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100
Multicast capacity for large scale wireless ad hoc networks
 In ACM Mobicom
, 2007
"... In this paper, we study the capacity of a largescale random wireless network for multicast. Assume that n wireless nodes are randomly deployed in a square region with sidelength a and all nodes have the uniform transmission range r and uniform interference range R> r. We further assume that eac ..."
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Cited by 68 (23 self)
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In this paper, we study the capacity of a largescale random wireless network for multicast. Assume that n wireless nodes are randomly deployed in a square region with sidelength a and all nodes have the uniform transmission range r and uniform interference range R> r. We further assume that each wireless node can transmit/receive at W bits/second over a common wireless channel. For each node vi, we randomly pick k − 1 nodes from the other n − 1 nodes as the receivers of the multicast session rooted at node vi. The aggregated multicast capacity is defined as the total data rate of all multicast sessions in the network. In this paper we derive matching asymptotic upper bounds and lower bounds on multicast capacity of random wireless networks. We show that the total multicast capacity is Θ( � n log n · W √ k) when k = O ( n log n
Multicast capacity of wireless ad hoc networks
 IEEE/ACM Trans. Netw
, 2009
"... Abstract—We study the multicast capacity of largescale random extended multihop wireless networks, where a number of wireless nodes are randomly located in a square region with side length a = p n, by use of Poisson distribution with density 1. All nodes transmit at a constant power P, and the powe ..."
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Cited by 67 (22 self)
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Abstract—We study the multicast capacity of largescale random extended multihop wireless networks, where a number of wireless nodes are randomly located in a square region with side length a = p n, by use of Poisson distribution with density 1. All nodes transmit at a constant power P, and the power decays with attenuation exponent> 2. The data rate of a transmission is determined by the SINR as B log(1 + SINR), where B is the bandwidth. There are ns randomly and independently chosen multicast sessions. Each multicast session has k randomly chosen terminals. n We show that when k 1 and ns (log n) 2n 1=2+, the capacity that each multicast p session can achieve, with high proban bility, is at least c8 p, where 1, 2, and c8 are some special conn k stants and> 0 is any positive real number. We also show that for k = O( n), the perflow multicast capacity under Gaussian log n p n channel is at most O ( p) when we have at least ns = (log n) n k random multicast flows. Our result generalizes the unicast capacity for random networks using percolation theory.
The multicast capacity of large multihop wireless networks
 In Proc. of ACM MobiHoc ’07
, 2007
"... We consider wireless ad hoc networks with a large number of users. Subsets of users might be interested in identical information, and so we have a regime in which several multicast sessions may coexist. We first calculate an upperbound on the achievable transmission rate per multicast flow as a fun ..."
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Cited by 49 (2 self)
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We consider wireless ad hoc networks with a large number of users. Subsets of users might be interested in identical information, and so we have a regime in which several multicast sessions may coexist. We first calculate an upperbound on the achievable transmission rate per multicast flow as a function of the number of multicast sources in such a network. We then propose a simple combbased architecture for multicast routing which achieves the upper bound in an order sense under certain constraints. Compared to the approach of constructing a Steiner tree to decide multicast paths, our construction achieves the same orderoptimal results while requiring little location information and no computational overhead.
Capacity of large scale wireless networks under gaussian channel model
 in Mobicom08
, 2008
"... In this paper, we study the multicast capacity of a large scale random wireless network. We simply consider the extended multihop network, where a number of wireless nodes vi(1 ≤ i ≤ n) are randomly located in a square region with sidelength a = √ n, by use of Poisson distribution with density 1. ..."
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Cited by 49 (21 self)
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In this paper, we study the multicast capacity of a large scale random wireless network. We simply consider the extended multihop network, where a number of wireless nodes vi(1 ≤ i ≤ n) are randomly located in a square region with sidelength a = √ n, by use of Poisson distribution with density 1. All nodes transmit at constant power P, and the power decays along path, with attenuation exponent α> 2. The data rate of a transmission is determined by the SINR as B log(1 + SINR). There are ns randomly and independently chosen multicast sessions. Each multicast has k rann domly chosen terminals. We show that, when k ≤ θ1 (log n) 2α+6, and ns ≥ θ2n 1/2+β, the capacity that each multicast session can n achieve, with high probability, is at least c8 √ , where θ1, θ2, ns k and c8 are some special constants and β> 0 is any positive real number. Our result generalizes the unicast capacity [3] for random networks using percolation theory.
A Unifying Perspective on the Capacity of Wireless Ad Hoc
"... Abstract—We present the first unified modeling framework for the computation of the throughput capacity of random wireless ad hoc networks in which information is disseminated by means of unicast routing, multicast routing, broadcasting, or different forms of anycasting. We introduce (n, m, k)casti ..."
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Cited by 44 (14 self)
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Abstract—We present the first unified modeling framework for the computation of the throughput capacity of random wireless ad hoc networks in which information is disseminated by means of unicast routing, multicast routing, broadcasting, or different forms of anycasting. We introduce (n, m, k)casting as a generalization of all forms of onetoone, onetomany and manytomany information dissemination in wireless networks. In this context, n, m, and k denote the total number of nodes in the network, the number of destinations for each communication group, and the actual number of communicationgroup members that receive information (i.e., k ≤ m), respectively. We compute upper and lower bounds for the (n, m, k)cast throughput capacity in random wireless networks. When m = k = Θ(1), the resulting capacity equals the wellknown capacity result for multipair unicasting by Gupta and Kumar. We demonstrate that Θ(1 / √ mn log n) bits per second constitutes a tight bound for the capacity of multicasting (i.e., m = k < n) when m ≤ Θ (n/(log n)). We show that the multicast capacity of a wireless network equals its capacity for multipair unicasting when the number of destinations per multicast source is not a function of n. We also show that the multicast capacity of a random wireless ad hoc network is Θ (1/n), which is the broadcast capacity of the network, when m ≥ Θ(n / log n). Furthermore, we show that Θ ( √ m/(k √ n log n)), Θ(1/(k log n)) and Θ(1/n) bits per second constitutes a tight bound for the throughput capacity of multicasting (i.e., k < m < n) when Θ(1) ≤ m ≤ Θ (n / log n), k ≤ Θ (n / log n) ≤ m ≤ n and Θ (n / log n) ≤ k ≤ m ≤ n respectively.
Bounds for the capacity of wireless multihop networks imposed by topology and demand
 in Proc. ACM MobiHoc
, 2007
"... Existing work on the capacity of wireless networks predominantly considers homogeneous random networks with random work load. The most relevant bounds on the network capacity, e.g., take into account only the number of nodes and the area of the network. However, these bounds can significantly overes ..."
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Cited by 35 (0 self)
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Existing work on the capacity of wireless networks predominantly considers homogeneous random networks with random work load. The most relevant bounds on the network capacity, e.g., take into account only the number of nodes and the area of the network. However, these bounds can significantly overestimate the achievable capacity in real world situations where network topology or traffic patterns often deviate from these simplistic assumptions. To provide analytically tractable yet asymptotically tight approximations of network capacity we propose a novel spacebased approach. At the heart of our methodology lie simple functions which indicate the presence of active transmissions near any given location in the network and which constitute a tool well suited to untangle the interactions of simultaneous transmissions. We are able to provide capacity bounds which are tighter than the traditional ones and which involve topology and traffic patterns explicitly, e.g., through the length of Euclidean Minimum Spanning Tree, or through traffic demands between clusters of nodes. As an additional novelty our results cover unicast, multicast and broadcast and are asymptotically tight. Notably, our capacity bounds are simple enough to require only knowledge of node location, and there is no need for solving or optimizing multivariable equations in our approach.
ABSTRACT Multicast Capacity for Hybrid Wireless Networks
"... We study the multicast capacity of a random wireless network consisting of ordinary wireless nodes and base stations, known as a hybrid network. Assume that n ordinary wireless nodes are randomly deployed in a square region and all nodes have the uniform transmission range r and uniform interference ..."
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Cited by 33 (15 self)
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We study the multicast capacity of a random wireless network consisting of ordinary wireless nodes and base stations, known as a hybrid network. Assume that n ordinary wireless nodes are randomly deployed in a square region and all nodes have the uniform transmission range r and uniform interference range R> r. We further assume that each ordinary wireless node can transmit/receive at W bits/second over a common wireless channel. In addition, there are m additional base stations (neither source nodes nor receiver nodes) placed regularly in this square region and connected by a highbandwidth wired network. For each ordinary node v, we randomly pick k − 1 nodes from the other n − 1 ordinary nodes as the receivers of the multicast session rooted at node v. The aggregated multicast capacity is defined as the total data rate of all multicast sessions in this hybrid network. We derive asymptotic upper bounds and lower bounds on multicast capacity of the hybrid wireless networks. The total multicast capacity is O ( √ n √ · log n √ m · W) when k = O ( k n), k = log n k O(m), √ → ∞ and m = o ( m a2 r2); the total multicast capacity is Θ ( √ n √ log n · W √ k) when k = O ( n log n), k = Ω(m) and m
Multicast Capacity of Large Homogeneous Multihop Wireless Networks
"... Abstract—Most existing work on multicast capacity of large homogeneous networks is based on a simple model for wireless channel, namely the Protocol Model [12], [19], [22]. In this paper, we exploit a local capacity tool called arena which we introduced recently in order to render multicast accessib ..."
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Cited by 29 (0 self)
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Abstract—Most existing work on multicast capacity of large homogeneous networks is based on a simple model for wireless channel, namely the Protocol Model [12], [19], [22]. In this paper, we exploit a local capacity tool called arena which we introduced recently in order to render multicast accessible to analysis also under more realistic, and notably less pessimistic channel models. Through the present study we find three regimes of the multicast capacity (λm) for a homogeneous network depending on the ratio of terminals among the nodes of the network. We note that the upper bounds we establish under the more realistic channel assumptions are only � log(n) larger than the existing bounds. Further, we propose a multicast routing and time scheduling scheme to achieve the computed asymptotic bound over all channel models except the simple Protocol Model. To this end, we employ percolation theory among other analytical tools. Finally, we compute the multicast capacity of large mobile wireless networks. Comparing the result to the static case reveals that mobility increases the multicast capacity. However, the mobility gain decreases when increasing the number of terminals in a fixed size mobile network. I.
Delay and capacity tradeoff analysis for MotionCast
 IEEE/ACM Transactions on Networking
, 2012
"... Abstract—In this paper, we define multicast for an ad hoc network through nodes ’ mobility as MotionCast and study the delay and capacity tradeoffs for it. Assuming nodes move according to an independently and identically distributed (i.i.d.) pattern and each desires to send packets to distinctive ..."
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Cited by 27 (6 self)
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Abstract—In this paper, we define multicast for an ad hoc network through nodes ’ mobility as MotionCast and study the delay and capacity tradeoffs for it. Assuming nodes move according to an independently and identically distributed (i.i.d.) pattern and each desires to send packets to distinctive destinations, we compare the delay and capacity in two transmission protocols: one uses 2hop relay algorithm without redundancy; the other adopts the scheme of redundant packets transmissions to improve delay while at the expense of the capacity. In addition, we obtain the maximum capacity and the minimum delay under certain constraints. We find that the pernode delay and capacity for the 2hop algorithm without redundancy are and , respectively; for the 2hop algorithm with redundancy, they are and , respectively. The capacity of the 2hop relay algorithm without redundancy is better than the multicast capacity of static networks developed by Li [IEEE/ACM Trans. Netw., vol. 17, no. 3, pp. 950–961, Jun. 2009] as long as is strictly less than in an order sense, while when , mobility does not increase capacity anymore. The ratio between delay and capacity satisfies delay/rate for these two protocols, which are both smaller than that of directly extending the fundamental tradeoff for unicast established by Neely and Modiano [IEEE Trans. Inf. Theory, vol. 51, no. 6, pp. 1917–1937, Jun. 2005] to multicast, i.e., delay/rate . More importantly, we have proved that the fundamental delay–capacity tradeoff ratio for multicast is delay/rate , which would guide us to design better routing schemes for multicast. Index Terms—Capacity, delay, multicast, scaling law. I.
Motioncast: On the capacity and delay tradeoffs
 in Proc. ACM Mobihoc
, 2009
"... In this paper, we define multicast for ad hoc network through nodes ’ mobility as MotionCast, and study the capacity and delay tradeoffs for it. Assuming nodes move according to an independently and identically distributed (i.i.d.) pattern and each desires to send packets to k distinctive destinatio ..."
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Cited by 21 (12 self)
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In this paper, we define multicast for ad hoc network through nodes ’ mobility as MotionCast, and study the capacity and delay tradeoffs for it. Assuming nodes move according to an independently and identically distributed (i.i.d.) pattern and each desires to send packets to k distinctive destinations, we compare the capacity and delay in two transmission protocols: one uses 2hop relay algorithm without redundancy, the other adopts the scheme of redundant packets transmissions to improve delay while at the expense of the capacity. In addition, we obtain the maximum capacity and the minimum delay under certain constraints. We find that the pernode capacity and delay for 2hop algorithm without redundancy are Θ(1/k) and Θ(n log k), respectively; and for 2hop algorithm with redundancy they are Ω(1/(k √ n log k)) and Θ ( √ n log k), respectively. The capacity of the 2hop relay algorithm without redundancy is better than the multicast capacity of static networks developed in [3] as long as k is strictly less than n in an order sense; while when k = Θ(n), mobility does not increase capacity anymore. The ratio between delay and capacity satisfies delay/rate ≥ O(nk log k) for these two protocols, which is smaller than that of directly extending the fundamental tradeoff for unicast established in [1] to multicast, i.e., O(nk 2).