# Delay and Capacity Tradeoff Analysis for MotionCast - capacity of static networks developed in [3]...

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Delay and Capacity Tradeoff Analysis forMotionCast

Xinbing Wang, Wentao Huang, Shangxing Wang, Jinbei Zhang, and Chenhui Hu

AbstractIn this paper, we define multicast for ad hoc networkthrough nodes mobility as MotionCast, and study the delay andcapacity tradeoffs for it. Assuming nodes move according to anindependently and identically distributed (i.i.d.) pattern and eachdesires to send packets to k distinctive destinations, we comparethe delay and capacity in two transmission protocols: one uses2-hop relay algorithm without redundancy, the other adopts thescheme of redundant packets transmissions to improve delaywhile at the expense of the capacity. In addition, we obtainthe maximum capacity and the minimum delay under certainconstraints. We find that the per-node delay and capacity for2-hop algorithm without redundancy are (1/k) and (n log k),respectively; and for 2-hop algorithm with redundancy they are(1/k

n log k) and (

n log k), respectively. The capacity of

the 2-hop relay algorithm without redundancy is better than themulticast capacity of static networks developed in [3] as long ask is strictly less than n in an order sense; while when k = (n),mobility does not increase capacity anymore. The ratio betweendelay and capacity satisfies delay/rate O(nk log k) for thesetwo protocols, which are both smaller than that of directlyextending the fundamental tradeoff for unicast established in [1]to multicast, i.e., delay/rate O(nk2). More importantly, wehave proved that the fundamental delay-capacity tradeoff ratiofor multicast is delay/rate O(n log k), which would guide usto design better routing schemes for multicast.

Index TermsMulticast, Capacity, Delay, Scaling Law

I. INTRODUCTION

A mobile ad hoc network (MANET) consists of a collectionof wireless mobile nodes dynamically forming a temporarynetwork without the support of any network infrastructure orcentralized control. In these networks, nodes often operate notonly as sources, but also as relays, forwarding packets forother mobile nodes. With the fast progress of computing andwireless networking technologies, there are increasing interestsand use of MANETs. Examples where they may be employedare the establishment of connections among handheld devicesor between vehicles.

Multicast is a fundamental service for supporting informa-tion communication and collaborative task completion amonga group of users and enabling cluster-based system designin a distributed environment [2]. Different from in the wirednetworks, multicast in MANETs is faced with a more chal-lenging environment. In particular, one needs to deal withnode mobility and thus frequent and possible drastic topologychanges [1]. Numerous protocols have then been proposed for

The authors are with Department of Electric Engineering, Shanghai JiaoTong University, China.E-mail: {xwang8, wht, wsx, zjb, hch}@sjtu.edu.cn

The early version of this paper is appeared in the Proceedings of ACMMobiHoc 2009 [21].

multicast in MANETs. They include traditional tree- or mesh-based protocols [3, 4, 5, 6], stateless protocols [7, 8], flooding-based protocols [9], location-based protocols [10] and hybridprotocols [11]. Some of them have already pointed out thatbecause links can be shared by several destinations, multicastis beneficial to improve performance comparing to multipleunicast.

However, the feasible performance gains, in terms of boththroughput capacity and delay, that can be achieved by exploit-ing multicast, as well as the resulting scaling laws in a networkwith increasing number of nodes have not been investigatedso far. In this paper, we bridge the theoretical analysis offundamental scaling laws in multicast mobile ad hoc networkswith the insights already gained through practical protocoldevelopment. By so doing, we provide a theoretical foundationto the design of intelligent communication schemes whichexploit multicast, analytically showing the potential of suchschemes in terms of capacity delay tradeoffs.

The theoretical analysis of scaling laws in wireless networksis initiated by the seminal work of Gupta and Kumar [4].Several interesting studies have later emerged aiming at estab-lishing the fundamental scaling laws for networks with multi-cast traffic. Li et al. [3][22][23] study the capacity of a staticrandom wireless ad hoc network for multicast where each nodesends packets to k 1 destinations. They show that the per-node multicast capacity is ( 1

n lognk) when k = O( nlogn );

and is ( 1n ) when k = (n

logn ). Their results generalizeprevious capacity bounds on unicast [4] and broadcast [5].Under a more general Guassian channel model, multicastcapacity is investigated in [6] using percolation theory. Jacquetet al. [7] consider multicast capacity by accounting the ratio ofthe total number of hops for multicast and the average numberof hops for unicast. Shakkottai et al. [8] propose a comb-basedarchitecture for multicast routing which achieves the upperbound for capacity in an order sense.

In contrast to the above discussed static networks, Goss-glauser and Tse [9] for the first time have shown that a constantunicast per-node capacity can be achieved in mobile ad hocnetworks by exploiting the store-carry-forward communicationparadigm, i.e., by allowing nodes to store the packets andphysically carry them while moving around the network.Although this communication scheme incurs a tremendousaverage delay of (n) [1], [10], it has laid the foundationof an entire new area of research, usually referred to as delaytolerant or disruption tolerant networks (DTNs), which hasrecently attracted a lot of attention. A typical DTN consistsof a set of fixed or mobile nodes, and is characterized by

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intermittent connectivity and frequent network partitioning,such that node mobility is essential to ensure end-to-endcommunication. Many interesting applications of DTN havebeen already envisioned and experimented upon, such asvehicular networks based on WiFi [13-16], networks based onhuman mobility [17], disaster-relief networks [18] and Internetaccess to remote villages [19].

The asymptotic capacity delay tradeoff in MANETs ex-ploiting store-carry-forward schemes has attracted significantattentions and is studied by many authors under variousmobility models. The mostly studied model is arguably thei.i.d. mobility model, where all nodes are reshuffled in anew time slot, due to its mathematical tractability. Withthis assumption, Neely and Modiano [1] present a strategyutilizing redundant packets transmissions along multiple pathsto reduce delay at the cost of capacity. They establish thenecessary tradeoff of delay/capacity O(n), and proposeschemes to achieve (1),(1/

n) and (1/(n log n)) per-

node capacity, when the delay constraint is (n),(n)

and (log n), respectively. In [16], Toumpis and Goldsimthconstruct a better scheme that can achieve a per-node capacityof (n(d1)/2/ log5/2 n) under fading channels when thedelay is bounded by O(nd). Lin and Shroff [2] later studythe fundamental capacity-delay tradeoff and identify the lim-iting factors of the existing scheduling schemes in MANETs.Recently, Ying et al. [15] propose joint coding-schedulingalgorithms to improve capacity-delay tradeoffs while Garettoand Leonardi [A20] show that under a restricted i.i.d. mobilitymodel, it is possible to exploit node heterogeneity to achieveboth constant capacity and constant delay.

To the best of our knowledge, this is the first work tostudy capacity and delay tadeoffs in MANETs with multicasttraffics. Because a key feature of multicast in MANETs isthat packets can be delivered via nodes mobility, we refer itas MotionCast. Intuitively, delay and capacity tradeoffs stillexist for MotionCast, but are more complicated than unicastscenarios. Since packets can be delivered through the mobilityof relay nodes, a higher per-node multicast capacity than instatic networks is expected. However, the scheduling designbecomes more difficult because of the permanent change of thenetwork topology as well as the fact that multiple destinationsfor a packet will imply a larger delay. Hence, some challengingissues raised naturally in this context are:

What is the maximum per-node MotionCast capacity? What is the delay for maximal capacity achieving

schemes and and what is the minimum possible delay? What is the delay and capacity tradeoff for MotionCast?

Answering these questions would provide helpful fundamen-tal insights on the understanding and design of large scalemulticast MANETs.

In this paper, we study the scaling laws in a cell partitionedMANET with multicast traffic. To start with, we proposea 2-hop relay algorithm without redundancy. This algorithmis a generalized version of the algorithm presented in [1],and corresponds to a decoupled queuing model. Because kdestinations are associated with a source, the delay for apacket is defined as the total time needed to deliver it toall destinations. For a specific packet, we first divide nodes

other than the source into relays and destinations (referred toas non-cooperative mode). In this case, the packet may becarried to the destinations either through the relays or viathe source, but will not be passed from one destination toanother. Once a packet is sent to a relay, the relay will be incharge of delivering it to all its destinations. Otherwise, if thesource encounters a destination before a relay, it will take fullresponsibility of the rest multicast session. The MotionCastdelay and capacity are calculated under this model.

Then, we loose the constraints of our initial model bypermitting information dissemination among destinations (co-operative mode). In this scheme, we do not discriminatedestinations against the remnant nodes except the source. Wedefine the first node that a source me