Ad Hoc Networks 2 (2004) 185–202 www.elsevier.com/locate/adhoc
Ad hoc networking with Bluetooth: key metrics and distributed protocols for scatternet formation
Tommaso Melodia *, Francesca Cuomo INFOCOM Department, University of Rome ‘‘La Sapienza’’, Via Eudossiana 18, 00184 Rome, Italy Received 13 June 2003; received in revised form 29 July 2003; accepted 31 July 2003
Abstract
Bluetooth is a promising technology for personal/local area wireless communications. A Bluetooth scatternet is composed of simple overlapping piconets, each with a low number of devices sharing the same radio channel. A scatternet may have different topological configurations, depending on the number of composing piconets, the role of the devices involved and the configuration of the links. This paper discusses the scatternet formation issue by analyzing topological characteristics of the scatternet formed. A matrix-based representation of the network topology is used to define metrics that are applied to evaluate the key cost parameters and the scatternet performance. Numerical examples are presented and discussed, highlighting the impact of metric selection on scatternet performance. Then, a distributed algorithm for scatternet topology optimization is introduced, that supports the formation of a ‘‘locally optimal’’ scat- ternet based on a selected metric. Numerical results obtained by adopting this distributed approach to ‘‘optimize’’ the network topology are shown to be close to the global optimum. 2003 Elsevier B.V. All rights reserved.
Keywords: Ad hoc networks; Bluetooth; Scatternet formation; Topology optimization; Distributed protocols
1. Introduction 1 Mbit/s gross rate in a so-called piconet, where up to 8 devices can simultaneously be interconnected. Bluetooth (BT) is a promising technology for The radius of a piconet (transmission range––TR)is ad hoc networking that could impact several about 10 m for Class 3 devices. A BT based stan- wireless communication fields providing WPAN dard has been released by the IEEE 802.15, which (Wireless Personal Area Networks) extensions of also addresses coexistence with the 802.11 wireless public radio networks (e.g., GPRS, UMTS, In- LAN technology, in the un-licensed 2.4 GHz ISM ternet) or of local area ones (e.g. 802.11 WLANs, (Industrial, Scientific and Medical) band [4]. Home RF) [1,2]. The BT system is described in One of the key issues associated with the BT the Bluetooth Specifications 1.1 [3] and supports a technology is the possibility of dynamically setting- up and tearing down piconets. Devices (named also nodes in the following) can join and leave piconets. * Corresponding author. Different piconets can coexist by sharing the spec- E-mail addresses: [email protected] (T. trum with different frequency hopping sequences, Melodia), [email protected] (F. Cuomo). and interconnect in a scatternet. When all nodes
1570-8705/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S1570-8705(03)00054-4 186 T. Melodia, F. Cuomo / Ad Hoc Networks 2 (2004) 185–202 are in radio visibility, scenario which we will refer slave exchange data by hopping at a frequency of to as single hop, the formation of overlapping pic- 1600 hops/second on the 79 available channels. onets allows more than 8 nodes to contemporary Different hopping sequences are associated to dif- communicate and may enhance system capacity. In ferent masters. a multi-hop scenario, where nodes are not all in A master can connect with up to 7 slaves within radio vicinity, a scatternet is mandatory to develop a piconet. Devices belonging to the same piconet a connected platform for ad-hoc networking. share a 1 Mbit/s radio channel and use the same This paper addresses the scatternet formation frequency hopping sequence. Only communica- issue by considering topological properties that tions between master and slaves are permitted. affect the performance of the system. Most works Time is slotted and the master, by means of a in literature aim at forming a connected scatternet polling mechanism, centrally regulates the access while performance related topological issues typi- to the medium. Thanks to the FHSS, which is cally remain un-addressed. To this aim we intro- robust against interference, multiple piconets can duce a matrix based scatternet representation that co-exist in the same area. Considerable perfor- is used to define metrics and to evaluate the rele- mance degradation only occurs for a high number vant performance. We then propose a distributed of co-located piconets (in the order of 50) [5]. algorithm that performs topology optimization by To overcome the limits imposed by the low relying on the previously introduced metrics. We number of devices that can simultaneously com- conclude by describing a two-phases scatternet municate (up to 8) and by the channel capacity formation algorithm based on the optimization (less than 1 Mbit/s) in a piconet, the BT specifi- algorithm. To the best of our knowledge, this is the cations introduced the concept of ‘‘scatternet’’, first scatternet formation algorithm explicitly defined as an interconnection of overlapping pico- aimed at optimizing network topology. nets. Each device can join more than one piconet, The paper is organized as follows. Section 3 and participates to communications in different briefly summarizes the state of the art in scatternet piconets on a time-division basis. Devices that formation, while in Section 4 we present a frame- belong to more that one piconet are called gate- work for scatternet analysis, based on a matrix ways or BridGing units (BG). representation of the scatternet. Section 5 presents In Fig. 1 we show an example of scatternet, some metrics that can be used to evaluate a scat- composed of 8 devices organized in 3 piconets. ternet; related numerical results are shown in Devices number 1, 5 and 6 are masters; devices 4 Section 6. Section 7 presents the Distributed and 7 are slaves in two different piconets. Thus, Scatternet Optimization Algorithm (DSOA) while they act as BGs between them, i.e., they can for- Section 8 describes a two-phase scatternet forma- ward traffic from and to devices belonging to the tion algorithm based on DSOA. Section 9 con- two different piconets. cludes the paper.
2. From piconets to scatternets
BT exploits an 83.5 MHz band, divided into 79 equally spaced 1 MHz channels [1,3]. The multiple access technique is the FHSS–TDD (frequency hopping spread spectrum–time division duplex- ing). Two BT units exchange information by means of a master-slave relationship. Master and slave roles are dynamic: the device that starts the communication acts as master, the other one as slave. After connection establishment, master and Fig. 1. An example of scatternet made up of 3 piconets. T. Melodia, F. Cuomo / Ad Hoc Networks 2 (2004) 185–202 187
It is easy to see that there are many topological A second class of multi-hop proposals is con- alternatives to form a scatternet out of the same cerned with algorithms based on clustering schemes. group of devices. The way a scatternet is formed These algorithms principally aim at forming con- considerably affects its performance. nected scatternets. In [13,14] the BlueStars and BlueMesh protocols are described respectively. The BlueStars protocol has three phases: device dis- 3. Related works covery, partitioning of the network into Bluetooth piconets and interconnection of the piconets into a Scatternet formation in BT has recently re- connected scatternet. It is executed at each node ceived a significant attention in the scientific with no prior knowledge of the network topology, literature. Existing works can be classified as sin- thus being fully distributed. The selection of the gle-hop [6–9] and multi-hop solutions [10–15]. Bluetooth masters is driven by the suitability of a Paper [6] addresses the BT scatternet formation node to be the ‘‘best fit’’ for serving as a master. with a distributed logic that selects a leader node Finally, the generated scatternet is a connected which subsequently assigns roles to the other mesh with multiple paths between any pair of nodes in the system. The scheme works for a nodes, which guarantees robustness. Simulation number of nodes 6 36. In [7] a distributed for- results are provided which evaluate the impact of mation protocol is defined, with the goal of re- the Bluetooth device discovery phase on the per- ducing formation time and message complexity. In formance of the protocol. Also the protocol in both [7,8], the resulting scatternet has a number of BlueMesh forms scatternets without requiring the piconets close to the theoretical minimum. The BT devices to be all in each otherÕs transmission works in [9–11] form tree shaped scatternets. The range. BlueMesh scatternet topologies are meshes tree structure is shown to be simple to realize and with multiple paths between any pair of nodes. efficient for packet scheduling and routing. The BlueMesh piconets are made up of no more than 7 work [9], by Tan et al., presents the TSF (Tree slaves. Simulation results in networks with over Scatternet Formation) protocol. The topology of 200 nodes show that BlueMesh is effective in the scatternet is a collection of one or more rooted quickly generating a connected scatternet in which spanning trees, each autonomously attempting to each node, on average, does not assume more than merge and converge to a topology with a smaller 2.4 roles. Moreover, the route length between any number of trees. TSF assures connectivity only in two nodes in the network is comparable to that of single-hop scenarios since trees can merge only if the shortest paths between the nodes. Also [15] their root nodes are in transmission range of each defines a protocol that limits the number of slaves other. Zaruba et al. propose a protocol which per master to 7 by applying the Yao degree re- operates also in a multi-hop environment [10]. duction technique, assuming that each node This latter protocol is based on a process that is knows its geographical position and that of each initiated by a unique node (named blueroot)and neighbor. repeated recursively till the ‘‘leaves’’ of the tree are Recently, the work in [16] proposed a new on- reached. In order to operate in a distributed way demand route discovery and construction ap- and to avoid deadlocks the algorithm is based on proach which, however, requires substantial modi- time-outs that could affect the formation time. fications to the Bluetooth standard to guarantee SHAPER [11] also forms tree-shaped scatternets, acceptable route-setup delay. but is fully distributed, works in a multi-hop set- Some other works discuss the optimization of ting, has very limited formation time and assures the scatternet topology. This issue is faced in self-healing properties of the network, i.e. nodes [17,20] by means of centralized approaches. In [17] can enter and leave the network at any time the aim is minimizing the load of the most con- without causing loss of connectivity. The Bluenet gested node in the network while [20] discusses the protocol in [12] forms a scatternet which has rea- impact of different metrics on the scatternet to- sonably good connectivity. pology. A distributed approach based on simple 188 T. Melodia, F. Cuomo / Ad Hoc Networks 2 (2004) 185–202 heuristics is presented in [21]. In [18], an analytical under the hypothesis that a master in a piconet model of a scatternet based on queuing theory is does not assume the role of slave in another pic- introduced, aimed at determining the number of onet; in other words, by adopting this model, the non-gateway and gateway slaves to guarantee ac- BGs are slaves in all the piconets they belong to. ceptable delay characteristics. We rely on this hypothesis to slightly simplify the In this framework the objectives of our contri- scatternet representation, the complexity in the bution are description of the metrics and to reduce the space of possible topologies. Moreover, intuitively, the • provide a framework for scatternet topology use of master/slave BGs can lead to losses in sys- analysis based on matrices which turns out to tem efficiency. If the BG is also a master, no be a very simple and effective design tool; communications can occur in the piconet where it • identify metrics that can be used to form and to plays the role of master when it communicates as evaluate scatternets; we emphasize differences slave. However, to the best of our knowledge, this between traffic dependent metrics and traffic in- claim has never been proved to be true. Future dependent ones and we show selected numerical work will thus extend the results presented in this results; paper to non-bipartite graphs. • to present the building blocks for the implemen- The bipartite graph GB can be represented by a tation of a distributed algorithm that optimizes rectangular M Â S binary matrix B [19]. In B, each the scatternet topology. row is associated with one master and each column with one slave. Element bij in the matrix equals 1 iff slave j belongs to master iÕs piconet. The scat- 4. The scatternet formation issue ternet of Fig. 1 may be represented by the fol- lowing matrix B (Eq. 1a). Before addressing the issue of scatternet for- In addition, a path between a pair of nodes (h, mation, we introduce a suitable scatternet repre- k) can be represented by another M Â S matrix h;k h;k sentation. P ðBÞ, whose element pij equals 1 iff the link between master i and slave j is part of the path 4.1. Scatternet representation between node h and node k ð1 6 i; j; h; k 6 NÞ.As an example, and referring again to Fig. 1, the path Let us consider a scenario with N devices. The between nodes 2 and 8 can be represented by the scenario can be modeled as an undirected graph matrix P2;8ðBÞ of Eq. (1b) GðV ; EÞ, where V is the set of nodes and an edge 23478 eij, between any two nodes vi and vj, belongs to the 23478 1 11100 1 10100 set E iff distðvi; vjÞ < TR, i.e., if vi and vj are within : each otherÕs transmission range. GðV ; EÞ can be B= 5 00110 P2,8 (B)= 5 00110 6 00011 (a) 6 00011 represented by a N Â N adjacency matrix A ¼½aij, (b) whose element aij equals 1 iff device j is in the TR ð1Þ of device i (i.e., j can directly receive the trans- mission of i). Given a set V of N nodes, and an adjacency matrix Besides the adjacency graph GðV ; EÞ, in accor- A, we can build the M Â S matrix B ¼½bij by as- dance to, we use a bipartite graph GBðVM ; VS ; LÞ,to sociating its rows to a VM non-empty subset of M model the scatternet, where jVM j¼M is the num- nodes in V , and the columns to a VS non-empty ber of masters, jVS j¼S is the number of slaves, subset of S nodes in V (with N ¼ M þ S, and L is the set of links (with N ¼ M þ S, VM \ VS ¼f0g and VM [ VS ¼ V ), and by selecting VM \ VS ¼f0g, VM \ VS ¼ V ). A link may exist a subset of links in E. The resulting matrix B between two nodes only if they belong to the two represents a ‘‘BT-compliant’’ scatternet with M different sets VM and VS. Obviously, for any feasible masters and S slaves if the following properties scatternet, we have L E. This model is valid apply: T. Melodia, F. Cuomo / Ad Hoc Networks 2 (2004) 185–202 189
6 6 1.P Each master is connected at least to a slave, in the scatternet, with Mmin M Mmax the num- S j¼1 bij P 1; i ¼ 1; ...; M. ber of possible choicesP of roles for the network 2. No more than seven slaves belong to a piconet, Mmax N N P nodes is equal to M¼M M , since there are M S 6 min j¼1 bij 7; i ¼ 1; ...; M. possible ways of selecting M masters among N 3.P Each slave is connected at least to a master, nodes. Each choice implies a set L0 of possible links M 0 0 i¼1 bij P 1; j ¼ 1; ...; S. (with L E) and we consider every subset L L 4. The resulting network is connected, the matrix which gives rise to a scatternet that respects prop- B does not have a block structure, row permu- erties 1–4. All these scatternets constitute our B tations notwithstanding. matrices. We consider Mmin ¼dN=ð7 þ 1Þe and Mmax ¼bN=2c. A number of masters greater than 4.2. A framework for scatternet topology analysis half the nodes introduces inefficiencies (e.g., inter- ference) without bringing benefits to the scatternet. By exploiting the above matrix representations, The B matrices are evaluated by applying suit- we are interested in able metrics described in Section 5. For a given metric, the output of the overall process is the (a) characterize the space of solutions; i.e., all the identification of the optimal B (indicated with BÃ), B matrices compliant with rules 1–4; which represents the scatternet with the optimal (b) define metrics to evaluate the scatternet perfor- topology, and a distribution of the metric values. mance; (c) single out the optimal scatternet (BÃ) with re- spect to a selected metric; 5. Metrics for scatternet evaluation (d) analyze the topological properties of the ex- tracted solutions. Metrics for scatternet evaluation can either be dependent on or independent of the traffic loading We stress that our objective is to enucleate the scatternet. In the traffic independent (TI) case, scatternet characteristics related to specific metrics the scatternet is formed without a priori knowl- that could be adopted in the formation process. edge of traffic patterns among involved devices. We do not aim at proposing sophisticated algo- The scenario is described only by means of the rithms that elaborate the matrix A to derive the adjacency matrix A, without associating to possi- optimal scatternet, also because, due to the com- ble pairs of devices a description of the related plexity of the problem, they probably shall operate exchanged traffic. On the other hand, it may be in a centralized manner while scatternet formation useful to form a scatternet by taking into account should be solved by adopting distributed opera- traffic patterns, if such information is available. In tions performed by all network nodes. To work that case, the traffic patterns can conveniently be out points (a) and (c) we rely on space state enu- described by a traffic matrix, T. In the following meration that pays the complexity of examining we refer to this case as traffic dependent (TD). and listing all potential scatternets but on the other In the following, we introduce several metrics; hand allows us to completely characterize the each of them has pros and cons. space of possible solutions. In the following we briefly describe our approach to go along steps a–d, while further details can be found in [20]. 5.1. TI metrics: scatternet with maximum capacity We randomly generate communication scenar- ios taking as inputs the number of devices, N,and A first traffic independent metric is the overall the dimensions of the area where the nodes are capacity of the scatternet. Evaluating such a ca- located; the scenario is represented by the A matrix. pacity is not an easy task, since it is related to the We then identify and enumerate all the ‘‘BT- capacity of the composing piconets which in turn compliant’’ scatternets that may be obtained from depends on the intra-piconet and interpiconet the scenario; if we let M be the number of masters scheduling policies. To the best of our knowledge, 190 T. Melodia, F. Cuomo / Ad Hoc Networks 2 (2004) 185–202 no such evaluation is available in literature. In the As an example, let us consider the scatternet of following, we introduce a simple model to estimate Fig. 1. The matrices OTIðBÞ and RTIðBÞ are the capacity of a scatternet and we exploit this evaluation for scatternet formation. In the model we assume that
• a master may offer the same amount of capacity ð5Þ to each of its slaves by equally partitioning the piconet capacity; • a BG slave spends the same time in any piconet it belongs to.
These assumptions are tied to intra and inter and the related matrix CTIðBÞ is piconet scheduling; here, for the sake of simplicity, we assume policies that equally divide resources; however the model can be straightforwardly ex- ð6Þ tended to whatever scheduling policy. The scatternet capacity will be evaluated by normalizing its value to the overall capacity of a The resulting normalized capacity is c ðBÞ¼3 piconet (i.e., 1 Mbit/s). Let us define two M  S TI ( ¼ 3 Mbit/s). matrices, O ðBÞ¼½o , and R ðBÞ¼½r with TI ij TI ij Eq. (4) is valid in the ideal case where both in- o ¼ b =s and r ¼ b =m , where s denotes the ij ij i ij ij j i terference from co-located piconets and switching number of slaves connected to master i and m j overhead, caused by BGs that change piconet, are denotes the number of masters connected to slave j neglected. In order to include these two effects, (for j ¼ 1; ...; S and i ¼ 1; ...; M): Eq. (4) can be rewritten as XM mj ¼ bij for j ¼ 1; ...; S; cTIðBÞ¼ðcTIðBÞÀDðBÞÞ Á IðBÞ; ð7Þ i¼1 XS where DðBÞ represents a loss of capacity due to the si ¼ bij for i ¼ 1; ...; M: ð2Þ switching overhead and IðBÞ is a decreasing factor j¼1 that accounts for interference from co-located
The matrix OTIðBÞ represents the portions of ca- piconets. pacity a master may offer to each of its slaves. The RTIðBÞ matrix represents the portions of capacity a 5.2. TD metrics: scatternet with maximum residual slave may ‘‘spend’’ in the piconet it is connected capacity or minimum average load to. The overall capacity of the scatternet is given by the sum of the capacities of all links. The ca- We consider two traffic dependent metrics: (i) pacity cij of link (i; j) is the minimum between the the so-called residual capacity (i.e., the capacity capacity oij and the capacity rij. Let us define the that remains available in a scatternet, after that all matrix CTIðBÞ, whose elements represent the nor- pre-defined traffic patterns are accommodated); (ii) malized link capacity, as the nodes’ average load.
CTIðBÞ¼½cij¼½minðoij; rijÞ: ð3Þ The evaluation of the above metrics is TD, and as such, is dependent on the adopted routing The associated metric is the normalizedcapacity strategy too. As an example, given a traffic pattern, cTIðBÞ of a scatternet defined as for instance a data flow between device h and de- XM XS vice k (with 1 6 h, k 6 N), the capacity that such cTIðBÞ¼ minðoij; rijÞ: ð4Þ flow requires from the overall scatternet depends i¼1 j¼1 on the number of hops that make up the path T. Melodia, F. Cuomo / Ad Hoc Networks 2 (2004) 185–202 191 between device h and device k. In our analysis, we according to Eq. (3), the residual capacity matrix, assume without loss of generality, that a shortest is given by path routing algorithm is adopted. Cres;TDðBÞ¼CTIðBÞÀCTDðBÞ¼bfijc: ð12Þ To evaluate the metrics, we start by describing the traffic relationships with an N Â N traffic ma- The information contained in this matrix can be trix T ¼½thk, whose element thk represents the ca- summarized in a single parameter, the residual pacity, normalized with respect to the piconetÕs capacity, cres;TDðBÞ, given by capacity, required by the (h; k) relationship, XM XS (1 6 h; k 6 N). We assume that the thk (normalized cres;TDðBÞ¼ fij: ð13Þ traffic rates) are fixed for each source–destination i¼1 j¼1 couple. We also denote by R the number of traffic Also in this case considerations about decreasing relationships expressed by this matrix. factors due to interference and switching overhead It is easy to see that the capacity required on can be applied. each link by the traffic relationship between node h According to this metric, a scatternet is optimal, h;k and node k is given by thkP ðBÞ. when the value of cres;TDðBÞ is maximized. The matrix of the overall normalized capacity Alternatively, we can adopt as metric the nodes’ required for each link to transport the traffic pat- average normalizedload . terns expressed by T is given by In accordanceP to Eq. (8) the normalized load on S M N N X X a slave j is lj ¼ i¼1Pdij, while the normalized load h;k M S CTDðBÞ¼ thk Á P ðBÞ on a master is li ¼ j¼1 dij. "h¼1 k¼1;k6¼h # The normalized load averaged over the N XN XN nodes, which we denote as lðBÞ,is h;k ¼ dij ¼ thk Á p : ð8Þ P P ij S lS þ M lM h¼1 k¼1;k6¼h lðBÞ¼ j¼1 j i¼1 i It is to be noted that the traffic relationships defined P NP M S by the matrix T can effectively be supported by the 2 Á dij 2 Á c ðBÞ ¼ i¼1 j¼1 ¼ TD : ð14Þ scatternet represented by B if the following condi- N N tions, that assure the steady state, are verified: With this metric, the target is the minimization of masters are not over-loaded lðBÞ; we point out that the minimization of the average load goes in the direction of a minimiza- XS tion of the average energy consumption of the ) dij 6 1 8i 2 M; ð9Þ j¼1 scatternet. slaves are not over-loaded 5.3. Metrics associatedto the path length XM ) dij 6 1 8j 2 S: ð10Þ As will be shown in Section 6 path lengths have i¼1 a considerable impact on scatternet performance. The total capacity required by the traffic rela- As a consequence, in this section, we define three tionships of matrix T is metrics that do take into account path lengths. The XM XS first two are not dependent on the traffic loading cTDðBÞ¼ dij: ð11Þ the scatternet and are defined as follows. i¼1 j¼1 Let us denote, for a scatternet represented by a Based on the above definitions, we can finally in- matrix B, the length of the path between device h troduce two TD metrics. The first measures the and device k (expressed in number of hops) as capacity that remains available in a scatternet, XM XS h;k h;k after all traffic patterns are accommodated. Re- q ðBÞ¼ pij : ð15Þ calling that the capacity of each link is assigned i¼1 j¼1 192 T. Melodia, F. Cuomo / Ad Hoc Networks 2 (2004) 185–202
The first metric that we introduce is the average Our analysis does not aim at identifying all path length, which is the path length averaged the possible metrics, however by following this over all possible source–destination couples, and is methodology many other metrics can be identified, given by as metrics related to the behavior of specific nodes/ XN XN links in the network (i.e., minimize the energy qh;kðBÞ q ðBÞ¼ ; ð16Þ consumption of the bottleneck node, maximize the TI N N 1 h¼1 k¼1;k6¼h Áð À Þ minimal residual capacity among the links). The six metrics in Table 1 have been introduced the optimization target of this metric is the mini- in order to measure some significant performance mization of q ðBÞ. TI parameters of the overall scatternet. In particular, Given the capacity of a scatternet c ðBÞ and TI while within TI metrics c ðBÞ simply measures the the relevant average path length q ðBÞ, on average TI TI potential of the scatternet in terms of capacity, the the capacity available for the generic source–des- other two are introduced to evaluate the scatternet tination couple among the nodes in B is by considering a generic source–destination couple cTIðBÞ obtained by averaging over all possible ones and aTIðBÞ¼ : ð17Þ qTIðBÞÁN ÁðN À 1Þ by assuming uniform traffic patterns. As for the TD metrics, the residual capacity has We will call this last metric average path capacity. been introduced to evaluate how the scatternet is The last metric we introduce depends on traffic able, in terms of capacity, to sustain adjunctive and thus it depends on the matrix T, which defines flows. The other two metrics, that are related to R traffic relationships. The metric is the path length the path lengths, are in favor of scatternets that averagedover the R traffic relationships , instead efficiently support the given traffic matrix T.If that over all possible N ÁðN À 1Þ relationships, as traffic patterns are balanced (i.e., all the traffic done in Eq. (15); it is given by relationship require the same capacity) the opti- X qh;kðBÞ mization of the two metrics q ðBÞ and l ðBÞ q ðBÞ¼ : ð18Þ TD TD TD R gives rise to the same optimal scatternet BÃ. ðh;kÞ2T ;h6¼k The associated target consists in minimizing this path length; this metric goes in the direction of 6. Numerical results minimizing the transfer delay related to the num- ber of hops. In this Section, we present numerical results Table 1 summarizes the metrics introduced and relevant to the metrics defined above obtained in briefly reports the significance of the metric accordance to Section 4.2. Each of the following themselves. figures represents the area containing the scatter-
Table 1 A summary of the defined metrics
Traffic independent Normalized capacity cTIðBÞ Capacity of the overall scatternet normalized with respect to the capacity of a piconet
Average path length qTIðBÞ Average number of hops of shortest paths between nodes Average path capacity aTIðBÞ Capacity available for the generic source–destination couple
Traffic dependent Residual capacity cres;TDðBÞ Residual capacity of the scatternet once traffic in T has been allocated
Average path length qTDðBÞ Average number of hops of shortest paths between nodes for patterns in T
Average normalized load lTDðBÞ Average load on nodes in the scatternet to support patterns in T T. Melodia, F. Cuomo / Ad Hoc Networks 2 (2004) 185–202 193 net; x and y axes are measured in meters. The TR is interference effect it becomes 4.7151. Although this assumed to be equal to 10 m. Nodes are numbered scatternet is the one with maximum normalized according to the order they are generated in the capacity, it has characteristics that make its to- communication scenario. Figures report nodes, pology undesirable: it presents large values of the their roles (master, slave or bridge) and radio average path length that could lead to high links connecting them. Since number of possible transfer delays, and, since for Class 3 devices no scatternets quickly becomes overwhelming with power control mechanisms have been defined, in- respects to the number of nodes, in this section creasing the number of hops per traffic relation- we analyze networks with a limited number of ship does not bring any benefit in terms of power devices. consumption and consumes capacity as function of the involved links. As an example, a single 500 6.1. Traffic independent metrics kbit/s bi-directional flow between node 10 and node 12 in Fig. 2 would use all scatternet capacity: This subsection shows examples of scatternets nodes along the path would spend half their time resulting from TI optimization. The scenario receiving traffic from one of the two directions and consists of 12 devices not all the nodes are in radio the remaining time relaying traffic in the opposite visibility. The scatternet in Fig. 2 is obtained by direction. selecting the one with maximum normalizedca- The peculiar structure produced by this metric pacity. The interference effect in Eq. (7) is evalu- is due to the following reasons: ated by relying on the model presented in [22]. The switching overhead, which depends on the adopted • The metric tends to favor scatternets formed by interpiconet scheduling policy [2], has been con- a large number of piconets, since each new pic- sidered here with simple assumptions on the onet increases the overall capacity with its con- switching frequency. tribution. It can be immediately noticed that the scatternet • The interference effect is not significant since the presents a linear structure, i.e., every node is con- number of co-located piconets is low (<50). nected with two other nodes only. The value as- • When the switching overhead effect is taken into sumed by cTIðBÞ, evaluated as in Eq. (4) is 5.5. account, a BG loses capacity as a function of When switching overhead is considered cTIðBÞ the number of piconets it is connected to. Thus, decreases to 5.2727 and by considering also the high performance, in terms of capacity, is at- tained when a bridge node is connected to only two piconets.
50 master These considerations explain why path lengths Node: 12 slave have to be taken into account. However, mini- 45 bridge mizing the path lengths without considering ca- Node: 7 40 pacity at the same time, could lead to undesirable Node: 8 Node: 6 scatternet topologies too since, if the nodes are 35 Node: 4 distributed in a small area, the resulting scatternet Node: 2
meters presents a fully meshed topology where every slave 30 Node: 1 is connected to every master. In this case, the re- Node: 3 sulting capacity is low because of the high number 25 Node: 9 of BGs connected to a high number of piconets. 20 Node: 5 Node: 10 Fig. 3 refers to the metric that minimizes the av-
Node: 11 erage path length in the same scenario of Fig. 2. In 15 65 70 75 80 85 90 95 100 this case the nodes in the lower part of the figure meters (which are in radio visibility of each other) are all Fig. 2. Scatternet with maximum normalized capacity. connected. 194 T. Melodia, F. Cuomo / Ad Hoc Networks 2 (2004) 185–202
50 900 master Node: 12 Mean value slave 800 (centralized 45 bridge approach) 700 Node: 7 40 600 Node: 8 Node: 6 500 35 Node: 4 Node: 2 400
meters 30
Numberof Scatternets 300 Node: 1 Node: 3 200 25 Node: 9 100 20 Node: 5 Node: 10 0 Cmin=0.0087 0.0132 0.0166 Cmax=0.0188 Node: 11 15 Average Path Capacity 65 70 75 80 85 90 95 100 meters Fig. 5. Distribution of the values of average path capacity. Fig. 3. Scatternet with minimum average path length.
the resulting capacity available for a generic Let us now look at Fig. 4, which shows a source–destination pair was 0.0082, in the case of scatternet obtained with a metric that maximizes Fig. 4 the average path length is 2.81 and the re- the average path capacity. This metric seems to be sulting capacity per source–destination pair is the most suited to maximize network performance, 0.0109. since both capacity and path length are taken into As a result, we select as suitable TI metric the account. The scatternet of Fig. 4 presents a ca- average path capacity. In order to better analyze pacity, c B equal to 4.667 (4.5271 taking into TIð Þ the space of feasible scatternets Fig. 5 shows the account the switching overhead and 4.0483 taking histogram of the average path capacity of all pos- into account also the interference effect). The sible ‘‘BT-compliant’’ scatternets obtained in a overall capacity is smaller than the value obtained scenario constituted by 10 nodes distributed in an by maximizing the normalizedcapacity , but, while area of 25 · 25 m but, as will be shown later, a in that case the average path length was 4.33, and similar distribution holds in general. As indicated in Section 4.2 the number of different feasible to- pology is huge. The values of aTIðBÞ are distrib- 50 uted in a range starting form aTI;minðBÞ¼0:0087 master Node: 12 slave (8 kbit/s for every possible node pair) to 45 bridge aTI;maxðBÞ¼0:0188 (19 kbit/s per pair); the mean Node: 7 value of aTIðBÞ is also shown (equal to 0.0132). 40 Node: 6 Node: 8 Note that the mean value is quite distant from the 35 Node: 4 maximum value, which corresponds to the one Node: 2 associated with the optimal scatternet. Moreover,
meters 30 a few scatternets have a high value of aTIðBÞ and Node: 1 are thus contained in the right tail of the histo- Node: 3 25 Node: 9 gram. This is an interesting result because it indi- cates that topology optimization is going to be a 20 Node: 5 Node: 10 fundamental issue for Bluetooth scatternets: in Node: 11 15 fact, this distribution of the metric values means 65 70 75 80 85 90 95 100 that it is highly unlikely to obtain a high perfor- meters mance scatternet by randomly selecting a topol- Fig. 4. Scatternet with maximum average path capacity. ogy. We need to deploy protocols that not only T. Melodia, F. Cuomo / Ad Hoc Networks 2 (2004) 185–202 195
Table 2 Traffic relationships Traffic relationship Required normalized capacity Traffic relationship Required normalized capacity 1 $ 2 0.08 5 $ 6 0.125 1 $ 5 0.1 6 $ 2 0.125 3 $ 4 0.1 7 $ 8 0.05 3 $ 9 0.1 10 $ 7 0.1 4 $ 9 0.1 10 $ 8 0.05
search for a connected scatternet but also explicitly 20 Node: 7 master aim at maximizing its performance. 18 slave bridge 16 6.2. Traffic dependent metrics Node: 6 14 In this Section, we show results derived by ap- 12 Node: 5 plying the TD metrics. The scenario is composed 10 of 10 nodes; the relevant traffic relationships are meters 8 Node: 2 Node: 9 shown in Table 2. In Fig. 6 we depict the scatternet 6 with maximum residual capacity. It can be noticed Node: 8 Node: 3 that this metric suffers from the same drawbacks of 4 Node: 10 normalizedca- 2 the metric it is derived from (i.e., Node: 1 Node: 4 pacity, see Fig. 2): the resulting scatternet is likely 0 0 5 10 15 20 25 to present a linear structure. meters In Fig. 7 we show the scatternet presenting the Fig. 7. Scatternet with minimum average path length per traffic minimum average path length per traffic relation- relationship. ship, see Eq. (18). In this case the scatternet pre- sents a more connected structure, with respect to that of Fig. 6. 20 Finally, in Fig. 8 we minimize the average nor- Node: 7 mastermaster malizedload . The resulting normalized loads are 18 0.15 slaveslave bridgebridge 16 Node: 6
14 0.25 20 Node: 7 master 12 0.15 slaveslave Node: 5 18 bridgebridge 10 0.935
16 meters Node: 2 Node: 9 8 Node: 6 0.205 0.2 14 0.55 6 Node: 8 12 0.7 4 Node: 3 Node: 10 Node: 5 0.2 0.15 10 0.73 meters 2 Node: 1 Node: 4 8 Node: 2 Node: 9 0.18 0.7 0.66 0.5 0 0 5 10 15 20 25 6 Node: 3 Node: 8 meters 0.7 0.7 4 Node: 10 0.15 Fig. 8. Scatternet with minimum average load. 2 Node: 1 Node: 4 0.5 0.48 0 0 5 10 15 20 25 reported in the figure, next to each node. The meters scatternet average load is 0.3058. It can be noticed Fig. 6. Scatternet with maximum residual capacity. that nodes that are located in specific positions 196 T. Melodia, F. Cuomo / Ad Hoc Networks 2 (2004) 185–202 have to take care of all the forwarding load (i.e., Since with DSOA the nodes sequentially select traffic handled on behalf of other nodes). Never- how to connect, each node must be in TR of at theless, since reducing load means reducing energy least another already entered node. The following consumption, this scatternet consumes 70% of the proofs that it is always possible to obtain such an energy required by the scatternet of Fig. 6 (the ordering of the nodes, i.e. that this procedure al- average load for the latter scatternet is 0.4267). ways ends.
Theorem 1. Given a connected graph GðV ; EÞ, the 7. A distributed algorithm for topology optimization procedure ORDER_NODES always terminates, and jW j¼N. In this section we describe a Distributed Scat- ternet Optimization Algorithm (DSOA) that aims Proof. Suppose that at some step k of the proce- at optimizing the topology to obtain a perfor- dure, k < N, we have W ¼fw1; w2; ...; wkÀ1g and mance (in terms of the chosen metric) as close as no couple (v; w)withv 2 V n W , w 2 W exists such possible to the optimum. Note that the selection of that distðv; wÞ < TR. Therefore, since W V , there the optimized topology is decoupled from the es- exist two disconnected components, namely W and tablishment of the links that compose it, as will V n W ,ofGðV ; EÞ. h become clearer in Section 8, where we will describe a two-phases distributed scatternet formation al- At the end of this procedure, then, node k is in gorithm based on DSOA. transmission range of at least one of the nodes 1; 2; ...; k À 1. The second procedure is the core of 7.1. Distributedscatternet optimization algorithm the algorithm. Here we let eij be the link between (DSOA) the nodes wi and wj of a scatternet ði; j 2 1; ...; NÞ. This part of the algorithm is dependent on the We consider the adjacency graph GðV ; EÞ. First, selected metric M. At each step k, node wk ‘‘enters’’ We aim at obtaining an ordered set of the nodes in in the scatternet in the best possible way, accord- V . The first procedure orders the nodes in the ing to M. graph according to a simple property: a node k SCATTERNET_OPTIMIZATION_ALGORITHM must be in transmission range of at least one node (SOA) in the set 1 ...k À 1. Input: W , GðV ; EÞ, M ORDER_NODES Output:locally optimal scatternet Input: GðV ; EÞ BÃ Output: ordered set of the nodes in V , begin W ¼fwkg, k ¼ 1; 2; ::; N, N ¼jV j VM ¼ Ø begin VS ¼ Ø w1 ¼ random selection of VM ¼ VM [ w1 a node v from V VS ¼ VS [ w2 2 W ¼fw1g B ¼½1 for k ¼ 1 : N for k ¼ 3 : N wk ¼ random selection of a node v case 1) consider wk in VM from V such that: * derive all BT-compliant ma- k (1) m 62 W trices B with jVM jþ1 rows and (2) 9 u 2 W such that distance jVS j columns ðu; vÞ 6 TR calculate values of MðBkÞ W ¼ W [fwkg case 2) consider wi in VS endfor * derive all BT-compliant ma- k end trices B with jVM j rows and T. Melodia, F. Cuomo / Ad Hoc Networks 2 (2004) 185–202 197
jVSjþ1 columns the other 6 slaves has to be disconnected. How- calculate values of MðBkÞ ever, it was proven in [10] that in a piconet with at select the Bk with optimal MðBk) least 5 slaves, at least 2 of them are in TR of each if optimum in case 1) other. Thus, at least one of the slaves can become then master and select another slave. The network can VM ¼ VM [ wk therefore be reconfigured by forcing the seventh else slave that connected to wi to become master of if optimum in case 2) another slave of wi, to minimize reconfigurations. VS ¼ VS [ wk If it is not in TR of any other slave of wi, we can else try with the sixth, and so on. At least one of the six kÀ1 RECONFIGURE(B ; VM ; VSÞ slaves must be able to become master and select endif one of the other 5 as its slave. endif The local optimization in SOA (steps with endfor mark *) can be performed by means of state space end enumeration, as in the simulations results we show, or, e.g., by means of randomized local search The RECONFIGURE procedure is executed in algorithms. the (unlikely) case when wk is only in transmission The distributed version of the SOA (distributed range of master nodes that have already 7 slaves in SOA, DSOA) straightforwardly follows. At each their piconet. For the sake of simplicity, details of step k, a new node wk receives information on the this procedure are only given in the following topology selected up to that step ðBkÀ1 matrix) and proof of correctness. In this case, one of the 7 selects the role (master or slave) it will assume and slaves is forced to become master of one of the the links it will establish, with the aim of maxi- other slaves. This is shown to be always possible. mizing the global scatternet metric. If the node The following proves the correctness of SOA, becomes a master it will select a subset of the i.e. it is always possible for a node to enter the slaves in its TR already in the scatternet; if it be- network respecting the Bluetooth properties. comes a slave it will select a subset of the masters Proof of correctness. Node w2 is in transmission in its TR, already in the scatternet. ORDER_NODES range of w1, thus the two nodes can connect. Each is needed to guarantee that, when node k enters, it node wk, with k > 2 can always establish a new can connect to at least one of the previously en- piconet, thus connecting as a master, whenever a tered nodes. DSOA can be classified as a greedy node v 2fw1; w2; ...; wkÀ1g exists s.t. v 2 VS and algorithm, since it tries to achieve the optimal so- distance ðwk; vÞ 6 TR, i.e. one of the slave lution by selecting at each step the locally optimal nodes already in the network is in transmission solution, i.e. the solution that maximizes the met- range of wk. If no slaves are in transmission range ric of the overall scatternet, given local knowledge of wk, whenever a node v 2 VM exists, with and sequential decisions. Greedy algorithms do distance ðwk; vÞ 6 TR, and slaves ðvÞ <¼ 7, wk not always yield the global optimal solution. As can be a slave of v. Otherwise, at least one node will be shown in the next subsection, the results wi 2 VM must exist, with distance ðwk; vÞ 6 TR, obtained with DSOA are close to the optimum. and slaves ðvÞ¼7, with i 6 k. The RECONFIGURE procedure can always be executed in this way. If at 7.2. Examples andnumerical results step i node wi selected more than 1 slave, it can disconnect from the slave that causes the minimum In this section we show some results obtained decrease/increase in the metric value. The topology with DSOA, by using average path capacity as a is still connected, and wk can select wi as its slave. metric. As previously discussed, we believe that If, otherwise, wi selected only one slave at step i, average path capacity is a good metric since it this cannot be disconnected, since this could cause takes into account both capacity and average path loss of connectivity for the network. Thus, one of length of the scatternet. 198 T. Melodia, F. Cuomo / Ad Hoc Networks 2 (2004) 185–202
88 900 Node: 3 Node: 2 master slave Mean value 86 800 (centralized bridge approach) 84 700 Mean value 600 (distributed 82 Node: 9 approach) Node: 7 80 500 Node: 1 400 78
meters Node: 10 300 76 Node: 8 Number of Scatternets 200 74 Node: 4 Node: 6 100 72 0 ( a (B)=0.0188 70 a B)=0.0087 0.0132 0.0166 Node: 5 TI,min TI,max Average Path Capacity 68 40 45 50 55 60 65 meters Fig. 11. Comparison between results obtained with DSOA and results derived from scatternet space enumeration. Fig. 9. Scatternet formed with DSOA.
value of aTIðBÞ is also shown (equal to 0.0132). 88 Note that the mean value is quite distant from the Node: 2 master 86 bridge maximum value, which corresponds to the one Node: 3 associated with the optimal scatternet. Moreover, 84 a few scatternets have a high value of aTIðBÞ and 82 Node: 9 thus are contained in the right tail of the histo-
80 Node: 1 Node: 7 gram. This is an interesting results because it 78 suggests that topology optimization is a funda-
meters mental issue for Bluetooth scatternets: in fact, this 76 Node: 10 Node: 8 distribution for the metric values means that it is 74 Node: 4 Node: 6 highly unlikely to obtain a high performance 72 scatternet by randomly selecting a topology. We 70 need to deploy protocols that explicitly aim at Node: 5 68 maximizing performance. 40 45 50 55 60 65 As regards the DSOA, the vertical lines in Fig. meters 11 correspond to the values of aTIðBÞ for 100 dif- Fig. 10. Optimal scatternet. ferent scatternets formed by using 100 different randomly chosen sequential orders. The lines are An example is shown in Figs. 9 and 10, where concentrated in the right part of the figure (i.e., the 10 nodes are distributed in an area of 25 · 25 m scatternets formed have a value of aTIðBÞ greater (the same scenario of Fig. 5). The first figure re- than the overall mean value of all possible scat- ports the scatternet formed with the DSOA (with ternets). The mean value of aTIðBÞ of these 100 an aTIðBÞ¼0:0145). Fig. 10 depicts the optimal DSOA scatternets is equal to 0.0166. The un- scatternet (that presents an aTIðBÞ¼0:0188Þ. Fig. normalized values of the average capacity per path 11 shows a comparison between the optimal aTIðBÞ obtained with DSOA is about 17 kbit/s, while the and the one obtained with the DSOA. The dotted maximum possible value is 19 kbit/s; this confirms curve shows the histogram of the average path the good behavior of the DSOA. capacity of all possible ‘‘BT-compliant’’ scatternets Fig. 12 shows a similar distribution in a scenario feasible in this scenario. The values of aTIðBÞ are with 15 nodes in a multi-hop context. In Fig. 13 a distributed in a range starting form aTI;minðBÞ¼ distribution mediated on 100 different scenarios, 0:0087 (8 kbit/s for every possible node pair) to with varying number of nodes is shown, while Fig. aTI;maxðBÞ¼0:0188 (19 kbit/s per pair); the mean 14 reports the distribution of the values obtained T. Melodia, F. Cuomo / Ad Hoc Networks 2 (2004) 185–202 199
Fig. 14. Distribution of average path capacity for DSOA Fig. 12. Distribution of average path capacity for 15 nodes. scatternets.
spondingly, the value of the metric obtained with DSOA is close (sometimes equal) to the one ob- tained with the centralized approach. The same behavior has been observed in numerous experi- ments, carried out with different metrics and num- ber of nodes.
8. A two-phases scatternet formation algorithm
The actual Distributed Scatternet Formation Protocol is divided in two phases:
1. Tree scatternet formation (SHAPER). 2. DSOA and new connections establishment. Fig. 13. Distribution of average path capacity on different scenarios. To implement DSOA we need a mechanism to distribute the ‘‘right’’ to enter in the network to with DSOA in the same scenarios. The probability every node k at step k, and to convey the topology of obtaining a value of the metric between the op- selected by the previous k À 1 nodes (BkÀ1 matrix). timal and 70% of the optimal by randomly selecting The distributed implementation in Bluetooth a topology is very low; by using DSOA this prob- however is not simple since the system lacks a ability is close to 1. For a higher number of nodes, shared broadcast medium that would allow sig- the state-space enumeration approach, which has naling among nodes. been useful in obtaining the distribution of the A good solution which guarantees: (i) the re- metric values, becomes unfeasible. quired ordering of the nodes; (ii) synchronization of The conclusion we can draw from the above the decisions; (iii) a shared communication medium, figures is that scatternets formed with DSOA have is to form a tree-shaped ‘‘provisional’’ scatternet. a structure quite similar to the optimal ones, A tree-shaped scatternet can asynchronously obtained with the centralized approach. Corre- be formed in a distributed fashion. In [11], we 200 T. Melodia, F. Cuomo / Ad Hoc Networks 2 (2004) 185–202 proposed a new protocol for tree scatternets 1,11,25 (SHAPER), which works in an asynchronous and totally distributed fashion, thus allowing the self- 1 organized formation of a tree shaped scatternet in 2,10 7 a multi-hop context. We showed that a tree scat- 2 12,24 ternet can be formed in a few seconds time, and that less time is required when nodes are denser. 3,5,7,9 3 13,23 After the tree has formed, a simple recursive 8 visit procedure can be executed on it, which allows 8 implementing the DSOA topology optimization 14,16,18,20,22 56 process. It is easy to see that a sequential visit of all 4 4 9 nodes in the tree, from the root down to the leaves, 6 guarantees the order provided by ORDER_NODES. 10 11 12 13 We let parent(v) be the parent of v in the tree and children(v) be the set of children nodes for v. Step k 15 17 19 21 of the distributed procedure is executed on a node Fig. 15. Visit procedure on the tree. when it receives an execute_enter (BkÀ1; k) message from its parent. BkÀ1 is the matrix repre- senting the topology selected by the previously have taken their decision. Fig. 15 shows how a visited nodes. The root node resulting from SHA- simple tree, composed of 13 nodes, can be visited in PER starts the distributed execution of such pro- 25 steps to execute DSOA. The numbers inside the cedure at the expiration of a timeout. circles represent the order in DSOA, i.e., the order in which nodes enter the network. The numbers PROCEDURE ENTER (BkÀ1; k) Bk ¼ DSOAðBkÀ1Þ outside the circles represent the ‘‘path’’ followed by foreach v 2 children the B matrix in the visit procedure. send (execute_enter (Bk; k þ 1), v) The last step concerns the actual connection wait_answer() establishment. The root node broadcasts the ma- ½Bkþc; c¼answerðvÞ trix representing the final scatternet structure. The k ¼ k þ c matrix is recursively broadcasted at every level of endforeach the tree. Once a node has broadcast the matrix send (branch_entered (Bk; k), parent) down to its children in the tree, it enters the re- When a given node v starts the ENTER proce- configuration phase. During reconfiguration it can dure, it executes the DSOA, i.e. it decides how to start establishing the connections that will com- enter in the network. Then, the node randomly pose the ‘‘optimized’’ scatternet. Every link that is picks up one of its children nodes, and sends it the not already part of the tree topology has to be execute_enter(Bk, k þ 1) message. This causes established. Redundant links have to be torn the execution of the ENTER procedure on the child. down. Every node alternates between a communi- After sending the execute_enter command, v cation state and a formation state. During the latter waits for an answer message (branch_entered) the node tries to establish the new links, while from the child. This contains information about the during the former user data is transmitted so as to topology selected by the whole branch which goes guarantee the continuity of service during the re- down from v to the leaf nodes. After the answer configuration phase. from the child is received, v selects another child If a node has a master role in the optimized and does the same. When v receives the answer from scatternet, it pages its first slave. When the con- its last child, it informs its parent of the topology nection is established, it continues with the other selected by itself and by all of its descendents with ones. If the node has a slave role, it will page scan the branch_entered message. When the root for incoming connections. Priority is given to node receives the answer from its last son, all nodes previously entered masters so as to avoid dead- T. Melodia, F. Cuomo / Ad Hoc Networks 2 (2004) 185–202 201 locks. Every node starts tearing down the old links lative evaluation of the time needed to set-up a only when the new ones have been established, so scatternet and its performance in presence of dif- as to preserve connectivity. ferent traffic patterns. Since all nodes know the overall topology, the routing task is also simplified. Route discovery References algorithms have to be implemented only when mobility has to be dealt with or in other particular [1] J.C. Haartsen, The Bluetooth radio system, IEEE Personal situations. Communications 7 (1) (2000) 28–36. The most time consuming phase of the algo- [2] P. Johansson, M. Kazantzidis, R. Kapoor, M. Gerla, rithm is the formation of the tree, which, as said Bluetooth––an enabler for personal area networking, IEEE Network 15 (5) (2001) 28–37. before, becomes necessary because Bluetooth lacks [3] Bluetooth SIG Specification of the Bluetooth System, a shared broadcast medium. However, we showed Version 1.1––Core, February 2001. in [11] that the tree can be formed in a few seconds. [4] IEEE Std 802.15.1TM-2002, Available from
[16] Y. Liu, M.J. Lee, T.N. Saadawi, A Bluetooth scatternet- Francesca Cuomo received her ‘‘Lau- route structure for multihop ad hoc networks, IEEE rea’’ degree in Electrical Engineering Journal on Selected Areas in Communications 21 (2) in 1993, magna cum laude, from the University of Rome ‘‘La Sapienza’’, (2003) 229–239. Italy. She earned the Ph.D. degree in [17] M. Ajmone Marsan, C.F. Chiasserini, A. Nucci, G. Information and Communication En- Carrello, L. De Giovanni, Optimizing the topology of gineering in 1998, also from the Uni- Bluetooth Wireless Personal Area Networks, IEEE INFO- versity of Rome ‘‘La Sapienza’’. Since 1996 she is a ‘‘Researcher’’ (Assistant COMÕ02. Professor) at the INFOCOM Depart- [18] R. Kapoor, M.Y.M. Sanadidi, M. Gerla, An analysis of ment of this University. She teaches Bluetooth scatternet topologies, Proceedings of the ICC courses in Telecommunication Net- 2003, 2003. works. Her main research interests focus [19] P. Bhagwat, S.P. Rao, On the characterization of Blue- on: Modeling and Control of broadband integrated networks, tooth scatternet topologies, Available from