1536 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 17, NO. 5, OCTOBER 2009 Scalability and Performance Evaluation of Hierarchical Hybrid Wireless Networksweb.stanford.edu/class/ee360/previous/suppRead/read1/scalability_zhao.pdf ·

1536 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 17, NO. 5, OCTOBER 2009

Scalability and Performance Evaluation ofHierarchical Hybrid Wireless Networks

Suli Zhao, Member, IEEE, and Dipankar Raychaudhuri, Fellow, IEEE

Abstract—This paper considers the problem of scaling ad hocwireless networks now being applied to urban mesh and sensornetwork scenarios. Previous results have shown that the inherentscaling problems of a multihop “flat” ad hoc wireless network canbe improved by a “hybrid network” with an appropriate propor-tion of radio nodes with wired network connections. In this work,we generalize the system model to a hierarchical hybrid wirelessnetwork with three tiers of radio nodes: low-power end-user mo-bile nodes (MNs) at the lowest tier, higher power radio forwardingnodes (FNs) that support multihop routing at intermediate level,and wired access points (APs) at the highest level. Scalability prop-erties of the proposed three-tier hierarchical hybrid wireless net-work are analyzed, leading to an identification of the proportionof FNs and APs as well as transmission range required for linearincrease in end-user throughput. In particular, it is shown analyt-ically that in a three-tier hierarchical network with APs,FNs, and MNs, the low-tier capacity increases linearly with

, and the high-tier capacity increases linearly with when� �� and � �� . This analytical result is vali-

dated via ns-2 simulations for an example dense network scenario,and the model is used to study scaling behavior and performanceas a function of key parameters such as AP and FN node densitiesfor different traffic patterns and bandwidth allocation at each tierof the network.

Index Terms—Ad hoc network, hierarchical wireless network,hybrid network, mesh network, multihop routing, performanceanalysis, scalability, sensor network, simulation models.

I. INTRODUCTION

T HIS paper describes a self-organizing hierarchical hybridwireless network designed to provide significant improve-

ments in capacity scaling and performance relative to conven-tional “flat” ad hoc networking approaches. The proposed hier-archical architecture is motivated by the scalability bottleneckthat arises in flat ad hoc networks. Conventional mobile ad hocnetwork (MANET) architectures that use shared medium accesscontrol (MAC) protocols along with multihop routing, such as

Manuscript received March 26, 2007; revised December 17, 2007 andSeptember 23, 2008; approved by IEEE/ACM TRANSACTIONS ON NETWORKING

Editor D. M. Chiu. First published June 30, 2009; current version publishedOctober 14, 2009. This work was supported in part by NJCST Grant03-2042-007-12 and NSF NRT Grant ANI-0335244.

S. Zhao was with Rutgers University, New Brunswick, NJ 08901 USA. She isnow with Qualcomm Inc., San Diego, CA 92121 USA (e-mail: [email protected]).

D. Raychaudhuri is with the Wireless Information Laboratory (WINLAB),Electrical and Computer Engineering Department, Rutgers University, NewBrunswick, NJ 08901 USA (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TNET.2008.2011987

Fig. 1. Scaling issues in flat ad hoc wireless networks with different trafficmodels. (a) Flat ad hoc network with uniform peer-to-peer traffic model. (b) Flatad hoc network with majority of traffic flows to/from the Internet.

dynamic source routing (DSR) [1] or ad hoc on-demand dis-tance vector (AODV) [2], suffer from decreasing throughputper node as node density increases. In particular, Gupta andKumar’s well-known theoretical result [3] for multihop wire-less networks [illustrated in Fig. 1(a)] indicates that achievableend-to-end per-node throughput decreases in proportion to thesquare root of the number of radio devices.

When considering scalability, it is also important to note thatmost applications involve traffic flows to and from the Internetin addition to peer-to-peer communication between radio nodes.The scaling problem in flat networks becomes even more diffi-cult due to traffic bottlenecks around gateway nodes when a sig-nificant fraction of packets have to be routed to a correspondenthost within the wired Internet, as shown in Fig. 1(b). This kindof scenario requires effective integration of wired access points(APs) with the ad hoc wireless network.

The above considerations motivate a network with more thanone tier of ad hoc radio nodes, in which lower tiers aggregatetraffic up to intermediate radio relays, while continuing to userobust ad hoc self-organization and routing protocols as in flatad hoc networks. Several early papers have appeared on MACand routing protocols for hierarchical radio networks [4]–[6].The results reported in these papers tend to indicate that scal-ability can be improved by introducing hierarchical structuresin radio ad hoc networks. In particular, in [4], Gerla shows thatthe concept of MAC-layer “clustering” can improve system ca-pacity and performance by making it possible to introduce effi-cient channel access procedures and localize control in responseto network state changes.

Another approach is to introduce some proportion of wiredor wireless “infrastructure” nodes that serve to organize the net-work into a hierarchy with “shortcut” paths for traffic that wouldhave required larger numbers of hops in a flat ad hoc network.Fig. 2(a) depicts a “hybrid network” with two hierarchical tiers(i.e., radio ad hoc nodes and wired APs). In [7], Liu and Towsley

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ZHAO AND RAYCHAUDHURI: SCALABILITY AND PERFORMANCE EVALUATION OF HIERARCHICAL HYBRID WIRELESS NETWORKS 1537

Fig. 2. (a) Two-tier hybrid network. (b) K-tier hierarchical hybrid network.

proved that linear scaling of throughput can be approached in atwo-tier hybrid network as long as the number of access pointsgrows asymptotically faster than the square root of the numberof radio nodes. In addition, results of [8]–[11] have also shownthat adding infrastructure nodes to ad hoc networks can effec-tively reduce the average number of end-to-end hops and ulti-mately help achieve better performance than flat networks. Allthese results demonstrate that ad hoc mesh networks benefitfrom a hierarchical “hybrid” wired/wireless architecture both interms of scalability and effective integration with the Internet.However, we note that with this two-tier architecture, wired in-frastructure cost can be high, especially for dense usage sce-narios.

Based on the above considerations, we further generalize thetwo-tier hierarchy of the “hybrid network” in Fig. 2(a) to a

-level hierarchy with tiers of radio nodes and a top tierof APs, as shown in Fig. 2(b). Multiple radio tiers can providefurther performance improvements by facilitating shorter routesbetween distant nodes, improving MAC efficiency via traffic ag-gregation and less stringent transmit power constraints, whilepotentially reducing the required number of wired APs relativeto the two-tier hybrid network case. A key technology enablerfor the generalized hierarchical wireless network is the so-called“radio forwarding node” or “radio router” that has two or moreradio interfaces to permit it to handle packets going to or fromone layer of the hierarchy to another. It is also observed thateach radio tier can avoid interfering with the layers above andbelow by orthogonal assignment of frequencies if so desired.

Note that the proposed architecture does not have a stricthierarchy in the sense that all radio nodes are allowed to ac-cess those that are more than one tier above them; for example,a low-tier radio node can directly connect to a nearby accesspoint when available. Also, (with the exception of the lowesttier) radio nodes at a given level of hierarchy can communicatevia paths on the same tier or can go up and then down by oneor more tiers, whichever is considered to be preferable by therouting algorithm. The restriction on the lowest-tier nodes is in-tended to avoid the need for multihop routing functionality atend-user radio nodes, which may be expected to have both pro-cessing and power constraints. Observe that lowest-tier nodesare allowed to associate with more than one higher tier node atthe same time (i.e., “dual homing” is permitted). Radio nodesat intermediate tiers may, in general, have more than one radioin order to handle different bit-rate, coverage, and access con-trol needs at each level of the hierarchy. For example, a hier-

archical system with three tiers may have IEEE 802.11b [12]radios at the lowest tier, dual 802.11b and 3G [13] cellular ra-dios at the intermediate tier, and 3G base stations at the toplayer to create an integrated local area/wide area hybrid networksolution. This “network of wireless networks” architecture notonly has the potential to provide scalability and improve per-formance, but is also a very natural framework for integratingemerging ad hoc wireless devices with existing network infra-structure. The goal is to design the system in such a way that adhoc network advantages of dynamic self-organization and lowrouting overhead/complexity are retained at the lower tiers ofthe system while providing the capacity and scaling advantagesof a hierarchical hybrid network structure.

The key protocol design and evaluation problems that arise inconjunction with the proposed architecture include MAC, dis-covery procedures, and multihop ad hoc routing. In additionto the standard IEEE 802.11, which may be used in ad hocmode to build a hierarchical network, MAC enhancements, suchas “IRMA” proposed in [14], can be used to improve perfor-mance via scheduling approaches that reduce MAC contention.Discovery procedures, such as “BEAD” proposed in [15], canbe used by radio nodes to identify and self-organize themselvesinto a network topology that considers not only connectivity,but also throughput, delay, and energy requirements or con-straints. For ad hoc routing, algorithms that take into account thehierarchical nature, aggregated traffic, and QoS requirements,as well as enhanced routing metrics, such as the cross-layer“PARMA” proposed in [16], may also be appropriate in a hi-erarchical network.

In this paper, we focus on the system concept, capacityscaling, and network performance of the proposed hierarchicalwireless network. We make three contributions. First, we pro-pose the concept of a general multitier hierarchical wirelessnetwork and outline its protocol architecture. Second, we provethe asymptotic throughput capacity of a three-tier hierarchicalnetwork, refine the linear scaling regime by providing boththe upper and lower bounds, and identify the conditions ontransmission range and node density for scalability to bemaintained. Finally, we verify the scaling properties of thethree-tier network with detailed system simulations (for densenetwork scenarios) and relate the experimental results obtainedwith the analytical asymptotic results. The simulation modelis implemented with realistic MAC and routing protocols andis also useful for providing insight into the choice of systemparameters, such as the ratio of different types of nodes, orthe channel bandwidth allocation required for each tier of thenetwork.

The system concept and protocol architecture is presentedin Section II. In Section III, a general analytical model for theasymptotic capacity and scaling properties of the proposedthree-tier network are developed. We also define and studyrandom aggregate networks in this part. In Section IV, theachievable throughput and other end-user performance, as wellas the scaling properties of an 802.11-based three-tier wirelessnetwork, are evaluated using ns-2 [17] simulation models fordense network scenarios. The impact of the relative proportionsof different types of nodes and the relative bandwidth allocationat high and low tiers on the achievable throughput are also


Fig. 3. Proposed hierarchical hybrid wireless network with three tiers.

investigated in this section. Section V summarizes the mainconclusions.

II. SYSTEM MODEL OVERVIEW

As shown in Fig. 3, a typical realization of the proposedsystem has three tiers of radio nodes: low-power end-user mo-bile nodes (MNs) at the lowest tier, higher powered radio for-warding nodes (FNs) that support multihop routing at the secondlevel, and wired APs at the third and highest level. The APsand FNs use a self-organizing discovery protocol to form a mul-tihop routed wireless infrastructure network. MNs in this systemsimply connect to the nearest available (i.e., strongest signal) APor FN in order to conserve power and are thus not required tocarry any intermediate multihop routed traffic. This architectureis applicable to a number of emerging ad hoc networking sce-narios including hybrid cellular/ad hoc networks, urban meshnetworks, home wireless networks, and large-scale sensor nets.In each of these scenarios, the introduction of an FN as an in-termediate radio router helps to scale network throughput andreduce infrastructure deployment cost.

It is observed that the proposed hierarchical architectureis radio independent in the sense that different radio accesstechnologies can be used for each tier depending on the spe-cific scenario being addressed. For example, in a wide-area“hotspot” data service application, the low-tier nodes can useIEEE 802.11b WLAN radios, while the FNs and APs (or basestations) can use a broadband wide-area radio standard such asWCDMA/3G [13] or WiMax/IEEE 802.16 [18]. Alternatively,a sensor net scenario could use a low-power access protocolsuch as Zigbee [19] for access from MNs and 802.11b for linksbetween FNs and APs. Of course, an all-802.11 solution is alsopossible for application scenarios such as mesh WLANs forcommunity networking. Note that when the lower and uppertiers of the hierarchical network use different radio technolo-gies, the FNs must be equipped with multiple radio interfacesand be able to forward packets between them.

Each of the network entities in the proposed system are de-fined in further detail.

• Mobile node (MN) is a mobile end-user device (such as apersonal digital assistant or a sensor) at the lowest tier ofthe network. The MN attaches itself to one or more nodesat the higher tiers of the network in order to obtain serviceusing a discovery protocol. For instance, the MN may use

a single 802.11a, b, or g radio operating in ad hoc mode tocommunicate with the point(s) of attachment. As an end-user node, the MN is not required to route multihop trafficfrom other nodes, although it does participate in the routingprotocol used by the network as a whole. It is noted that asa battery-operated end-user device, the MN will typicallyhave energy constraints.

• Forwarding node (FN) is a fixed or mobile intermediateradio relay node capable of routing multihop traffic to andfrom all three tiers of the network’s hierarchy. As an in-termediate node without traffic of its own, the FN is onlyresponsible for multihop routing of transit packets. An FNwith one 802.11 radio interface uses the same radio to con-nect in ad hoc mode to MNs, other FNs, and the highertier APs defined below. Optionally, an FN may have tworadio cards, one for FN–MN transmissions and the otherfor intra-FN and FN–AP traffic flows (typically carried ondifferent frequencies). Specific nodes that an FN will con-nect to at each of the three tiers are identified using a dis-covery protocol that includes a distributed topology opti-mization algorithm. The FN is typically a compact radiodevice that can be plugged into an electrical outlet, but incertain scenarios, may also be a battery-powered mobiledevice. Thus, the FN is also energy-constrained, but thecost of power is typically assumed to be an order of mag-nitude lower than that of the defined MN.

• Access point (AP) is a fixed radio access node at thehighest tier of the network, with both a radio interface(e.g., 802.11) and a wired interface to the Internet. The APis capable of connecting to any lower tier FN or AP withinrange, but unlike 802.11 typical WLAN deployments, itoperates in ad hoc mode for each such radio link. The APalso participates in discovery and routing protocols used inthe lower tier FNs and MNs and is responsible for routingtraffic within the ad hoc network as well as to and fromthe Internet. Logically, the AP tier is no different from theFN tier when routing internal ad hoc network traffic—thewired links between APs are reflected in (generally) lowerpath metrics. Since the AP is a wired node, it is usuallyassociated with an electrical outlet, and energy cost is thusconsidered negligible.

Fig. 4 depicts the high-level protocol architecture of an802.11-based hierarchical network. The MAC layer in eachof the radio devices provides the capability of discoveringother ad hoc nodes as well as resolving contention betweenpackets to be transmitted on the channel. Clearly, the physical(PHY) and MAC layers are radio-specific: for an all-802.11solution, the current ad hoc-mode beaconing procedure in theMAC layer needs to be modified to identify the type of node(MN, FN, or AP) and its transmit power level so that othernodes can execute a suitable distributed discovery protocol todetermine network connectivity. The details of the enhancedMAC protocol and the related discovery protocol were reportedin [20]. As shown in the protocol diagram, a radio-independentad hoc routing protocol runs between the MN, FN, and APnodes, with the AP providing a gateway between the wired IPnetwork and the ad hoc wireless subnet. Note that MNs in thissystem implement a simplified client version of the routing


Fig. 4. Protocol architecture of proposed three-tier 802.11-based network.

protocol in view of the fact that they typically connect to onlya single FN or AP, while FNs and APs are required to maintaincomplete multihop routing tables.

III. CAPACITY OF THREE-TIER HIERARCHICAL HYBRID

WIRELESS NETWORKS

In this section, we develop a general analytical model for theasymptotic capacity and scaling properties of three-tier hierar-chical hybrid wireless networks. First, we briefly review the rel-evant notations and the related work.

A. Background and Notation

1) Interference Model: In this work, we use the protocolinterference model [3]. The interference model describes thesuccessful reception of a transmission over one hop. Let thecommon transmission range be . A transmission from nodeis successfully received by node if:

• the distance between and is no more than , i.e.,;

• for every other node simultaneously transmitting overthe same channel, ;

where defines the size of the guard zone.Suppose node is transmitting to node and

. If there is another node that is transmitting at the sametime and the distance satisfies , then there is acollision at node , and obtains no information about thetransmitted packets.

Nodes can be organized into certain type of groups, e.g., clus-ters. Similar to [3], we define that two groups are interferingneighbors if there is a node in one group that is within a dis-tance of of a node in the other group. Therefore, in theprotocol interference model, if two groups are not interferingneighbors, a transmission from one group does not collide witha transmission from the other group; i.e., simultaneous trans-missions from these two groups are allowed.

2) Time Scheduling: In our wireless network model, time isdivided into slots of fixed durations. A node is scheduled to senddata in each time slot on a wireless channel. A slotted packetscheduling is used to eliminate transmission collisions and in-terference for nodes in the interfering neighborhood.

3) Feasible Throughput: A throughput of bits persecond (bps) for each source node is feasible if there exists aspatial and temporal scheme of transmissions such that eachsource node can transmit bps on average to its destinationnode.

The throughput capacity of a wireless network, , is oforder bps if there are deterministic constantsand such that

is feasible

is feasible

The aggregate throughput capacity of a wireless network, ,is , in which each source node achieves throughput of

.

B. Related Work

In [3], Gupta and Kumar obtain the capacity of multihop wire-less networks with identical randomly located nodes, each ca-pable of transmitting at bps, using a fixed range and undera noninterference protocol, which is bps pernode for randomly chosen destinations.

Capacity scaling laws for two-tier hybrid wireless networkshave been studied in [7]–[11]. Suppose a hybrid network con-sists of ad hoc nodes and base stations (BSs) or APs. In [7],Liu and Towsley have proved that, for the deterministic routingstrategy with regular placement of BSs for the protocol model,the aggregate throughput capacity grows linearly with when

and all bandwidth is allocated to the traffic thatgoes through the infrastructure.

When ad hoc nodes and APs are randomly distributed, athroughput capacity of can be achieved, providedthat scales linearly with [8]. Also, the transmission rangeis chosen to ensure an optimal routing scheme in which ad hocnodes communicate directly with infrastructure nodes.

The results on the capacity of hybrid networks obtained in [9]are similar to those reported in [7], but a spatial-diversity schemeis used to achieve the maximum throughput that is fairly sharedamong the ad hoc nodes.

Employing power control allows better scaling of capacity inwireless networks. In [21], the authors show that a rate isachievable in flat ad hoc networks of randomly located nodes.In [10], it is shown that a throughput to some nodescan be guaranteed in a hybrid network.

Linear scaling of capacity can be achieved whenin a hybrid network with ar-

bitrarily placed infrastructure nodes [11]. In this work, linearityis achieved by letting ad hoc nodes communicate directly viainfrastructure nodes, thus requiring power control.


Fig. 5. Analytical system model.

In addition to power control, capacity gain can also beachieved from node mobility [22] or node cooperation andMIMO communication [23].

In order to facilitate system evaluations with practical modelsand realistic protocols, in our analysis, we employ bandwidthpartitioning and consider the Internet traffic and local trafficseparately. This is because bandwidth partitioning can be im-plemented with the multichannel capability provided by currentradio devices, and different traffic types have different scalingbehaviors. At the highest tier, multihop wireless transmissionsare allowed between APs and FNs, which does not impose re-strictions on transmission power as in [8] and [11]. In particular,we use a common power level with regularly placed APs. Gen-erally, the analytical model adopted here is closely related topractical systems. Note that the approach of bandwidth parti-tioning can also be applied to the -tier hierarchicalnetwork that is introduced in Section I.

C. Analytical Model

We suppose there are APs, FNs, and MNsin a disk of unit area on the plane. MNs are in-

dependently and uniformly distributed, while APs and FNs areplaced in a regular pattern. Through the ad hoc network dis-covery procedure, each MN is associated with the nearest FNvia direct transmission (assuming there is always at least one FNwithin its transmission range), and each FN is associated withits nearest AP via one-hop or multihop transmissions. After as-sociations, all nodes in the disk form nonoverlapping clusters,each of which consists of one AP, its associated FNs, and theirassociated MNs, as shown in Fig. 3. Also, each FN and its as-sociated MNs form a subcluster.

The wireless channel is divided into two subchannels: Oneis carried on frequency , and the other on , with band-width and , respectively. is used for transmissions toand from MNs (denoted low-tier transmissions); is used fortransmissions not involving MNs (denoted high-tier transmis-sions). Each FN is equipped with two radios, and can thus par-ticipate in both low- and high-tier transmissions using differentradios. All nodes working on one frequency have a commontransmission range, but the range could be different from trans-missions on the other frequency. Let the transmission range on

and be and , respectively, and the guard zone sizebe and , respectively. The network model of a planarlayout is shown in Fig. 5.

In the three-tier hierarchical network, MNs are at the lowesttier and perform end-user functions such as mobile computingor sensing/actuation. MNs do not forward packets for others,

but send out and receive their own packets. FNs do not have anytraffic needs of their own, but forward packets for other nodes.APs are interconnected through an infrastructure network of in-finite capacity.

1) Traffic Pattern: As discussed before, we need to considerboth traffic to/from the Internet and peer-to-peer traffic. Accord-ingly, we define the Internet traffic as traffic between MNs andAPs, and the local traffic as traffic between MNs.

2) Routing: We assume that the Internet traffic must gothrough the FN tier, even if the MN is only one hop away fromthe AP tier. For the local traffic, depending on the relativelocations of the communicating pairs, it is either intraclusteror intercluster traffic. It is intracluster traffic if the sourceand destination MNs are in the same cluster; otherwise, it isintercluster traffic. We assume that intracluster traffic is relayedby the FNs of the same cluster via ad hoc mode transmissions;while intercluster traffic always goes through the infrastructureusing a mix of multihop wireless links and wired infrastructurepaths.

3) Capacity Separation: Since low-tier and high-tier trans-missions use different subchannels, and there is no interferencebetween them, we can look at capacity contributed by transmis-sions at these two tiers separately (denoted low-tier capacity andhigh-tier capacity, respectively). Fig. 5 shows a subcluster andthe low-tier transmissions in it. High-tier transmissions are illus-trated in Fig. 6, where Fig. 6(a) depicts a network cluster havingthe Internet traffic and intercluster local traffic at the high tier,and Fig. 6(b) displays a network cluster with the intraclusterlocal traffic at the high tier. Before the capacity analysis, wemodel the random aggregate network for deriving the aggregatethroughput capacity of the network in Fig. 6(a) and the requiredtransmission range.

D. Random Aggregate Networks: Randomly Located Nodesand Aggregate Traffic Pattern

In a random aggregate network scenario, source nodes areindependently and uniformly distributed in a disk of unit areaon the plane. We randomly place a node in the disk as the des-tination. Thus, all source nodes have a common destination,to which each of them wishes to transmit packets at rate bps(whereas the destination is randomly chosen for each sourcenode in the “Random Networks” scenario of [3]). We furtherassume that all nodes employ the same transmission range andare capable of transmitting at bps.

Theorem 1: In the protocol interference model, a random ag-gregate network of source nodes and one destination node ona planar disk has the following properties.

• The order of the throughput capacity is bps,and the order of the aggregate throughput capacity is

bps.• The transmission range is chosen as

.• For regular networks, the optimal transmission range can

be reduced as long as is satisfied.Proof: We provide the proof in the Appendix.

Theorem 1 will be applied to the high-tier network clustershaving Internet traffic or intercluster local traffic, which are pre-sented in Fig. 6(a).


Fig. 6. High-tier transmissions in a cluster. (a) The Internet traffic and intercluster local traffic. (b) The intracluster local traffic.

E. Capacity of Three-Tier Hierarchical Hybrid Networks

1) Low-Tier Capacity and Transmission Range: The disk isdivided into subclusters, each of which consists of one FNand its associated MNs. All low-tier transmissions have to gothrough the associated FNs, and each FN can only handle dataat the rate of bps at any time. Therefore, the per subclusterthroughput capacity, , is upper-bounded by . For the lowerbound, since each MN is one hop away from its associated FN,there is a schedule for each MN to communicate with its asso-ciated FN in a round-robin fashion, resulting in a throughput of

. Hence, it follows .There may exist interference among subclusters. Note that in

the protocol interference model, if two subclusters are not inter-fering neighbors, transmissions in one subcluster do not inter-fere with transmissions in the other subcluster.

The regular placement of FNs results in a hexagon tessel-lation, with each hexagon corresponding to the area of a sub-cluster. We can prove the following lemma (see [24] for theproof).

Lemma 1: Each subcluster (or hexagon) has no more thaninterfering neighbors, and is a constant that depends only on

when the transmission range satisfies

(1)

According to the vertex coloring result of graph theory [25],there is a transmission schedule such that each subcluster getsone time slot to transmit in every time slots. Therefore,the low-tier capacity, denoted , is given as

Suppose each MN carries traffic of rate bps on average;then

(2)

It is observed that the low-tier aggregate throughput ca-pacity increases linearly with the number of FNs when

. Traffic carried by MNs instead of their exactnumber counts in (2), which implies that the system’s scalingbehavior does not depend on the number of ad hoc nodes. This

is a great improvement upon flat and two-tier wireless net-works. It also suggests that we can increase either the numberof FNs or the bandwidth allocated to low-tier transmissions toaccommodate the traffic of the network.

2) High-Tier Capacity and Linear Scaling Regime: We as-sume that the bandwidth allocated to the Internet traffic andthe local traffic carried by high-tier multihop transmissions (de-noted high-tier Internet traffic and high-tier local traffic) are

and , respectively, and .a) High-tier Internet traffic: The results of random ag-

gregate networks, given in Theorem 1, can be applied to eachcluster carrying the high-tier Internet traffic. Therefore, the per-cluster throughput capacity contributed by the high-tier Internettraffic is given by .

There are clusters in the hierarchical network. Notice thatthe regular placement of APs results in a hexagon tessellation,with each hexagon corresponding to the area of a cluster. Byapplying Lemma 1, the number of interfering neighbors of eachcluster is bounded by a constant that depends only on if thehigh-tier transmission range satisfies

(3)

Thus, there is a scheduling such that each cluster gets one slot totransmit in every constant number of time slots. Therefore, theaggregate throughput capacity contributed by high-tier Internettraffic is given by

(4)

According to Theorem 1, the high-tier transmission range forregularly placed FNs is chosen as . Combinedwith (3), it gives

(5)

which is the upper bound of the scaling regime for the high-tiercapacity to scale linearly with the number of wired APs.

If FNs are randomly distributed, the transmission range hasto be chosen as , which leads tothe upper bound of for randomly placedFNs. The upper bound implies that further investments in theinfrastructure do not lead to improvement in capacity scaling.


b) High-tier local traffic: Suppose the bandwidth allocatedto high-tier intercluster and intracluster traffic are and

respectively, and .We treat these two types of high-tier local traffic separately.

Intercluster Local Traffic:Intercluster traffic is assumed to always go through the infra-

structure. In particular, the intercluster traffic enters the infra-structure at the source FN’s associated AP and leaves it at thedestination FN’s associated AP. Note that this may not be theoptimal route. For instance, if the source and destination FNsare neighbors, it may be preferable to have direct FN–FN con-nections rather than using the infrastructure. However, under theuniform traffic assumption in which destination nodes are uni-formly chosen within the disk, the fraction of such local con-nections (i.e., sources and destinations are close neighbors) goesto zero when the number of FNs goes to infinity. Therefore, inthis case, the adverse effect of the routing protocol is negligibleasymptotically.

According to our routing assumption, in the wireless network,one intercluster communication can be decomposed into twoparts: One is from FN to AP in the source cluster, and the otheris from AP to FN in the destination cluster. Only one part iscounted in the throughput capacity.

For each cluster, we can apply Theorem 1 and obtain the ag-gregate throughput capacity contributed by high-tier interclusterlocal traffic as follows:

(6)

when is chosen as in (3).Intracluster Local Traffic:Suppose APs do not participate in transferring intracluster

local traffic. There are clusters in the network, andFNs in each cluster. According to the scaling property ofwith respect to , there are two cases: and

. We apply the results of [7] to the analysisbelow.

First, we consider the case of . From [7],the aggregate capacity contributed by high-tier intracluster localtraffic is given as

Taking into account (6) and [7, Corollary 1], the aggregatethroughput capacity contributed by all high-tier local traffic ismaximized when . The achieved capacityis given as

(7)

when . Hence, in this case it is more beneficialto assign bandwidth to intracluster traffic.

In the second case of , the aggregatethroughput capacity contributed by high-tier intracluster localtraffic is

When , the aggregate throughput ca-pacity contributed by all high-tier local traffic is maximized [7,Corollary 2], and the achieved capacity is

(8)

when . This shows that it is more effective toallocate bandwidth to carry intercluster traffic in this case, andthe achieved capacity increases linearly with .

c) Capacity of high-tier transmissions: From (4), (5), (7),and (8), the high-tier capacity can be achieved.

For

(9)

For and

(10)

These results are obtained when is chosen as in (3).Equation (10) reveals that the capacity improvement achieved

by adding APs can be significant if grows asymptoticallyfaster than but slower than and the achieved capacityhas the linear relationship with the number of APs. This capacityis shared among the nodes whose packets are routed through theinfrastructure as determined by the defined routing scheme.

F. Discussions

It is shown that in a three-tier hierarchical hybrid wirelessnetwork of APs, FNs, and MNs, the low-tier ca-pacity increases linearly with when the low-tier transmissionrange satisfies . Also, the high-tier capacityincreases linearly with in the scaling regime that satisfies

and ,when the high-tier transmis-sion range satisfies . In this identified linearscaling regime, the capacity improvement achieved by addingAPs can be significant.

In the three-tier network, APs do not need to cover the wholearea; thus, the network coverage is improved. Linear scaling ofthroughput capacity can be achieved with less number of APsrelative to the two-tier network, and the system’s scaling be-havior does not depend on the number of ad hoc nodes. Sincethe investment and recurrent wired access cost for APs or BSs issignificantly higher than that for FNs, system costs can be sig-nificantly reduced with the three-tier approach, especially fordense networks.

The above asymptotic capacity and scaling regimes are ob-tained by deploying a specific system model and the determin-istic routing approach, similar to the two-tier model in [7]. Otherstudies on two-tier hybrid networks use different system modelsand routing schemes, which lead to different asymptotic boundsfor different scaling regimes [8]–[11]. It can be shown that thecapacity improvement and infrastructure cost saving have sim-ilar properties when extending these results to our proposedthree-tier architecture.

Since both the low-tier and high-tier transmissions are in-volved in each traffic flow, numerically low-tier capacity needsto be equal to high-tier capacity. Our analysis suggests that,


when designing the three-tier hierarchical network, we can ad-just and (or and ) such that FNs can accommo-date network traffic, and the scaling properties can be achievedby satisfying and . In the nextsection, we will study a three-tier, 802.11-based network viadetailed system simulations and show how protocol overheadaffects the practical system’s scaling behavior.

IV. SYSTEM EVALUATION

The overheads of wireless medium access and routing controlin system and protocol design can be quite high and will gener-ally tend to degrade system performance. Hence, we investigatethe system performance and scaling properties of the three-tiernetwork system with MAC and routing protocols typical of areal implementation. It is of interest to see whether the analyti-cally obtained scaling relationships hold for system simulationswith realistic protocol and traffic assumptions. For this purpose,we set up an 802.11-based hierarchical hybrid network simula-tion model using the ns-2 simulator [17].

First, we compare the hierarchical system performance ofdense network scenarios with a conventional flat ad hoc net-work in order to estimate the potential performance improve-ment with the three-tier hierarchy. We also look at the impact ofthe number of ad hoc nodes. As discussed in the last section, theperformance improvements and capacity gain with the three-tierhierarchy come at the expense of increased investment in mul-tiradio forwarding node hardware and total system bandwidth.This motivates us to next study the scaling behavior of such anetwork in terms of relative node densities, traffic pattern, andchannel bandwidth allocation at each tier of the network. Wealso apply different ad hoc routing protocols to the hierarchicalsystem and evaluate how different routing protocols work in thehierarchical mode.

Combined with the analytical results, these experimental re-sults are intended to provide a more complete understanding onhow hierarchy, infrastructure, and multichannel capability helpin the design of a scalable network.

A. Methodology and Simulation Model

We assume a network in which all nodes use the IEEE 802.11MAC protocol with distributed coordination function (DCF)[12]. A static discovery procedure precomputes a well-balancedhierarchical network topology. We consider different ad hocrouting protocols, including DSR, AODV, and destinationsequence distance vector (DSDV) [26], which are modifiedappropriately for use in the hierarchical network.

1) Hierarchy Construction and Node Modeling: First, ad hocnodes (i.e., MNs) are randomly distributed in the network. Then,FNs and APs are added to the network to form the cluster-basedhierarchy. In particular, APs are placed in a regular pattern. MNsand FNs are associated to a nearest AP based on the geographicdistance, assuming each node has the location information ofitself and all the APs. As in the analytical model, each clusterconsists of one AP and an arbitrary number of FNs and MNs,and the AP works as the gateway of the cluster to the infrastruc-ture. This assumes that the discovery protocol supports identifi-cation of gateway APs and association of related FNs and MNsin each cluster.

As discussed in Section I, the hierarchical system can be de-signed flexibly. Using an appropriate discovery protocol withthe MAC protocol, an “optimized” self-organizing hierarchicaltopology can be maintained over time. For example, an opti-mized hierarchy may be achieved by introducing dynamic nodereassociations to balance workload and manage node mobilityover clusters. Under this assumption, we can simply implementthe hierarchical network by dividing the simulated site into acertain number of clusters, with the gateway AP located at thecenter of each cluster and approximately the same number ofnodes and same traffic load in each cluster. In this way, simula-tions can always be conducted over well-balanced hierarchicaltopologies.

MNs are modeled as simple wireless nodes without routingcapability offered to any other nodes. FNs offer multihoprouting capability to the nodes of their own clusters. APsprovide both wireless and wired access and are fully connectedby 100 Mbps high-speed wired links. The delay caused by thewired link is defined as the packet transmit time plus propaga-tion delay, where the former is the ratio of the packet size tothe link bandwidth, and the latter is 2 s (which is equivalentto a cable of length 500 m). With ns-2 wired-cum-wirelessscenarios [17], each communication between clusters goesthrough APs, as our analysis assumes.

We have implemented dual-radio nodes with two network in-terfaces, which allow simultaneous transmissions over two non-interfering channels. In order to disseminate routing informationover the network, routing messages are sent via both networkinterfaces. The routing protocol decides the network interfacethrough which each data packet is transmitted.

Although the analysis suggests use of optimal transmis-sion range by satisfying (1) or (3), for simplicity we choosea common transmission range of 250 m for both tiers. Theinterfering range is 550 m.

2) Traffic Pattern: We consider both the Internet and localtraffic, which have been defined in Section III-C1, and only up-link is considered for the Internet traffic. Therefore, all traffic inthe network is originated at the MNs. The relative proportionsof these two types of traffic can be adjusted parametrically. AtMNs, traffic is generated according to an exponential ON/OFF

model [17], with an average of 500 ms for both the “ON” (burst)and “OFF” (idle) periods. Packets are sent at a specific rate onlyduring “ON” periods, and this rate is varied as an input param-eter in order to gradually increase the offered load to the net-work. The packet size is 64 bytes. Each MN can simultaneouslysupport up to two traffic flows to different destinations.

3) Performance Metrics: We use the following performancemetrics for system evaluation.

• Packet delivery fraction: measured as a ratio of the numberof data packets delivered to their eventual destinations andthe number of data packets generated by sources.

• Average end-to-end delay: includes all possible delays be-fore data packets arrive at their destinations.

• Normalized routing overhead: measured as the number ofrouting packets transmitted (in the wireless network) perdata packet delivered at destinations. Each wireless hopis counted as one transmission for both routing and datapackets sent over multihop paths.


TABLE ISIMULATION PARAMETERS FOR BASELINE COMPARISON

• System throughput: measured as the total number of bits ofdata received at destinations over simulated time.

The simulations are run for multiple independent replications[17] with different ad hoc node placements or source–destina-tion pair distributions. Each result represents an average of fiveindependent runs lasting 550 s of simulated time.

B. Baseline Comparison

1) Simulation Parameters: Our baseline simulations are foran example dense (sensor) network deployed over a square ge-ographical area with dimension 1000 m 1000 m. We dividethe coverage area into four 500 m 500 m smaller squares,each corresponding to a cluster with one AP and several FNsand MNs. FNs and MNs are randomly placed within the clus-ters, with a nominal uniform density of 20 FNs and 100 MNsspread over the entire coverage area. FNs move according tothe random waypoint model [1] with a randomly chosen speed(uniformly distributed between 0 and 1 m/s) and a pause timeof zero (i.e., FNs do not stop during their journey). Half ofthe MNs are static; the remaining half move according to thesame random waypoint model as FNs. In order to measure thesystem improvement achieved by the three-tier hierarchy, weuse single-radio FNs for the baseline comparison. Also, we onlyconsider the Internet traffic here. The key parameters are sum-marized in Table I.

We assume that there are separate entries (i.e., APs) into theInternet, each of which serves some set of MNs. In the flat adhoc network model, each packet uses multihop wireless path toits assigned AP without the help of infrastructure. Furthermore,there is no FN in the flat network, and MNs deploy the samedistribution and mobility pattern as in the hierarchical peer.

2) Results and Discussions: From Fig. 7(a), which showsthroughput as a function of offered load from MNs for 40 com-municating pairs with DSR, we see that the hierarchical systembegins to saturate when the packet generation rate per sourcereaches 16 kbps, while the flat system saturates at about 4 kbps.For the 802.11b bandwidth of 1 Mbps used here, system capac-ities are found to be around 320 kbps for the hierarchical caseand about 77 kbps for the flat case, respectively.

We observe that for a specific network model with four APs,the system capacity roughly increases by a factor of 4 if the pro-posed hierarchical architecture is adopted. This is a significantscaling increase over the flat network, and the increase factoris consistent with the number of APs deployed. The averageend-to-end delay, packet delivery fraction, and routing over-head curves are illustrated in Fig. 7(b)–(d). The improvement ofpacket delivery fraction shows that the three-tier hierarchy helps

Fig. 7. Baseline comparison. DSR case, 40 communication pairs.

deliver packets in mobility scenarios. The simulations were re-peated for two other cases corresponding to 20 and 60 commu-nication pairs, and results similar to the 40-pair case were ob-served. This verifies that the system capacity is independent ofthe number of MNs.

In the cluster-based hierarchy, each MN communicatesthrough a few FNs and a gateway AP, thus reducing the averagenumber of hops to reach the Internet, where most packetsfrom MNs have their destinations (100% here). In addition,MNs do not join the full distribution of routing messages, thusreducing routing overhead significantly. Of course, the capacityincrease comes at the expense of increased hardware (FNs andAPs) relative to a flat network, and in that sense, it is not an“apples-to-apples” comparison.

We replaced DSR with AODV routing and repeated the sim-ulations. The results with AODV are comparable to those withDSR and show that the performance of the three-tier networkis relatively insensitive to the choice of routing protocol be-tween DSR and AODV. The hierarchical system works wellwith on-demand routing protocols with low-mobility nodes.

C. Scaling Behavior: Impact of Node Density

Our experiments have shown that the system throughput in-creases significantly for dense network scenarios with nominalparameters chosen above. Next, we investigate the impact of twoimportant factors that influence network capacity: the relativedensities of APs and FNs and the traffic pattern.

For the three-tier hierarchy under consideration, we observethat the core wireless network is formed by FNs and APs,while MNs feed traffic into nearby FNs or APs, as illustratedin Fig. 8(a). As a result, the key parameters for the system’sscaling behavior include the offered traffic load density fromMNs (denoted , in bps/m ), the density of FNs (denoted

), and the density of APs (denoted ). In order to ensurethat all MNs are reachable, we adopt a heuristic approach ofcovering the entire service area with FNs and then determiningthe right number of APs necessary for the network to scale in a


Fig. 8. Parameter definitions and the regular planar network topology.

TABLE IIPARAMETERS FOR SCALING SIMULATIONS

balanced way. We measure the normalized system throughput(per unit area) as a function of while varying , given afixed value of , and obtain the normalized system capacityas the maximum throughput.

1) Simulation Parameters: We consider a square simulatedregion, where APs and FNs are placed in the regular pattern.Although this regular spatial model is expected to produce op-timistic results relative to random spatial model, it is consid-ered useful for estimating the achievable capacity [27]. The dis-tances between neighboring FNs are all 200 m. With the spec-ified 802.11b transmission range of 250 m, this separation islikely to yield close to the maximum throughput [28], and thisFN density provides full coverage over the simulated region. Weuse two simulation cases with dimensions of 1200 m 1200 mand 800 m 800 m, respectively, in order to explore the sensi-tivity to physical assumptions. With identical FN density, thereare a total of 16 FNs for the 800 m 800 m case and 36 FNs forthe 1200 m 1200 m case, as depicted in Fig. 8(b) and (c) (sup-pose there are four APs in Fig. 8(b) and two APs in Fig. 8(c),and MNs are not plotted in the figures).

MNs are randomly distributed in the network with an iden-tical density. In order to investigate the scaling behavior affectedby the three-tier hierarchy, we use a single radio for FNs. Thenumber of APs is varied for each dimension to see how the hi-erarchical throughput changes with the ratio of FNs to APs. Weconsider with both DSR and DSDV for routing. The mobilitypattern of MNs and the traffic pattern are set differently for eachsimulation and will be described separately in later sections.Table II lists the key parameters. For other parameters, pleaserefer to Table I.

2) Results and Discussions:a) Experiments with DSR: When DSR is used, MNs move

according to the same random waypoint model as in the baselinecomparison, and only the Internet traffic is considered.

Simulation results for the 1200 m 1200 m case are shownin Fig. 9. Fig. 9(a) shows that the normalized system throughputincreases when the number of APs increases from one to nine.

Fig. 9. Impact of AP density. DSR case, 100% Internet traffic,1200 m� 1200 m field, 36 FNs. DSDV curve is given in (b) for comparison.

Observe that once the number of APs reaches four, the systemthroughput tends to increase at a slower rate. As expected, thehighest capacity is obtained with nine APs since nine APs givealmost the full coverage over the simulated site in our model.When the number of APs is greater than nine, the overlappingof the coverage areas of the neighboring APs becomes a factor,which results in interference between APs; thus, the normalizedcapacity begins to decrease.

Fig. 9(b) summarizes the normalized capacity with differentnumbers of APs. We observe that the achievable throughput in-creases almost linearly before the number of APs increases tofour, while the curve saturates rather rapidly as this number is in-creased further. Note that the “knee” of this curve is a good oper-ating region for system designers because it achieves near-max-imum network capacity with a modest investment in wired APs.In this case, a system designer should aim to provision the net-work with about four to six APs for a region that requires around36 FNs for full coverage.

We repeat the experiments for the 800 m 800 m case andobserve similar results. In this case, the knee of the capacitycurve is reached with about three to four APs. It is also observedthat the normalized capacities of these two cases are compa-rable, as might be expected as the simulated region grows larger.

b) Experiments with DSDV: For the DSDV case, we as-sume MNs to be stationary. This setting is used to avoid the in-fluence of node movement, which would tend to degrade systemperformance in a proactive routing protocol. We adjust the frac-tion of the Internet traffic to see the impact of traffic pattern andassign local traffic to be either intercluster or intracluster trafficwith equal probability.

Fig. 10 shows the capacity versus the number of APs for dif-ferent Internet traffic fractions. It is observed that the throughputgrows as the Internet traffic fraction grows from 20% to 100%for the two, three, four, nine, and 12 APs cases, but it is reversedfor the single AP case. The analytical result suggests that, forthe local traffic, it is more effective to allocate bandwidth tocarry intercluster traffic for large number of APs and to carryintracluster traffic for small numbers of APs. Since the Internettraffic has the same scaling property as the intercluster localtraffic, these simulation results are consistent with the analysisin terms of the traffic pattern. The capacity curves in Fig. 10have similar behavior as the DSR case given earlier, and allthe curves approach saturation in the region of four. A roughsquare-law relationship between the density of FNs and APs


Fig. 10. Normalized capacity versus the number of APs. DSDV case, staticnetwork, different Internet traffic fractions, 1200 m � 1200 m field, 36 FNs.

(i.e., ) around the knees of the capacity curvesmay be inferred.

The simulation results demonstrate that the achievablethroughput grows linearly with the number of APs only insome region of this number. The most important reason for thisis that the assumptions on perfect medium access (includingscheduling) and routing in the analysis do not hold in practicalsystems. The system performance degraded by protocol over-head would deteriorate when the node density increases. Theanalysis also assumes the transmission range chosen as in (1)or (3). Therefore, throughput is expected to be improved byemploying an optimal transmission power. If the transmissionrange shrinks as the APs get denser, the saturation region isexpected to move to larger numbers of APs. Otherwise, thenumber of the interfering neighbors of each AP would increaseas the AP density increases, invalidating the linearity. Both theprotocol overhead and nonoptimal transmission power causedeviations from the theoretical bound obtained earlier.

It is also observed from Fig. 9(b) that the hierarchical systemachieves higher throughput with on-demand routing thanproactive routing due to the reduced overhead with on-demandrouting.

D. Scaling Behavior: Impact of Bandwidth Allocation

The analytical results suggest that we could increase eithernode density or channel bandwidth to improve capacity. Notethat different AP or FN densities require different optimal trans-mission ranges based on (1) or (3), which might require an ap-propriate power control algorithm. As we do not consider powercontrol in this work, we choose to allocate dedicated frequencybands to each tier of the network.

Numerically, the high-tier capacity is required to be equal tothe low-tier capacity. This suggests that when the total networkbandwidth is given, it should be allocated in suitable proportionsto each tier in order to achieve a good system capacity. Since theasymptotic results do not explicitly reveal how bandwidth allo-cation affects system capacity, we conducted some additionalsimulations to investigate this issue.

TABLE IIIAVERAGE HOP COUNT AT TWO TIERS

1) Dual-frequency system model: In the analytical model,only FNs are equipped with dual radios, while APs are assumedto have a single radio. However, this assumption results in anavoidable performance degradation due to extra hops throughFNs even when direct MN-AP connections are possible. Theabove limitation of single-radio APs has been verified by sim-ulations for the scenario in Section IV-C2b. Therefore, we em-ploy a system model that deploys dual radios at both FNs andAPs. In this model, the high-tier capacity is numerically equiv-alent to the low-tier capacity less any traffic that does not gothrough the FN tier.

2) Bandwidth Allocation: Bandwidth should be allocated totwo tiers in proportion to the traffic load at each of the two tiersof transmissions. The MAC throughput (or one-hop throughputin [28]) can be used as a measure of traffic load and is de-fined as the total number of bits of data sent by all nodes persecond, including forwarded bits. According to the definition, itcan be obtained from the product of the end-to-end throughputand the average hop count of data packets delivered at destina-tions. Therefore, the bandwidth allocation depends on the ratioof average hop count at two tiers. Note that the dual-frequencysystem defined here chooses the same route for each packetas the single-frequency system. Therefore, when using the av-erage hop count as a measure of traffic load, we can obtain thevalues of the average hop count at two tiers of the dual-fre-quency system from the single-frequency system.

Suppose the measured average hop count of a single-fre-quency system is ; then, in the corresponding dual-frequencysystem, the average hop count at the high tier is for Internettraffic and for local traffic. If the Internet traffic fractionis 80%, the average hop counts of the dual-frequency systemat the low and high tiers can be estimated as 1.2 and ,respectively. Considering the single-frequency system scenario(with DSDV and 80% Internet traffic) in Section IV-C2b as anexample, we measure its average hop count and estimate theaverage hop counts at two tiers of the corresponding dual-fre-quency system, with results given in Table III. We have verifiedthat these estimated values are consistent with the measuredvalues.

3) MAC Throughput: As a more direct illustration of trafficload, in Fig. 11, we plot the MAC throughput at the low and hightiers as a function of the number of APs. As expected, low-tiernetwork throughput increases with the number of APs due toincreased direct MN–AP connections. We also observe the factthat network throughput increases rapidly with just a few APs,and for the case with four APs, the high-tier throughput con-tributes quite nicely to the overall network throughput that isonly a few percentage points lower than the maximum systemthroughput obtained with nine APs. This justifies the use of FNsto replace wired APs as motivated by the analytical results ob-tained earlier.


Fig. 11. End-to-end throughput and MAC throughput. DSDV case, static net-work, 80% Internet traffic fraction, 1200 m � 1200 m field.

TABLE IVDUAL-FREQUENCY CHANNEL BANDWIDTH ALLOCATION SCHEMES

By observing the average hop count while changing the of-fered load, we find that most of the bandwidth is used to carrypackets over short distances when the maximum throughputis achieved. This unfairness of bandwidth use between trafficrouted over different distances contributes to short average hopcounts in Table III. In addition, there are other factors such asthe network size that influence the hop count.

4) Results and Discussions: Based on the estimated ratiosof average hop count at two tiers, we define several possiblebandwidth allocation ratios between the high and low tiers inTable IV. Single-frequency allocation, which may be consideredan imperfect type of dynamic allocation via the MAC protocol,is also considered for comparison purposes.

Fig. 12 shows the achievable network throughput for each ofthe bandwidth ratios defined in Table IV and also for the single-frequency cases. From the results shown, we first observe thatthe achievable throughput for the case with one AP and singlefrequency is limited by access to the wired network, and thereis very little gain from doubling the available bandwidth from1 to 2 Mbps. The throughput gain with increased bandwidth isbetter in the four and nine AP single-frequency cases, but stillnot very significant even though the channel bandwidth has beendoubled. This can be attributed to the fact that 802.11 MAC in-volves significant and nonlinear overhead for MAC layer con-trol and routing (both of which use the basic rate 1 Mbps) as datarate increases, along with the fact that our traffic model (e.g., forsensor net) uses relatively short 64-byte packets. This motivatesallocation of separate frequency bands to high and low tiers ofthe network to avoid the increased MAC layer overheads andscheduling inefficiency that arise in the single-channel case.

Considering the two frequency allocation cases shown inFig. 12, we observe that the total throughput can be increasedfurther, provided the right ratio of high-tier and low-tier band-width is maintained. For the single AP case, as expected, the

Fig. 12. Impact of channel bandwidth allocation. DSDV case, static network,80% Internet traffic fraction, 1200 m � 1200 m field.

gains are small irrespective of single-frequency or dual-fre-quency assignment since the system is limited by the AP’scapacity to handle traffic to the Internet. Fig. 12 also shows thatfor the practically interesting (i.e., low cost, high performance)case with four APs, dual-frequency assignment with the rightbandwidth allocation (i.e., bandwidth allocation index 1 and 2)can provide significant gains (about 30%) over the baseline.On the other hand, when the number of APs is large (i.e.,the nine APs case), system capacity does not benefit fromdual-frequency assignment since most traffic is at the low tier.

The above results show that the highest throughput is ob-tained when the bandwidth is allocated according to the relativetraffic load carried at two tiers. We have figured out that thisload ratio can be computed from the average number of hopsof the single-frequency system as well as the ratio of local andInternet-bound traffic. Since the average hop count of single-fre-quency systems can be roughly estimated from network size andAP density, this approach can be used to allocate bandwidth totwo tiers in a general way. For more advanced approaches, ahierarchical network with dual radios and separate frequencybands could be designed to have an adaptive algorithm to esti-mate parameters and allocate bandwidths accordingly.

V. CONCLUSION

In this paper, we have introduced the concept of a multitierhierarchical hybrid wireless network, then developed a generalanalytical model for the asymptotic throughput capacity andscaling properties of the proposed network. In a three-tier hier-archical network with access points, forwarding nodes,and mobile nodes, the low-tier capacity increases linearlywith , and the high-tier capacity increases linearly withwhen and . In this identifiedscaling regime, linear scaling of capacity can be achieved witha smaller number of APs relative to the two-tier network, andthe system’s scaling behavior does not depend on the numberof ad hoc nodes. Also, the transmission range should be chosenas and .

We have also investigated the scaling properties and systemdesign principles for such a hierarchical hybrid network via sim-ulations with realistic MAC and routing protocols. The perfor-


mance of an example hierarchical ad hoc network was evalu-ated, and significant improvements in performance and systemthroughput relative to the flat network have been demonstrated.We also studied the impact of the relative densities of APs,FNs, and MNs as well as the traffic pattern on the achievablethroughput and compared the results with the analysis. The sim-ulation results demonstrate a well-defined saturation effect asthe density of APs is increased relative to a fixed density of FNs,thus leading to simple guidelines for determining the numberof nodes at each tier of the hierarchy. Furthermore, we inves-tigated the impact of the relative channel bandwidth allocatedto two tiers on the achievable throughput of the dual-frequencyhierarchical system. The results verify that dedicated allocationof frequency bands to each tier of the network can further im-prove throughput provided that the bandwidths of high and lowtiers are allocated according to the relative traffic load carriedat two tiers. Our simulation results show that protocol overheadhas great impact on a system’s scaling behavior and underscorethe importance of designing efficient channel access and packetscheduling protocols.

Overall, the results indicate that it is possible to scale networkcapacity quite well with a mix of several (lower cost) radio FNsand just a few wired APs. Both the analytical and simulationresults demonstrate the value of adding FNs to improve scalingbehavior and reduce the required number of APs relative to thetwo-tier case. We believe that these results are particularly rele-vant for emerging mesh and sensor network deployments wherereducing the number of wired access points is a priority.

APPENDIX

PROOF OF THEOREM 1

We use a Voronoi tessellation [29] of the planar disk to provethis theorem, assuming the edge effects are ignored. It can beshown that the special properties of the Voronoi tessellation ofthe surface of the sphere, described in [3, Lemma 4.1], hold forthe planar disk. The lemma can be rewritten as follows.

Lemma 2: For every , there is a Voronoi tessellationof the disk on the plane such that every Voronoi cell contains adisk of radius and is contained in a disk of radius .

Let . Lemma 2 implies that thereexists a Voronoi tessellation such that each Voronoi cell

contains a disk of radius and is contained in a diskof radius . Define adjacent cells as the Voronoi cells thatshare a common point. Set the transmission range .The following lemma can be proved as in [3].

Lemma 3: For the chosen and , the constructed Voronoitessellation has the following properties:

• Each Voronoi cell in contains at least one node (withprobability approaching 1 as ).

• Every node in a Voronoi cell is within a distance fromevery node in its own cell or adjacent cells.

• Every Voronoi cell has no more than interfering neigh-bors. depends only on the guard zone size .

Now, let be the common destination node, be a sourcenode, and be the straight-line segment connecting to ,for . We choose the routes to approximate thestraight-line segments, which intersect the Voronoi cells in .More specifically, each packet is relayed from the source cell

to the destination cell in a sequence of hops. According toLemma 3, in each hop, the packet can be transferred from oneVoronoi cell to an adjacent cell along the straight-line segments.In the last hop, the packet is sent to the destination from an adja-cent cell of . The traffic generated at any source node that islocated within is directly transferred to the destination. Theabove multihop relaying scheme is feasible with probability 1when is large.

Next, we compute the mean number of routes served by thedestination cell . Since contains the final destination nodeand each multihop route from the source to the destination isfeasible, it follows:

intersects

number of lines in intersecting

Suppose each line carries traffic of rate bps. Since thetraffic handled by a Voronoi cell is proportional to the numberof lines passing through it, the rate at which the destination cellneeds to serve is .

From the vertex coloring of graphs [25] and considering thethird property of Lemma 3, we can design a schedule for trans-mitting packets in such a way that each Voronoi cell gets onetime slot to transmit in every slots, and no transmissioncollisions occur. Thus, the rate at which each Voronoi cell getsto transmit is bps.

Note that the traffic can be accommodated if it is less than therate available. Based on the scheduling scheme as described,the traffic handled by the whole network is restricted by thedestination cell , i.e., . Therefore, the rateper source node is feasible with probability1 when is large. This gives an achievable rate per source node(i.e., the lower bound of the per-source-node capacity). On theother hand, since can only handle data at rate of bps, theaggregate capacity is upper-bounded by . Therefore, the orderof the aggregate throughput capacity is given bywhen .

For regularly placed source nodes, the above multihop re-laying scheme is feasible in a deterministic manner. In addi-tion, the optimal transmission range can be reduced as long as

is satisfied for maintaining connectivity.This result implies that the asymptotic capacity of a random

network carrying aggregation traffic is independent of thenumber of hops required to reach the aggregation node as wellas the location of the aggregation node. Compared with similarresults obtained in [9] and [30], the proof presented here issimpler and allows a randomly placed aggregation node. Also,this approach makes it possible to derive that the mean numberof lines passing through a Voronoi cell isbounded by , where is the distanceof the cell center to the destination and is a constant (see[31]). For the cells that are close to the destination such that

, it implies that the traffic in close proximity of thedestination is proportional to the reciprocal of the distance tothe destination. This provides a basis for designing schedulingalgorithms to overcome the capacity bottleneck at the hotspotsaround the aggregation node.


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Suli Zhao (S’04–M’08) received the B.S. and M.S.degrees in electrical engineering from the BeijingUniversity of Posts and Telecommunications, Bei-jing, China, in 1994 and 1997, respectively, and thePh.D. degree in electrical and computer engineeringfrom Rutgers University, New Brunswick, NJ, in2007.

She is currently working as a Systems Engineer atQualcomm Inc., San Diego, CA. From 1998 to 2001,she was with Nokia Research Center, Beijing, China,

as a Research Engineer in the 3G Mobile Communications Group. Before that,she worked as an R&D Engineer at the CDMA R&D Center, Beijing, China. Herresearch interests include mobile communications and wireless networking, adhoc mesh networks, mobile cellular networks, system architecture and protocoldesign, and performance enhancement.

Dipankar Raychaudhuri(S’78–M’79–SM’87–F’95) received the B.Tech.(Hons.) degree from the Indian Institute of Tech-nology, Kharagpur, India, in 1976, and the M.S.and Ph.D. degrees in electrical engineering from theState University of New York, Stony Brook, in 1978and 1979, respectively.

Since 2001, he has held the position of Professorin the Electrical and Computer Engineering De-partment and Director of the Wireless Information

Network Laboratory (WINLAB) at Rutgers University, New Brunswick, NJ. AsWINLAB’s Director, he is responsible for a cooperative industry-university re-search center with focus on next-generation wireless technologies. WINLAB’scurrent research scope includes topics such as RF/sensor devices, cognitiveradio, ad hoc mesh networks, wireless security, future Internet architecture, andpervasive computing. Currently, he is the principal investigator for the NationalScience Foundation (NSF)-funded “ORBIT” open-access, next-generationwireless network testbed at Rutgers, and has served as a member of the plan-ning group for the NSF’s GENI Future Internet initiative. He has previouslyheld progressively responsible corporate R&D positions in the telecommuni-cations/networking industry, including Chief Scientist, Iospan Wireless, SanJose, CA (2000–2001); Assistant General Manager and Department Head ofSystems Architecture, NEC USA C&C Research Laboratories, Princeton, NJ(1993–1999); and Head of Broadband Communications Research, SarnoffCorporation, Princeton, NJ (1990–1992).

Prof. Raychaudhuri was Vice-Chair for WATM WG, ATM Forum(1997–1999), and Chair for the Data Communication Systems Com-mittee, IEEE Communications Society. He has served as an Editor for theIEEE/ACM TRANSACTIONS ON NETWORKING, the IEEE TRANSACTIONS ON

COMMUNICATION, IEEE Multimedia, and IEEE Communications Magazine.

Documents

1536 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 17, NO. 5, OCTOBER 2009 Scalability and Performance Evaluation of Hierarchical Hybrid Wireless Networksweb.stanford.edu/class/ee360/previous/suppRead/read1/scalability_zhao.pdf ·