the source’s and destination’s home-points.

25 The multi-hop relay scheme: the relays are selected in the cells that the line between source’s and destination’s home-points lines across. The capacity of unicast case The optimal throughput achieving scheme

26 Outline Introduction System model and main idea The impact of mobility on capacity for restricted mobility model   The capacity of unicast case   The capacity of multicast case   The multicast capacity gain The impact of mobility on delay for restricted mobility model Discussion Conclusion and future direction

27 The capacity of multicast case The throughput upper-bound Each source selects m destinations. The contact graph is also considered. Considering a circle cut dividing the contact graph into two parts as in the figure. The radius of the circle is. The numbers of packets transmitting into the circle and out of the circle are both. Therefore, the sum per-node throughput is bounded by the sum weight of the edges across the cut.   Based on the contact graph

28 The capacity of multicast case The throughput upper-bound Similar to the unicast case, the sum weight of the edges across the cut can be expressed as where Further computation where

29 After some mathematical manipulations, the throughput upper-bound can be obtained The capacity of multicast case The throughput upper-bound

30 The capacity of unicast case The optimal throughput achieving scheme   Case 1: α<2, similar to random i.i.d. mobility model.(2-hop, random relay selection)   Case 2:α≥2, Step1: build the Euclidean Minimum Spanning Tree (EMST) among the home points of the destinations and source. Step 2: Each edge of the EMST is treated as a unicast transmission.

31 Outline Introduction System model and main idea The impact of mobility on capacity for restricted mobility model   The capacity of unicast case   The capacity of multicast case   The multicast capacity gain The impact of mobility on delay for restricted mobility model Discussion Conclusion and future direction

32 The multicast capacity gain Definition of multicast capacity gain Multicast Capacity Gain: For a given network, we assume that the per-node capacity of multicast is. Moreover, if each node has m destinations, each multicast session can be treated as m unicast sessions (multi-unicast), and the corresponding sum per-node capacity is denoted as. Comparing the capacity of multicast and multi-unicast, we define the multicast capacity gain as The multicast capacity gain indicates the enhancement of per-node capacity by multicast transmission. Specially for the restricted mobility model, we use to represent the multicast capacity gain instead of since it is mainly related with and m.

33 The multicast capacity gain The multicast capacity gain of restricted mobility model According to the theoretical results of unicast and multicast, the multicast capacity gain can be expressed as

34 The multicast capacity gain The multicast capacity gain of restricted mobility model There is a gap when α=2 since there is a gap in the sum of p-series.

35 Outline Introduction System model and main idea The impact of mobility on capacity for restricted mobility model The impact of mobility on delay for restricted mobility model   The delay of unicast case   The delay of multicast case   The multicast delay gain Discussion Conclusion and future direction

36 The delay of unicast case Optimal delay achieving scheme: the flooding scheme In the restricted mobility model, the PDF of packet-holding nodes in the next time slot is determined by the packet-holding nodes in current time slot. Therefore, the transmission process in restricted mobility model can be treated as a Markov chain with 2 n-1 states. Moreover, there are 2 n-2 target states and 1 initial state. Hence, it is too complex to obtain the exact order of delay.

37   The upper-bound of the optimal delay is analyzed in this paper. In particular, we divide the transmissions into two groups, i.e., long distance transmission (LDT) and short distance transmission (SDT). LDT: the distance between the two transmission nodes’ home-points is. SDT: the distance between the two transmission nodes’ home-points is.   We calculate the following two kinds of delay: Delay 1: the delay of the packet transmitted from source to destination only through LDT. Delay 2: the delay of the packet transmitted from source to destination only through SDT. Consequently, the total delay of flooding scheme is upper-bounded by the minimum value of Delay 1 and 2. The delay of unicast case Optimal delay achieving scheme: the flooding scheme

38   Delay 1 (LDT delay) The event of LDT happens with probability For any nodes i and j, the event that i transmits a packet to j within two hops happens with probability, which is the same as in random i.i.d. mobility model in order sense. Thus, the Delay 1 equals to timing the delay of random i.i.d. mobility model. Hence, the Delay 1 satisfies The delay of unicast case Optimal delay achieving scheme: the flooding scheme

39   Delay 2 (SDT delay) To calculate Delay 1, we consider the condition that there is an region of radius centered at the home-point of source, and each node with home-point in holds a packet from i with probability. After time slots, there is a region of radius centered at the home-point of source, and each node with home-point in holds a packet from i with probability. This process is called region extension, which is illustrated in the figure, and is the region extension time. The delay of unicast case Optimal delay achieving scheme: the flooding scheme

40   Delay 2 (SDT delay) It should be noted that we ignore the transmissions out of as while as the relay to relay transmissions within the ring during the region extension. After some manipulations, the optimal relation between and is derived in our paper to minimize the number of ignored transmissions. The delay of unicast case Optimal delay achieving scheme: the flooding scheme

41   Delay 2 (SDT delay) It should be noted that the delay of case is mainly determined by Delay 1. The delay of unicast case Optimal delay achieving scheme: the flooding scheme

42   The upper-bound of the delay for flooding scheme (The minimum value of Delay 1 and Delay 2) The delay of unicast case Optimal delay achieving scheme: the flooding scheme

43 Outline Introduction System model and main idea The impact of mobility on capacity for restricted mobility model The impact of mobility on delay for restricted mobility model   The delay of unicast case   The delay of multicast case   The multicast delay gain Discussion Conclusion and future direction

44 The delay of multicast case Optimal delay achieving scheme: the flooding scheme To obtain the optimal delay for multicast case, we also adopt the flooding scheme under the same assumption that the transmission range is constant. When the flooding scheme is adopted, all of the nodes in the network will receive a replica of the packet from the source within the same time scale of the delay for unicast case. Therefore, for multicast case, the optimal delay is of the same order of unicast case, which is also proved in random i.i.d. mobility model in [10]. [10] X. Wang, Q. Peng, Y. Li, “Cooperation Achieves Optimal Multicast Capacity-Delay Scaling in MANET,” in IEEE Transactions on Communications, vol. 60, no. 10, pp , 2012.

45 Outline Introduction System model and main idea The impact of mobility on capacity for restricted mobility model The impact of mobility on delay for restricted mobility model   The delay of unicast case   The delay of multicast case   The multicast delay gain Discussion Conclusion and future direction

46 The multicast delay gain Definition of multicast delay gain Multicast Delay Gain: For a given network, we assume that the network delay of multicast is. Moreover, if each node has m destinations, the sum delay of the transmissions from the source to them by unicast is denoted as. Comparing the delay of multicast and multi-unicast, we define the multicast delay gain as The multicast delay gain indicates the enhancement of delay performance by multicast transmission.

47 The multicast gain The multicast delay gain of restricted mobility model   According to the definition of multicast delay gain, the multicast delay upper-bound gain of restricted mobility model can be expressed as

48 Outline Introduction System model and main idea The impact of mobility on capacity for restricted mobility model The impact of mobility on delay for restricted mobility model Discussion Conclusion and future direction

49 Discussion: capacity The upper-bound of the multicast capacity gain   The multicast session can be treated as multiple unicast sessions.   If the multicast is finished during one unicast session, the multicast capacity gain is maximized.

50 Discussion: capacity The lower-bound of the multicast capacity gain   The multicast session can be treated as multiple unicast sessions.   The random i.i.d. mobility model can achieve the lower-bound of multicast capacity gain

51 Discussion: capacity Framework of the multicast capacity gain   Mobility weakens the distinction between multicast and unicast, which is the cost of the capacity enhancement. Brief explanation: the unpredictability of mobility decreases the opportunity of flow aggregation. (Please see page 7)page 7

52   Other affecting factors The distribution of nodes The number of destinations …… Discussion: capacity Framework of the multicast capacity gain

53   The distribution of nodes also impacts the multicast gain The distribution of nodes determines the number of nodes covered by each hop. For a given transmission range, the opportunity of flow aggregation increases with the number of nodes covered by each hop. Therefore, we have following conjecture: Conjecture: The multicast gain is high if the nodes are distributed (or probabilistically distributed) close to a line (or a curve). An example can be found in page 46.page 46 Discussion: capacity Framework of the multicast capacity gain

54   The multicast gain is also related with the number of destinations Brief explanation: the additional destinations may help increase the opportunity of flow aggregation. Discussion: capacity Framework of the multicast capacity gain

55 Discussion: delay Framework of multicast delay gain In multicast case, assuming the unicast delay from source i to one of its destinations j is, the multicast delay gain can be expressed as Since in flooding scheme, the upper-bound of multicast delay gain is and the lower-bound is.

56 Discussion: delay The lower-bound achieving scheme With probability n -3, one node in one part can move to another part in one time slot, and then it moves back to its initial part in the next time slot. Therefore, where poly-logarithmic factors are ignored, i.e., the multicast delay gain is.

57 Outline Introduction System model and main idea The impact of mobility on capacity for restricted mobility model The impact of mobility on delay for restricted mobility model Discussion Conclusion and future direction

58 Conclusion and future direction   This paper studies the essential roles of multicast scheduling and mobility in one-to-many transmission networks. Based on the restricted mobility model, the theoretical analysis indicates that the mobility weakens the distinction between multicast and unicast, i.e., the probability of flow aggregation.   We further propose another two affecting factors of the multicast capacity gain, i.e., the distribution of the nodes and the number of destinations.   Therefore, three interesting future directions arise: What is the optimal delay/throughput tradeoff for restricted mobility model? And what is the corresponding scheme? What is the impact of mobility on multicast in a general mobility model? Is there any other affecting factors of the multicast capacity gain?

59 Comments ? Questions ? Thank you!