Ad Hoc Networks 11 (2013) Contents lists available at SciVerse ScienceDirect. Ad Hoc Networks

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1 Ad Hoc Networks (3) Contents ists avaiabe at SciVerse ScienceDirect Ad Hoc Networks journa homepage: Dynamic agent-based hierarchica muticast for wireess mesh networks Yinan Li, Ing-Ray Chen Department of Computer Science, Virginia Tech, Northern Virginia Center, 7054 Haycock Road, Fas Church, VA 243, United States artice info abstract Artice history: Received 6 August 2 Received in revised form 27 February 3 Accepted 4 March 3 Avaiabe onine 27 March 3 Keywords: Hierarchica muticast agorithm Muticast agent Wireess mesh networks Performance anaysis We propose and anayze a muticast agorithm named Dynamic Agent-based Hierarchica Muticast (DAHM) for wireess mesh networks that supports user mobiity and dynamic group membership. The objective of DAHM is to minimize the overa network cost incurred. DAHM dynamicay seects muticast routers serving as muticast agents for integrated mobiity and muticast service management, effectivey combining backbone muticast routing and oca unicast routing into an integrated agorithm. As the name suggests, DAHM empoys a two-eve hierarchica muticast structure. At the upper eve is a backbone muticast tree consisting of mesh routers with muticast agents being the eaves. At the ower eve, each muticast agent services those muticast group members within its service region. A muticast group member changes its muticast agent when it moves out of the service region of the current muticast agent. The optima service region size of a muticast agent is a critica system parameter. We propose a mode-based approach to dynamicay determine the optima service region size that achieves network cost minimization. Through a comparative performance study, we show that DAHM significanty outperforms two existing baseine muticast agorithms based on muticast tree structures with dynamic updates upon member movement and group membership changes. Ó 3 Esevier B.V. A rights reserved.. Introduction Wireess mesh networks (WMNs) are emerging in recent years as a promising cost-effective soution for providing ast-mie community-based broadband Internet access services. A WMN consists of two types of components: wireess mesh routers (MRs) and mesh cients (MCs) []. MRs form a static mesh networking infrastructure caed a wireess mesh backbone for MCs. MCs are end-user devices with wireess access capabiity, and unike MRs, they are usuay mobie and may change their ocations frequenty. A WMN is seamessy interconnected to the Internet through the gateway functionaity of MRs, Corresponding author. E-mai addresses: yinan926@vt.edu (Y. Li), irchen@vt.edu (I.-R. Chen). which can aso be used to integrate a WMN with existing wireess networks, for exampe, mobie ad hoc networks or wireess sensor networks. Generay, one or more MRs in a WMN serve as the Internet gateways and route network traffic originated from or destined to the Internet. Due to the broadcasting nature of wireess communications and the community oriented nature of WMNs, group communications [2] based on muticasting [3,4] are expected to be a common communication paradigm in WMNs. For exampe, many popuar network appications today are based on a singe-source group communication paradigm, and require efficient deivery of various types of contents, e.g., weather forecasts, stock prices, news, and rea-time audio/video streams, from a singe source to a group of mobie users in WMNs. These appications are muticasting in nature, and therefore can be efficienty /$ - see front matter Ó 3 Esevier B.V. A rights reserved.

2 684 Y. Li, I.-R. Chen / Ad Hoc Networks (3) impemented by a muticast agorithm. The mobiity of muticast group members, however, poses a chaenge to the design and deveopment of efficient muticast agorithms in WMNs. More specificay, the muticast agorithm must efficienty support user mobiity such that group members can continue to receive subscribed muticast contents and data when they move and change their serving MRs frequenty. In this paper, we propose and anayze a muticast agorithm for WMNs named Dynamic Agent-based Hierarchica Muticast (DAHM) that supports potentiay highy mobie users and dynamic muticast group membership. The contribution of the paper is as foows. First, we bring out the design notion of dynamic agent-based hierarchica muticast to minimize the overa network communication cost (in terms of traffic incurred) for packet deivery, mobiity management, and muticast tree maintenance. This directy contributes to end-to-end deay minimization and throughput maximization for muticast services in WMNs. Second, we bring out the design notion of integrated mobiity and muticast service management which empowers MRs to serve as muticast agents (MAs) for MCs dynamicay. A MC s MA is not ony the muticast packet reay station but aso the ocation database of the MC. Under our DAHM design, muticast packet routing is a two-step process. A muticast packet is first routed from the source to the MC s MA through a dynamic muticast tree connecting the source to a MAs and then is routed from the MC s MA to the MC. Packet routing is done efficienty because an MC s MA knows the ocation of the MC a the time. We achieve integrated mobiity and muticast service management by having each MC dynamicay determine whether it shoud seect the MR it just enters as its new MA, based on our anaysis resut. The optima MA service region for each MC is a critica system parameter for performance maximization in our DAHM design. The third contribution of the paper is that we deveop a mode-based approach based on stochastic Petri net (SPN) techniques [28] to determine the optima MA service region size on a per MC basis based on the MC s runtime mobiity and service characteristics, so as to maximize muticast performance. The ast but not the east contribution is that we demonstrate that DAHM outperforms two existing muticast agorithms in the iterature, namey, Regiona-Registration based Muticast (RRM) [5] and Dynamic Tree-based Muticast (DTM) through a comparative anaysis with simuation vaidation. RRM is based on a hierarchica tree structure consisting of pure unicast paths, whereas DTM is based on a shortest-path muticast tree structure [6] extended with dynamic updates upon member movement and group membership changes. The remainder of this paper is organized as foows. Section 2 surveys existing work on muticast routing and agorithms in mobie network environments and particuary in WMNs and contrasts our work with existing work. Section 3 gives a detaied introduction to DAHM. In Section 4 we deveop an anaytica mode for anayzing the performance of DAHM. Detaied performance evauation and a comparative performance study are given in Section 5, with both anaytica resuts and simuation vaidation presented. Section 6 discusses issues reated to the impementation of DAHM on rea mobie devices. The paper concudes with Section Reated work Muticast agorithms and muticast routing protocos within a mobie network environment have been intensivey studied for Mobie IP networks [7 0] and mobie ad hoc networks []. Due to significant differences in network architectura characteristics and design objectives, however, these agorithms and protocos cannot be appied to WMNs directy without major modification and performance penaty. For exampe, WMNs ack centraized management faciities such as home agents and foreign agents as in Mobie IP networks. Simiary, athough WMNs can be considered as a specia type of mobie ad hoc networks, muticast agorithms and routing protocos proposed for such networks are generay not appropriate for WMNs. The reason is that these agorithms and protocos are designed with consideration given specific to characteristics unique to mobie ad hoc networks, e.g., infrastructureessness, dynamic network topoogy, energy constraints and weak computing capabiity of mobie nodes, etc. Therefore, designing new muticast agorithms and routing protocos that take into consideration of the characteristics of WMNs is an important research topic. The research of muticast in WMNs is sti in its infancy. Very recenty a few muticast agorithms and routing protocos have been proposed for WMNs [6,2 8]. Zeng et a. [2] proposed two muticast agorithms, namey, the Leve Channe Assignment (LCA) agorithm and the Mutichanne Muticast (MCM) agorithm, with the objective to improve the muticast throughput in mutichanne and muti-interface WMNs. The agorithms focus on the construction of efficient muticast trees that minimize the number of reaying nodes and the tota hop count distance of the trees. By using a dedicated channe assignment strategy and partiay overapping channes, interference among channes is reduced and the throughput is improved. Pacifier [3] is a new muticast protoco that pursues high throughput and reiabiity. Pacifier buids an efficient muticast tree for tree-based opportunistic muticast routing to achieve high throughput, and utiizes intra-fow network coding to achieve high reiabiity, without the overhead of cassic techniques such as Automatic Repeat request (ARQ) and Forward Error Correction (FEC). Pacifier aso soves the crying baby probem such that the throughput of we-connected nodes is improved without sacrificing the throughput of poory-connected nodes. In [6], two primary methods for muticast routing, namey, shortest-path trees (SPTs) and minimum cost trees (MCTs) were investigated and evauated via extensive simuation using a variety of performance metrics such as packet deivery ratio, throughput, end-to-end deay, deay jitter, and muticast traffic overheads. Based on the comparative simuation resuts, the author recommended the SPT approach because SPTs performed consideraby better than MCTs in terms of these

3 Y. Li, I.-R. Chen / Ad Hoc Networks (3) performance metrics. DTM, one of the baseine agorithms for the comparative performance study in this paper, is essentiay based on an SPT augmented with the capabiity to perform dynamic tree updates for supporting member mobiity and dynamic group membership. In [4], a cross-ayer optimization framework was proposed for maximizing the muticast throughput in WMNs. By reaizing that the overa throughput tighty depends on per-ink data fow rates (which further depend on ink capacities controed by radio power eves on the physica ayer), the paper presented a cross-ayer framework spanning the network ayer, the ink ayer, and the physica ayer. Within the framework, the muticast routing probem and the wireess medium contention probem are iterativey soved and jointy optimized to generate optima soutions for the throughput maximization probem. Ruiz et a. [5] proposed an integrated soution for efficient muticast routing in WMNs connected to the Internet. The soution consists two components: a tree construction agorithm that buids an approximate minimum Steiner tree for efficient muticast routing, and an auto-configuration protoco that configures MRs with topoogicay correct IP addresses to achieve fu compatibiity with standard muticast routing protocos used in the Internet. Chakeres et a. [6] examined a wide range of muticast agorithms for WMNs based on the IEEE 802. standard. These agorithms provide different degrees of support to fast, efficient, and robust muticast in IEEE 802.s WMNs. Two of these agorithms are based on broadcast, namey, Defaut Broadcast (DB) which is the existing muticast agorithm in IEEE 802.s and Fast Broadcast (FB) which is an enhancement to DB. Another two agorithms are based on unicast, namey, Seective Unicast (SU) and Mutipe Unicast (MU), both of which provide robustness by L2 acknowedgments and retransmissions. The ast agorithm examined is the so-caed Ack-oriented in-mesh Muticast (AM) that aso provides robustness by packet acknowedgment and retransmission. Whie these agorithms and protocos contributed to various aspects that are key to impementing muticast in WMNs, the critica issue of supporting member mobiity and dynamic group membership during the ifetime of a muticast group was not addressed. Specificay, existing agorithms and protocos assume static muticast trees and focus on tree construction agorithms for throughput maximization. This assumption generay is not feasibe in rea mobie network environments, considering that muticast group members may be highy mobie and they may join or eave the group at arbitrary time. Further, frequent group changes due to member mobiity and dynamic group membership can cause the quaity and efficiency of a static muticast tree to degrade quicky. In contrast to these agorithms and protocos, DAHM expicity takes member mobiity and dynamic group membership into consideration and dynamicay handes mobiity management and muticast service management (muticast tree maintenance, group membership management, and muticast packet deivery) in an integrated manner foowing the design idea of micro-mobiity management [23 27]. 3. Dynamic agent-based hierarchica muticast 3.. System mode and assumptions We assume that a WMN has a singe Internet gateway, or concisey, a singe gateway. We aso assume that current and future wireess MRs are powerfu enough to host muticast agent software for integrated mobiity and muticast service management. Currenty avaiabe wireess MRs aready have good processing capabiity and expandabe memory capacity (via USB-based fash or hard drives) to be used for cooperative data caching in WMNs [9]. Therefore, we assume that they are aso capabe of performing integrated mobiity and muticast service management. We consider a muticast group that has a singe source and dynamic group topoogy and membership in a WMN. The muticast source can be in the Internet or within a WMN. If the muticast source is an MC within a WMN, the backbone muticast tree is rooted at the source. On the other hand, if the source is a host in the Internet, the backbone muticast tree is rooted at the gateway, as muticast packets wi first be routed to the gateway which is responsibe for deivering them to the group members. The muticast group is dynamic with respect to both group member ocations because of user mobiity and group membership because of member join and eave events. Thus, a muticast group may be characterized by high group dynamics in terms of member ocations and group membership. On the other hand, we assume that the source is static. Within the ifetime of a muticast group, a member may join or eave the group at arbitrary time. We assume that group member join and eave events can be modeed by Poisson processes with rates of k and, respectivey. That is, the inter-arriva and inter-departure times are exponentiay distributed with averages /k and /, respectivey. We further assume that k and have about the same vaue such that the muticast group size remains stabe over time. Fig. iustrates the two-eve hierarchica muticast structure empoyed by DAHM. We refer to a muticast group member simpy as a member. In Fig., members are abeed as MCs carrying mobie devices. For notationa convenience, we refer to an MR serving as the muticast agent for one or more members simpy as a muticast agent (MA). Any MR can be an MA when it is seected by a member to serve as the member s MA Overview DAHM is a dynamic two-eve hierarchica muticast agorithm featuring an integrated design that combines backbone muticast routing and oca unicast routing. At the upper eve of the hierarchy is the muticast tree backbone based on a shortest-path tree (SPT) rooted at the source. The muticast tree consists of MRs with the MRs at the eaves aso serving as MAs. In Fig., the muticast tree is connected by thick soid ines. At the ower eve of the hierarchy is an MA service area (a subtree rooted at an MA). In Fig., each MA s service area is connected

4 686 Y. Li, I.-R. Chen / Ad Hoc Networks (3) Fig.. The two-eve hierarchica muticast structure empoyed by DAHM. by dotted ines. To a member, the MA s service area is defined in terms of the number of hops (H) the member can be away from its MA. In Fig., the MA subtree at the bottom right has 4 members with their hop distances away from their MA being,, and 2, respectivey. Suppose H = 5 for the right bottom most member who is currenty 2 hops away from its MA. When it moves from one MR to another MR, it knows that it is sti within its MA service area, so it wi ony inform its address change to the MA instead of making the new MR it just moves into a new MA to avoid the muticast tree maintenance cost. On the other hand if H = 2, it wi make the new MR it just moves into as its new MA. This wi trigger an update to the muticast tree. In genera, the muticast tree is updated whenever an MA joins or eaves due to user mobiity and group membership changes. Muticast packets are first disseminated from the source to a the MAs via muticast routing through the SPT, and then deivered from the MAs to muticast group members individuay via oca unicast routing. The reason why unicast routing is used at the ower eve rather than muticast routing as in [,2] is twofod: The optima service region size of an MA that minimizes the overa communication cost, i.e., the optima threshod H optima for the number of hops a muticast group member can be away from its MA, can be quite diverse for different group members depending on their mobiity and service characteristics, as supported by the anaytica and simuation resuts presented in Section 5. Therefore, group members associated with the same MA can have very diverse hop distances to the MA, making the wireess broadcast advantage no onger vaid. Thus, using broadcast routing at the ower eve can adversey affect the communication cost, because the overhead of muticast routing can be consideraby high especiay when a sma number of receivers (group members associated with the same MA) are dispersed in a arge service area around the sender (the MA). Using unicast routing eiminates the need for muticast tree maintenance at the ower eve and simpifies mobiity management. Suppose that muticast routing is used at the ower eve, the need for mobiity management as we as muticast tree maintenance woud be frequent because muticast group members may have high mobiity. Specificay, when a muticast group member moves to a new serving MR, the new serving MR needs to be subscribed to and the od serving MR needs to be unsubscribed from the muticast tree rooted at the MA, thus incurring two tree maintenance operations. When the member moves out of the service region of its current MA and switches to a new MA, not ony changes to the muticast trees of both the od and new MAs need to be handed by the corresponding tree maintenance operations, group membership changes aso need to be processed. If unicast routing is empoyed at the ower eve, the overhead of muticast tree maintenance and muticast group membership

5 Y. Li, I.-R. Chen / Ad Hoc Networks (3) management at the ower eve woud be competey eiminated. The saving can be significant, considering that group members can have high mobiity and that the number of muticast groups at the ower eve can be potentiay arge. We use an SPT as the muticast backbone at the upper eve as it is shown in [6] that an SPT is superior to a minimum cost tree (MCT) such as an approximate minimum Steiner tree (MST) in terms of packet deivery ratio, throughput, average end-to-end deay, and deay average jitter. Another advantage of an SPT over a MST is that the probem of constructing a MST is NP-compete. Additionay, considering SPT instead of sophisticated tree agorithms that strive for high throughput (e.g., [2,3,7]) aows us to focus on the design and anaysis aspect of integrated mobiity and muticast service management. Indeed, we coud repace SPT with a more sophisticated agorithm and the design idea sti appies. Here we note that our idea is generic as can be appied to other network services such as mobie data access [22]. Aso note that we use hop count as in [2,6] rather than ink quaity as the metric for muticast routing in the SPT muticast backbone. This is because our focus is on network cost minimization via integrated mobiity and muticast service management and the tota network cost, defined as the tota number of hops of wireess transmissions incurred by DAHM in Section 4.2, is a function of the hop count. A MA serves as a regiona registration point for integrated mobiity and muticast service management. Each muticast group member is registered with and serviced by an MA, from which it receives muticast packets via oca unicast routing. The muticast group member aso sends its updated ocation information, i.e., the address of its current serving MR, to the MA, whenever it moves and switches to a new serving MR. Each MA maintains a ocation database that stores the up-to-date ocation information of each muticast group member it currenty services. A MA and those members it currenty services essentiay form a oca muticast group at the ower eve of the hierarchy. Like the muticast backbone, a oca muticast group is aso dynamic due to user mobiity and membership changes. Each MA covers a service region servicing a the members ocated within the region. The service region size of an MA is a key parameter controing the tradeoff between the communication cost incurred at the upper eve and that incurred at the ower eve. There exists an optima service region size that minimizes the overa communication cost. We mode the optima service region size as the optima threshod for the number of hops a member can be away from its MA, denoted by H optima. This optima threshod can be determined using the anaytica mode deveoped in Section 4. Beow we et H and H optima denote the threshod and the optima threshod, respectivey. range based on the wireess ink quaity, and sends a join request jjoin_reqj to the seected serving MR. If the new serving MR is not yet a eaf node of the muticast backbone (that is, if it is not an MA), it needs to join the backbone muticast tree as a eaf node and becomes a new MA for the MC. The MR joins the backbone muticast tree by sending jjoin_reqj to the source. Upon receiving jjoin_reqj from the MR, the source computes a shortest path to the MR and sends a join acknowedgment jjoin_ackj aong the path back to it. The MR further forwards jjoin_ackj to the MC, confirming that it becomes a new member of the muticast group. By having the MA process member join requests ocay, the signaing overhead of member join is significanty reduced. Fig. 2 iustrates the procedure for a member join event. jjoin_reqj and jjoin_ackj aso serve as an association request and an association acknowedgment, respectivey Member eave When a member eaves a muticast group, it notifies its MA such that the MA can deregister it. After the member eaves, the MA may no onger service any member, therefore it needs to be removed from the backbone muticast tree. The procedure for a member eave event is iustrated in Fig. 3. More specificay, the eaving member sends a eave request jleave_reqj to its MA, which responds with a eave acknowedgment jleave_ackj as a confirmation. If the MA needs to remove itsef from the backbone muticast tree because it no onger services any member, it forwards jleave_reqj to the source. Upon receiving jleave_reqj Fig. 2. Message exchange sequence for a member join event Member join and eave Member join A MC who intends to join a muticast group first seects a serving MR among a MRs within the wireess transmission Fig. 3. Message exchange sequence for a member eave event (dashed ines mean conditiona message exchanges).

6 688 Y. Li, I.-R. Chen / Ad Hoc Networks (3) from the MA, the source updates the backbone muticast tree and sends the MA a eave acknowedgment jleave_ackj in repy to the request. In some cases, a member disconnects (either vountariy or invountariy) and therefore is not abe to notify its MA. In DAHM, a member that disconnects is treated as a eaving member. The disconnection of a member can be detected by its MA when the MA tries to deiver muticast packets to the member. Once a member is detected to be disconnected, its MA deregister it and the MA needs to remove itsef from the backbone muticast tree if it no onger services any member Mobiity management and tree maintenance In DAHM, when a member moves and changes its serving MR, the foowing procedure is executed to hande the mobiity management and muticast tree maintenance: When the member moves and switches to a new MR, it sends an association request jasso_reqj to the new MR. The MR responds with an association acknowedgment jasso_ackj in repy to the request, confirming that the association is competed and the MR becomes the new serving MR of the member. If the new serving MR is not an MA and is within the service region of the member s MA, the member sends to its MA a ocation registration request jloc_reg_reqj containing the address of the new MR. The MA updates the member s ocation information and sends a ocation registration acknowedgment jloc_reg_ackj back to the member. In this way, the MA aways knows the up-to-date ocation information of members within its service region and is therefore abe to deiver muticast packets to them individuay through unicast routing. If the new serving MR is H hops away from the member s current MA, the threshod is reached and the new MR needs to join the backbone muticast tree as a eaf node and becomes the new MA of the member. In this case, a join request jjoin_reqj is sent to the source. Upon receiving jjoin_reqj from the MR, the source computes a shortest path to the MR and sends a join acknowedgment jjoin_ackj aong the path back to it. Fig. 4 shows the message exchange sequence in the case that the new MR is H hops away from the member s current MA. If the new MR is aready an MA, the member switches to the new MA and starts receiving muticast packets from the new MA. Fig. 5 shows the message exchange sequence in the case that the new MR is aready an MA. After being associated with the new MA, the member sends a deassociation request jdeasso_reqj to its od MA, which responds with a deassociation acknowedgment jdeasso_ackj. If the member s od MA no onger services any member, it removes itsef from the muticast tree by sending a eave request jleave_reqj to the source. Upon receiving jleave_reqj from the MA, the source updates the backbone muticast tree and sends the MA a eave acknowedgment jleave_ackj as a confirmation Muticast packet deivery In DAHM, muticast packets are deivered in a hierarchica manner from the muticast source to the muticast group members within a WMN. More specificay, muticast packet deivery in DAHM foows the foowing procedure: If the source is a host in the Internet, it wi first send muticast packets to the gateway, which is then responsibe for distributing the packet to the MAs. The gateway can be considered as a virtua source in this case. For each muticast packet, the (virtua) source creates a new packet that encapsuates the muticast payoad using a muticast address for the destination address fied, and disseminates the new packet to the MAs through the backbone muticast tree in muticast routing mode. Upon receiving the packet, each MA decapsuates the packet and encapsuates the payoad using the address of the serving MR of each member it services for the destination fied, and forwards the new packet to the MR via unicast routing. The address of the serving MR of each member can be found in the MA s ocation database. Each MR after receiving the muticast packet decapsuates the packet and deivers the packet to the designated member. 4. Performance mode In this section, we deveop a probabiity mode based on SPN techniques [28 3] for evauating the performance of DAHM. We choose SPN as the too for performance modeing because: () an SPN mode is a concise representation of the underying Markov or semi-markov chain that may have a arge number of states; (2) an SPN mode is capabe of reasoning the behavior of a member, as it migrates among states in response to system events. Tabe ists the parameters and notations used in the foowing sections. The physica meaning of the mobiity rate denoted by r is the average number of serving MR changes made by a muticast group member per time unit. The time unit used in this paper is second. If a group member moves and changes its serving MR once every 0 min, its mobiity rate is. The physica meanings of other 600 parameters are cear from the context. 4.. Stochastic Petri Net (SPN) Mode We assume that a WMN is structured as a two-dimensiona n n mesh with wraparound on the boundary such that each MR has exacty four neighbors, as iustrated in Fig. 6. Each MR can communicate directy with any of its four neighbors that are within its communication range. A member can change randomy from its current serving MR to any of the MR s four neighbors with equa probabiities of. The tota number of MRs in the network denoted 4 by N is simpy given by N = n 2. The average unicast path

7 Y. Li, I.-R. Chen / Ad Hoc Networks (3) Fig. 4. Message exchange sequence for the case that the new MR is H hops away from the member s current MA. Fig. 5. Message exchange sequence for the case that the new MR is aready an MA. Tabe Parameters and notations used in performance modeing and anaysis. Parameter r k p SMR k M n N c a x P MA P 0 P P MA N MA H T j L d Notation The average mobiity rate of muticast group members The muticast packet rate Service to mobiity ratio, defined as SMR ¼ kp r The rate of member join events The rate of member eave events The muticast group size The dimension of the WMN The number of MRs in the WMN The member density The average unicast path ength of the WMN The arriva rate of a singe member to an arbitrary MR The probabiity that an arbitrary MR is aso an MA The probabiity that an MR is not covering any member The probabiity that an MR covers exacty one member The probabiity that an MA services exacty one member The number of MAs The service region size of an MA The muticast tree size in terms of the tota number of tree nodes The muticast scaing factor The expected hop distance from the source to an MA The average degree of inner nodes Fig. 6. An n n mesh network mode.

8 690 Y. Li, I.-R. Chen / Ad Hoc Networks (3) ength (hop count) denoted by a in this n n mesh network mode is given by [32]: a ¼ 2n 3 ðþ We mode the process of arriva and departure of M muticast members to and from an MR using an M/M//M queue. Fig. 7 depicts the Markov chain for the M/M//M queueing mode, where x means the arriva rate of a singe member to an arbitrary MR, and is given by [7]: r x ¼ n 2 Using the M/M//M queueing mode, the probabiity P 0 that an MR covers no members and the probabiity P that an MR covers exacty one member can be derived as: P 0 ¼ M ð3þ n 2 P ¼ M M ð4þ n 2 n 2 ð2þ The dashed-ine square within the mesh structure shown in Fig. 6 iustrates the service region of an MA. Given that the threshod of the number of hops a member can be away from its MA is H, the number of MRs within the service region of an MA on average is 2H 2 2H +, in the n n mesh network mode. The probabiity denoted by P MA that an arbitrary MR is an MA in DAHM is therefore approximated by: P MA ¼ 2H 2 2H þ ð5þ Here we note that P MA given above is ony approximate because which MR is chosen as an MA for a muticast member depends on the user s mobiity. However, as vaidated by simuation reported in Section 5.3, this approximation does not affect the resut accuracy. A MA services exacty one member if a the MRs within its service region totay service exacty one member. Therefore, the probabiity denoted by P MA that an MA services exacty one member can be cacuated as foows: P MA ¼ 2H2 2H þ! P 2H2 2H 0 P ð6þ At the upper eve of the hierarchy, the number of MRs (incuding MAs) comprising the backbone muticast tree can be derived using the foowing method. First, the ratio of the tota number of muticast inks (among MRs) on the tree denoted by L m over the average unicast path ength of the network denoted by a is given by a power-aw [33,34] as foows: L m a ¼ Rj ) L m ¼ a R j ð7þ where j is the muticast scaing factor, and is found to be cose to 0.7 [33]. R denotes the number of eaves on the muticast tree, i.e., the number of MAs, and is cacuated as: R ¼ N MA ¼ P MA N ð8þ Given L m, the tota number of MRs (incuding the MAs) on the backbone muticast tree denoted by T is given as: T ¼ L m þ ¼ a ðn MA Þ j þ ð9þ The expected hop distance L from the source to an MA is the average ength of a paths from the source to the MAs, or, equivaenty stated, it is equa to the average depth of a MAs (eaves) on the backbone muticast tree rooted at the source. Hence, assuming a perfecty baanced backbone muticast tree, L is cacuated as foows: L ¼ og d T ð0þ where d is the degree of an inner node (we use d = 4 because each inner node has four neighbors). The optima threshod for the number of hops a member can be away from its MA, denoted by H optima, can be determined by using the SPN mode. Fig. 8 shows the SPN mode for describing the behavior of a singe group member. An SPN mode consists of paces, tokens, and Fig. 7. The Markov chain modeing the process of arriva and departure of M muticast group members to and from an MR. Fig. 8. The SPN mode for DAHM.

9 Y. Li, I.-R. Chen / Ad Hoc Networks (3) Tabe 2 The meanings of paces and transitions defined in the SPN mode for DAHM. Symbo Movement Hops Move MC2MA Join Reset Meaning jmark (Movement) = j means that the member moves and switches to a new serving MR jmark (Hops)j returns the number of hops the member is away from its MA A timed transition modeing the movement of the member A timed transition modeing the regiona ocation registration event A timed transition modeing that the new serving MR joins the muticast tree as a eaf node and becomes a new MA A timed transition modeing the event of registering with the new MR that is aready an MA transitions (for modeing events). Tabe 2 expains the meanings of paces and transitions defined in the SPN mode. In Fig. 8 we put in numbers in parenthesis to abe the SPN mode sequence beow. The SPN mode is constructed as foows:. The event of member movement is modeed by transition Move, the rate of which is r. When a member moves and switches to a new serving MR, a token is put into pace Movement. 2. The new MR may be either an ordinary MR or an MA. The SPN mode distinguishes between these two cases using two immediate transitions P and P2 that are associated with probabiities P MA and P MA, respectivey. 3. In the first case that the new MR is not an MA, the member sends its current MA a jloc_reg_reqj message that contains the address of the new serving MR. Upon receiving the message, the MA updates the ocation information of the member stored in the ocation database, and acknowedges the ocation update by a jloc_reg_ackj message. The message exchange is modeed by transition MC2MA. 4. After transition MC2MA is fired, a token is put into pace Hops. The number of tokens denoted by mark(hops) in pace Hops represents the number of hops the member is away from its MA. 5. When the number of tokens in pace Hops reaches the threshod denoted by H, i.e., when mark(hops) = H, transition Join is fired, modeing that the new serving MR joins the backbone muticast tree as a eaf node and becomes the new MA of the member. The firing of transition Join consumes a the tokens in pace Hops. 6. In the second case that the new MR is aready an MA, the member registers with the new MA, and starts receiving muticast packets from the new MA. This is modeed by transition Reset, the firing of which consumes a the tokens in pace Hops, meaning that the member is now directy serviced by the new MA and the hop counter is reset Performance metrics We use the average tota communication cost incurred per member per time unit (second) as the metric for performance evauation and anaysis, and the objective is to minimize this cost. In Section 5.4, we discuss how cost minimization is reated to throughput maximization and end-to-end deay minimization. We define the tota communication cost as the tota number of hops of wireess transmissions incurred, corresponding to the tota traffic incurred to the network since each hop invoves a packet transmission or reay. For exampe, the service cost incurred per muticast packet deivery per member is given by the average number of hops traveed per packet from the source to any member. More specificay, the average tota communication cost incurred per member per time unit by DAHM, denoted by C DAHM, incudes the service cost for muticast packet deivery denoted by k p C s, the signaing cost for mobiity management denoted by r C m, the signaing cost for processing member join requests denoted by k C j, and the signaing cost for processing member eave requests denoted by C. The equation for cacuating C DAHM is therefore given as foows: C DAHM ¼ k p C s þ r C m þ k C j þ C ðþ Here we note that H represents the service region size of an MA and hence the optima service region size is the optima H vaue (H optima ) under which C DAHM in Eq. () is maximized. C s, the service cost incurred per muticast group member per muticast packet deivery in DAHM, consists of two parts. The first part denoted by C s is the tota cost for disseminating the muticast packet from the source to a the MAs through the backbone muticast tree, namey T, divided by the muticast group size M. The number of wireess transmissions required to deiver a muticast packet from the source to the MAs (i.e., C s ) equas T because each MR on the tree transmits the packet ony once to a its downstream chidren [35]. The second part denoted by C 2 s is the average cost for deivering the muticast packet via unicast routing from an MA to a member it currenty services. Since a member can be i hops away from its MA with probabiity P i (0 6 i 6 H ), C 2 s is given by the probabiity-weighted average distance between the member and its MA. Therefore, C s is the sum of the two parts: C s ¼ C s þ C2 s ¼ T i¼h M þ X P i i i¼0 ð2þ C m, the mobiity management cost incurred per group member, depends on the event triggered by the movement of a member. More specificay, the mobiity management cost is incurred when there is an MA join (Join in the SPN mode), MA reset (Reset in the SPN mode), or MA update (MC2MA in the SPN mode) event as foows: MA join: When the new serving MR of a member is H hops away from its MA after a movement, the new serving MR needs to join the backbone muticast tree as a

10 692 Y. Li, I.-R. Chen / Ad Hoc Networks (3) eaf node and becomes the new MA of the member. In this event, the member competes the association with the new MR by sending an jasso_reqj message to it, which responds with an jasso_ackj message as an acknowedgment. The new MR joins the tree by sending a jjoin_reqj message to the source, which computes a shortest path to the MR and sends a jjoin_ackj message aong the path back to it. With probabiity P MA, the member s od MA no onger services any member, and it removes itsef from the backbone muticast tree by sending a jleave_reqj message to the source, which updates the tree and sends the MA a jleave_ackj message. MA reset: When the new serving MR of the member is aready an MA, the member switches to the new MA. In this event, the member competes the association with the new MA by sending an jasso_reqj message to the MA, which responds with an jasso_ackj message as an acknowedgment. After being associated with the new MA, the member sends a jdeasso_reqj message to its od MA, which responds with a jdeasso_ackjj message. With probabiity P MA, the member s od MA no onger services any member, and it removes itsef from the backbone muticast tree by sending a jleave_reqjj message to the source, which updates the tree and sends the MA a jleave_ackj message. MA update: When a member moves and changes its serving MR, the member sends to its MA a jloc_reg_reqj message containing the address of the new serving MR. The MA updates the ocation information of the member stored in the ocation database, and acknowedges the ocation update by a jloc_reg_ackj message. Based on the discussion above, C m is given by: 8 2 þ 2H þðþp MA Þ2L ifjoin00 >< 2 þ 2h þ P MA C m ¼ 2L ifreset00 2 þ 2h ifmc2ma00 >: ð3þ where h = mark(hops) represents the distance between the member and its MA. We use P MA for the probabiity that the member is the ony one currenty serviced by its MA. Therefore, once the ony member eaves, the MA wi no onger service any member, and it shoud be removed from the backbone muticast tree. C j, the signaing cost per member join event, is computed as foows. A MC joins an existing muticast group by sending a jjoin_reqj message to its newy seected serving MR. With probabiity P MA, the new serving MR is not yet a eaf node of the muticast backbone, and it needs to join the backbone muticast tree as a eaf node and becomes a new MA for the MC. The MR joins the muticast tree by sending jjoin_reqj to the source, which responds with a jjoin_ackj message as an acknowedgment. The MR further forwards jjoin_ackj to the MC, confirming that it becomes a new member of the muticast group. Therefore, C j is cacuated as: C j ¼ 2 þð P MA Þ2L ð4þ C, the signaing cost per member eave event, is computed as foows. The eaving member sends a jleave_reqj message to its MA, which responds with a jleave_ackj message as a confirmation. With probabiity P MA, the MA needs to remove itsef from the backbone muticast tree because it no onger services any member, and it forwards jleave_reqj to the source, which updates the backbone muticast tree and sends the MA a jleave_ackj message in repy to the request. Therefore, C is cacuated as: C ¼ 2 þ 2h þ P MA 2L ð5þ where h = mark(hops) represents the distance between the member and its MA. 5. Performance anaysis and numerica resuts In this section, we evauate the performance of the proposed hierarchica muticast agorithms, namey, DAHM, and the effect of various parameters on its performance. We aso compare DAHM with two baseine muticast agorithms for WMNs, namey, Regiona-Registration based Muticast (RRM) [5] and Dynamic Tree-based Muticast (DTM). Like DAHM, RRM is aso a hierarchica muticast agorithm and it aso empoys MAs for integrated mobiity and muticast service management. However, the hierarchica tree structure in RRM is simpy a union of pure unicast paths from the source to the group members. Therefore, RRM is a hierarchica unicast-based muticast agorithm. DTM transmits muticast packets through a dynamic shortest-path muticast tree whose eaves are MRs that directy service the members. The muticast tree in DTM is updated to maintain its structura properties every time a member moves and changes its serving MR. Therefore, DTM is essentiay based on the existing muticast agorithm that reies on a shortest-path tree [7] augmented with the capabiity to perform dynamic tree updates for supporting member mobiity and dynamic group membership. To evauate the effect of user mobiity on the performance of the three agorithms, we introduce a parameter caed service to mobiity ratio (SMR) defined as SMR= kp r. The physica meaning of SMR is the average number of muticast data packets transmitted from the source to a group member during the interva between two serving MR changes of the group member. SMR is an important parameter because it captures the service and mobiity characteristics of a group member, both of which can have a significant impact on the operations of DAHM and on the overa network cost. Tabe 3 ists the parameters and their vaues used in performance evauation. These vaues are seected to demonstrate diversey sized muticast groups consisting of mobie members characterized by a broad range of SMR. The member join and eave rates are chosen to aow dynamicay changing group membership, whie maintaining a stabe muticast group size. The range of n is seected to mode WMNs of reasonaby diverse sizes.

11 Y. Li, I.-R. Chen / Ad Hoc Networks (3) Tabe 3 Parameters and their typica vaues used in performance evauation. Parameter Meaning Typica vaue M Muticast group size [0,3] n Network size [5,5] k Muticast member join to eave rate ratio SMR Service to mobiity rate [8,6000] 5.. Performance evauation In this section we report anaytica resuts obtained from evauating Eqs. () (5). Specificay, we obtain the anaytica resuts by first assigning a state-dependent cost (specified by Eqs. (2) (4) or (5)) to each state of the underying semi-markov chain of the SPN mode, and then computing C DAHM (specified by Eq. ()) by the state probabiity-weighted average cost, using the SPNP package [28]. Fig. 9 pots C DAHM as a function of the threshod H, under different muticast group sizes. It can be seen in the figure that there exists an optima threshod H optima that minimizes C DAHM for each different M. Fig. 0 further shows C DAHM as a function of the threshod H, under different n n network sizes. Again, the optima threshod H optima exists for each different n. These resuts demonstrate that the service region size of an MA is key to the performance of DAHM, and there exists an optima service region size that optimizes the performance of DAHM. The optima service region size exists because of the tradeoff between the communication cost incurred at the upper eve and that incurred at the ower eve. Fig. pots C DAHM as a function of the member density denoted by c, which is defined as c ¼ M, i.e., the average N number of members serviced by one MR. As the figure shows, C DAHM decreases monotonicay with increasing c. This iustrates that muticast efficiency improves as the member density increases because the cost is effectivey amortized by the increasing member popuation. The improvement in muticast efficiency is particuary significant at the upper eve because the number of nodes on the backbone muticast tree increases subineary with increasing MAs (j <.0). Fig. 2 shows the optima threshod H optima as a function of c. It can be seen in the figure that H optima decreases as c increases, and it drops to when c is reasonaby arge. The service cost C s for muticast packet deivery in DAHM and accordingy C DAHM decreases with decreasing H optima, because the average distance over which muticast packets are transmitted at the ower eve decreases. Therefore, the resut conforms to the trend exhibited in Fig.. 50 C tota 90 M = 80 M = M = M = H γ Fig.. Cost vs. c in DAHM. Fig. 9. Cost vs. H, under different muticast group sizes in DAHM (n = 0) n = 2 n = 0 n = 8 n = H Fig. 0. Cost vs. H, under different network sizes in DAHM (M = 50). H optima 7 Optima H γ Fig. 2. H optima vs. c in DAHM.

12 694 Y. Li, I.-R. Chen / Ad Hoc Networks (3) Comparative performance study In this section, we compare DAHM with RRM and DTM, in terms of the average tota communication cost incurred per member per time unit. RRM is a hierarchica muticast agorithm based purey on unicast routing. It is worth emphasizing that because the tota communication cost is a per member per time unit metric, even a sma cost reduction of 5 0% wi be significant over time and over the entire group of members. For RRM (DTM), the average tota communication cost incurred per member per time unit denoted by C RRM (C DTM respectivey) consists of the service cost for muticast packet deivery denoted by k p C RRM s ðk p C DTM s respectivey), the signaing cost for mobiity management and muticast tree maintenance denoted by r C RRM m ðr CDTM m respectivey), the signaing cost for processing member join requests denoted by k C RRM j ðk C DTM j respectivey), and the signaing cost for processing member eave requests denoted by C RRM ð C DTM respectivey). The foowing equations cacuate C RRM and C DTM : C RRM ¼ k p C RRM s þ r C RRM m C DTM ¼ k p C DTM s þ r C DTM m þ k CRRM j þ C RRM þ k CDTM j þ C DTM ð6þ The service cost for muticast packet deivery in RRM denoted by C RRM s consists of the cost of forwarding the packet from the source to the MAs and the cost of deivering the packet from the MAs to the group members they service, both via unicast routing. Therefore, C RRM s is cacuated as: C RRM s C RRM m ¼ i¼h M ðn MA L þ M X P i iþ i¼0 ð7þ depends on the event triggered by the movement of a muticast group member. The equation for cacuating C RRM m is the same as that for cacuating C m in DAHM. Additionay, the equations for cacuating C RRM j and C RRM are aso the same as those for cacuating the same cost terms in DAHM, because DAHM and RRM share the same message sequences for muticast structure maintenance and member join and eave events. The service cost per muticast packet deivery in DTM is equivaent to the number of nodes on the muticast tree because each MR on the tree ony transmits the packet once to its downstream chidren. Therefore, the service cost incurred per member is: C DTM s ¼ T DTM M ð8þ where T DTM denotes the number of tree nodes on the shortest-path muticast tree in DTM. T DTM can be cacuated according to the power-aw [33,34] as: T DTM ¼ ar j þ ð9þ where R denotes the number of eaf nodes on the muticast tree in DTM, i.e., the number of MRs that service at east one member, which is simpy R =( P 0 ) N. The tree maintenance cost in DTM consists of the costs of MR association and deassociation, and possiby the costs of muticast tree updates, as cacuated by the foowing equation: C DTM m ¼ 4 þðp 0 þ P Þ2L ðþ In DTM, when a member joins a muticast group, it estabishes the association with a serving MR. With probabiity P 0, the MR needs to join the muticast tree as a eaf node because it is not aready a node on the tree. When a member eaves a muticast group, its association with its current serving MR is canceed. With probabiity P, the member is the ony one that the MR services, and the MR needs to remove itsef from the muticast tree because it wi no onger service any member. Therefore, C DTM j are cacuated as foows: C DTM and C DTM j ¼ 2 þ P 0 2L ð2þ C DTM ¼ 2 þ P 2L ð22þ Fig. 3 compares the average tota communication cost incurred per member per time unit by the three agorithms as a function of the muticast group size M. As can be seen in the figure, the cost decreases as M increases for a three agorithms. The reason is that the member density increases as M increases, given that n is fixed. This observation eads to the generaized concusion that muticast efficiency improves as the member density increases. It can aso be seen in the figure that DAHM is superior to both RRM and DTM. Fig. 4 compares the tota communication cost incurred per member per time unit by the three agorithms as a function of the network size n. As can be seen in the figure, for a the three agorithms, the cost increases with increasing n. This is because the member density decreases as n increases, given that M is fixed. Therefore, this observation aso generaizes to the concusion that muticast efficiency improves as the member density increases. Again, DAHM shows significanty better performance than both RRM and DTM. It is worth emphasizing again that because the tota communication cost is a per member per time unit metric, even a sma cost reduction of 5 0% wi be significant over time and over the entire group of members. Fig. 5 studies the effect of the mobiity rate denoted by r on the performance of the three agorithms, under RRM DTM DAHM M Fig. 3. Performance comparison: cost vs. M(n = 0).

13 Y. Li, I.-R. Chen / Ad Hoc Networks (3) RRM DTM DAHM n Fig. 4. Performance comparison: cost vs. n(m = 50). different member densities. As can be seen in the figure, as SMR increases, the costs decrease monotonicay because the contribution of the signaing cost for mobiity management and muticast tree maintenance to the tota communication cost decreases accordingy. As the figures show, DAHM performs consistenty better than RRM and DTM over a wide range of SMR and the member density. DAHM copes we with the impact of high user mobiity compared with RRM and DTM, due to its capabiity to dynamicay seect the optima service region size of an MA (i.e. H optima ) that minimizes the tota communication cost. RRM outperforms DTM when the members are highy mobie and the member density is ow. However, the advantage diminishes as the member density increases. When the members have high mobiity, DTM incurs a substantiay arger signaing cost for mobiity management and muticast tree maintenance, compared with DAHM and RRM. This is because DTM performs mobiity management and tree maintenance every time a member moves and changes its serving MR. Additionay, when the member density is ow, i.e., when a sma number of members are sparsey distributed within the network, the muticast tree in DTM has a reativey arge number of non-eaf MRs, eading to a reativey arge cost for muticast packet deivery RRM DTM DAHM SMR RRM DTM DAHM SMR RRM DTM DAHM SMR 5.3. Simuation vaidation Here we conduct simuation experiments to vaidate the numerica data obtained in the previous sections. We impement the simuation system using a discrete event simuation anguage caed Simuation Mode Programming Language (SMPL) [36]. In this simuation system, a operations in DAHM are represented by discrete events associated with costs. For exampe, ocation update operations, muticast packet deiveries, member join/eave operations, and muticast tree maintenance operations, are a discrete events. Events are schedued and executed in event occurrence time order, according to the agorithm description presented in Section 3. The average tota communication cost incurred per member per time unit is evauated and the mean cost is cacuated periodicay with an interva of min in simuation time. To ensure the statistica significance of simuation resuts, we use batch mean anaysis (BMA) techniques [36]. Each simuation RRM DTM DAHM SMR Fig. 5. Performance comparison: cost vs. SMR under different member densities. batch consists of a arge number of runs and therefore a arge number of observations for computing an average.

14 696 Y. Li, I.-R. Chen / Ad Hoc Networks (3) The simuation runs for a minimum of 0 batches, and stops unti the cacuated mean cost is within 5% from the true mean with a confidence eve of 95%. Fig. 6 shows the anaytica resuts vs. the simuation resuts for C DAHM as a function of H, under different muticast group sizes. As the figure iustrates, the simuation resuts show exceent correations with the anaytica resuts. This justifies that the anaytica resuts are vaid and there exists an optima service region size of an MA, under which DAHM is optimized. Simiary, exceent correations between the anaytica resuts and simuation resuts can be seen in Fig. 7, which iustrates the anaytica resuts vs. the simuation resuts for C DAHM as a function of c. Figs. 8 and 9 pot the anaytica resuts vs. the simuation resuts for the performance comparison among the three agorithms, as a function of M and n, respectivey. Again, the anaytica resuts are we correated with the simuation resuts in both figures. The perfect correation between the anaytica resuts and simuation resuts shown above justifies that the anaytica resuts obtained in the paper are vaid Discussion Based on the anaytica and simuation resuts presented above, we can draw the concusion that DAHM Anaytica; M = Simuated; M = Anaytica; M = Simuated; M = Anaytica; M = 80 Simuated; M = 80 Anaytica; M = 60 Simuated; M = H Fig. 6. Anaytica modeing vs. simuation: cost vs. H, under different muticast group sizes in DAHM (n = 0) Anaytica Simuated γ Fig. 7. Anaytica modeing vs. simuation: cost vs. c in DAHM Anaytica; RRM Simuated; RRM Anaytica; DTM Simuated; DTM Anaytica; DAHM Simuated; DAHM M Fig. 8. Anaytica modeing vs. simuation: cost vs. M(n = 0) Anaytica; RRM Simuated; RRM Anaytica; DTM Simuated; DTM Anaytica; DAHM Simuated; DAHM n Fig. 9. Anaytica modeing vs. simuation: cost vs. n(m = 50). significanty outperforms both RRM and DTM in a broad spectrum of configurations. This is because DAHM combines backbone muticast routing and oca unicast routing into an integrated agorithm, and dynamicay determines the optima service region size of MAs to optimize muticast packet deivery, muticast tree maintenance, and group membership management coectivey. Compared with RRM, the packet deivery cost at the upper eve of the hierarchy in DAHM is significanty reduced. Compared with DTM, in addition to the reduction of the muticast packet deivery cost, the signaing cost for muticast tree maintenance and membership management in DAHM is significanty reduced. The performance metric discussed thus far is based on C DAHM (specified by Eq. ()) which is the number of hops of wireess transmissions incurred per MC per time unit. Beow we reate C DAHM minimization with end-to-end deay minimization and throughput maximization. Since every hop incurs a packet transmission by an MR, C DAHM essentiay is the amount of traffic incurred to the network per MC. Let C DAHM,i denote the traffic generated by MC i. Then, the tota traffic incurred to the network by a MCs is given by P i C DAHM;i. Consequenty, the average input traffic toward each MR in the system is the tota traffic divided by the number of MRs in the network. By utiizing simpe arguments of coision theory [38] and queueing theory

15 Y. Li, I.-R. Chen / Ad Hoc Networks (3) [39], it can be proven that the per-hop packet deay (incuding the queueing deay and the retransmission deay because of coision) at any MR is minimized when the input traffic to the MR is minimized. Consequenty, the end-to-end deay of a muticast packet to an MC is aso minimized. By Litte s Law [39] which states that throughput mutipied with response time (end-to-end deay) is equa to the MC popuation, we can deduce that the network throughput is maximized when the end-to-end deay is minimized, which happens when MC i operates at the optima H optima vaue as identified in our anaysis to minimize C DAHM,i. 6. Practicabiity and impementation We discuss in this section practica issues reated to the impementation of DAHM on rea mobie devices that can be highy diverse with respect to their computing power and storage capacity. One important issue is how to dynamicay determine H optima at runtime. For powerfu mobie devices that are equipped with state-of-the-art processors, the computationa procedure deveoped in this paper can be easiy executed to determine H optima at runtime on a periodic basis. For mobie devices that are ess powerfu, a simpe tabe-ookup approach can be used to determine H optima at runtime. The ookup tabe ists the optima service region size H optima for minimizing C DAHM in Eq. (), given a set of input parameter vaues as input. The tabe is buit by appying the computationa procedure deveoped in the paper at design time over a perceivabe range of input parameter vaues (as isted in Tabe 3) specifying the operationa and environment conditions. At runtime, H optima can be determined by ooking up in the tabe using the estimated vaues of those parameters as keys. Overa, the impementation can be ightweight and very efficient. To execute the computationa procedure presented in the paper, a mobie device needs to first coect data for estimating the vaues of parameters such as the mobiity rate (r), the muticast packet rate (k p ), and the rates of member join/eave events (k and ). r can be estimated periodicay by an MC by counting the number of serving MR changes during a fixed interva, say, every min. A serving MR change can be detected by a change in the ID number of the current serving MR. Specificay, the MC maintains a counter for the number of serving MR changes, and the counter is incremented whenever the MC changes its serving MR. At the end of each interva, the mobiity rate is cacuated and the counter is reset. Simiary, the MC can dynamicay estimate k p by monitoring the sequence numbers of received muticast packets. k and can be monitored dynamicay by the source and periodicay distributed to the group members. 7. Concusion In this paper, we proposed an efficient muticast agorithms for WMNs, namey, Dynamic Agent-based Hierarchica Muticast (DAHM), which supports member mobiity and dynamic group membership during the ifetime of a muticast group. DAHM empoys a dynamic two-eve hierarchica muticast structure, consisting of an upper-eve backbone muticast tree rooted at the source with MAs as eaves, and ower-eve oca muticast groups rooted at the MAs. DAHM everages and dynamicay seects MAs for integrated mobiity and muticast service management. MAs are dynamicay seected and added to or removed from the backbone muticast tree due to the mobiity of muticast group members and dynamic group membership changes. The optima service region size of an MA that optimizes the performance of DAHM can be dynamicay determined using the anaytica method presented in the paper. Based on the anaytica and simuation resuts obtained through a comparative performance study, we showed that DAHM significanty outperforms two baseine muticast agorithms for WMNs, namey, Regiona-Registration based Muticast (RRM) and Dynamic Tree-based Muticast (DTM). There are severa research directions extending from this work, incuding (a) investigating how the proposed muticast agorithm can be adapted to support mutipe muticast groups simutaneousy active in a WMN; (b) utiizing MCs in addition to MRs serving as MAs when a group member cannot find a nearby MR and must rey on other MCs for network traffic reaying; (c) considering the effect of ossy and heterogeneous inks of WMNs as in [37] to enhance muticast service performance; (d) conducting more simuation vaidation based on ns3 in addition to SMPL; and (e) investigating how DAHM can be augmented and optimized to support reiabe and secure muticast in WMNs. References [] I.F. Akyidiz, X. Wang, W. 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Yinan Li received the B.S. degree from Xi an Jiaotong University in China, the M.S. degree from the University of Tennessee in 08, and the Ph.D. degree from Virginia Tech in 2, a in Computer Science. His research interests incude wireess networks, mobie ad hoc networks, sensor networks, network security, high performance computing, and dependabe computing. Ing-Ray Chen received the B.S. degree from the Nationa Taiwan University, Taipei, Taiwan, and the MS and Ph.D. degrees in computer science from the University of Houston. He is a professor in the Department of Computer Science at Virginia Tech. His research interests incude mobie computing, wireess systems, security, trust management, data management, rea-time inteigent systems, and reiabiity and performance anaysis. He is currenty serves as an editor for IEEE Communications Letters, IEEE Transactions on Network and Service Management, The Computer Journa, Wireess Persona Communications, Wireess Communications and Mobie Computing, and Security and Network Communications. He is a member of the IEEE and ACM.