MASTER'S THESIS. Scalable Route Caching Methods for Networks with Many Mobile Nodes. by Theodoros Salonidis Advisor: Leandros Tassiulas

Transcription

1 MASTER'S THESIS Scalable Route Cachng Methods for Networks wth Many Moble Nodes by Theodoros Salonds Advsor: Leandros Tassulas CSHCN M.S (ISR M.S. 99-3)

2 ABSTRACT Ttle of Thess: SCALABLE ROUTE CACHING METHODS FOR NETWORKS WITH MANY MOBILE NODES Degree Canddate: Theodoros Salonds Degree and year: Master of Scence, 999 Thess drected by: Assocate Professor Leandros Tassulas Department of Electrcal Engneerng A moble, ad hoc network (MANET) s a collecton of wreless moble hosts formng a network wthout the ad of any establshed nfrastructure or centralzed admnstraton. Generally a MANET may consst of many portable devces that are characterzed by processng and memory sze lmtatons and n practce t wll not be possble for a host to keep routng nformaton for all the nodes n a large network. Ths thess attempts to address the scalablty ssue by ntroducng a framework and strateges to quantfy the concept of destnaton cachng. The observaton that a source host can augment ts cache s routng table by usng the caches of other closely stuated hosts forms the bass of our approach. We propose algorthms that determne a host s cached nformaton by takng nto account the host s memory capacty, the network sze and the number and dentty of the destnatons ths host needs to cache nformaton about. Manly two classes of algorthms are ntroduced. The class of "Best State/Best Cost" algorthms (BSBC) tres to mnmze the floodng cost per route dscovery by

3 keepng the most "expensve" destnatons n each host s cache. However t does not mpose any floodng constrants for the non-cached destnatons. The second class of LEADERS algorthms adopts a dfferent vew by relaxng on the floodng cost optmalty and takng nto account a maxmum floodng constrant for each node. In ths way, the worst floodng case s controlled snce any node s guaranteed to fnd nformaton about any destnaton wthn a pre-specfed maxmum dstance.

4 SCALABLE ROUTE CACHING METHODS FOR NETWORKS WITH MANY MOBILE NODES by Theodoros Salonds Thess submtted to the Faculty of the Graduate School of the Unversty of Maryland at College Park n partal fulfllment of the requrements for the degree of Master of Scences 999 Advsory Commttee: Assocate Professor Leandros Tassulas, Char Assstant Research Scentst M. Scott Corson Assstant Professor Donald Yeung v

5 Copyrght by Theodoros Salonds 999 v

6 DEDICATION Dedcated to my famly Nkos, Anastasa, Mara, Elefthera and Penny v

7 ACKNOWLEDGEMENTS Frst of all I would lke to thank my advsor Dr Leandros Tassulas for proposng the topc of ths thess, and for the enlghtenng advce and gudance he provded durng the elaboraton of ths work. Many thanks to Dr Donald Yeung and Dr Scott Corson, who were n my commttee and provded wth a lot of nsghtful comments durng the presentaton and after the completon of ths thess. I am grateful to my roommates and frends Kyrakos Manousaks, Iordans Koutsopoulos and Nkos Kanls for ther frendshp and support durng all ths perod. I also thank Kostas Tsoukatos and Tassos Mchal for ther useful general advce as senor colleagues, Alexandros Lambrnds for our dscussons on clusterng algorthms and all my frends n the Greek Graduate students assocaton (DIGENIS) for creatng such a supportve, oyful and frendly envronment. Last but not least I would lke to thank my famly. Ther love, gudance and support s the man factor of success throughout all my years of studes. Ths work s dedcated to them. v

8 TABLE OF CONTENTS DEDICATION... v ACKNOWLEDGEMENTS... v TABLE OF CONTENTS... v LIST OF TABLES... v LIST OF FIGURES... v Chapter.... Introducton.... Moble Ad-hoc networks (M.A.NETs) Proactve Routng Protocols Destnaton Sequenced Dstance Vector Protocol (DSDV) Wreless Routng Protocol (WRP) Reactve Routng Protocols Dynamc Source Routng (DSR) Ad-Hoc On Demand Dstance Vector Protocol (AODV) Temporary Ordered routng Algorthm (TORA) The scalablty ssue Intellgent Cachng Algorthms for On Demand Routng Protocols...0 Chapter...3. General Framework...3. The Floodng Mechansm The problem at hand The Infnte Floodng Horzon (IHF) problem Damond Strategy Square Strategy Comparson of the damonds and squares strateges The Fnte Horzon Floodng (FHF) problem Soluton to Lmted Horzon Problem usng the Damond Strategy...45 *.5. The "best" startng floodng horzon h The optmum startng floodng horzon usng retry horzon step s= The optmal retry horzon step s...50 Chapter Introducton...55 v

9 3. A Lower Bound on the expected floodng cost of any cachng algorthm The class of BSBC algorthms The Local Best State/Best Cost (L-BSBC) algorthm The Global Best State/Best Cost (G-BSBC) algorthm Experments and smulaton of the BSBC algorthms Experment # : How does a BSBC algorthm behave for a fxed cache K as the number of desred destnatons M ncreases? Experment # : How bg a cache should be used n order to have a tolerable expected floodng cost? Experment #3 : The K/M rato and ts robustness to scalablty Experment #4: "How do BSBC algorthms perform n the case of unform traffc?" The LEADERS algorthms The "Sngle Pass" Leaders Algorthm (SPLA) The "Two Phase" Leaders Algorthm (TPLA) Experment # : "SPLA vs TPLA" Experment #: LEADERS vs BSBC...90 Chapter Summary, Conclusons and dscusson...95 v

10 LIST OF TABLES Table 3.. Experment # : M vares whle K= Table 3.. Experment #: K vares whle M= Table 3.3.: MaxCost "Equvalent" experments for the LEADERS and BSBC algorthms....9 v

11 LIST OF FIGURES Fgure.. : A 9x9 mesh...3 Fgure.. : Damonds strategy for N=5 and r = Fgure.3. : r=5(odd) and b=5(odd)...3 Fgure.4. : b=0, r =4 (even) : We have only regons of type A and B Fgure.5. : The damond strategy. In ths case, r=, D =, b = Fgure.6. : Damonds v.s Squares...40 Fgure.7. : Capacty and Average Cost Ratos for the two strateges (N=57)...4 Fgure.8. Damond strategy n the fnte horzon floodng context Fgure.9. : s=, r and h vary...48 Fgure.0. : % of network cached (K) and flooded per route dscovery (CavgMn)...49 Fgure.. : r=6, s and h vary...5 Fgure.. : For several (N,r) and at s= the best startng horzon s always r/-!...5 Fgure.3. : For several (N,r) the best horzon step s s=...53 Fgure 3.. : Experment #: N=5, K=0, M vares, expected floodng cost n the average case...68 Fgure 3.. : Experment #: N=5, K=0, M vares, expected floodng cost n the worst case Fgure 3.3. : Experment #: N=5, M=00, K vares, expected floodng cost on the average...7 Fgure 3.4. Experment #: N=5, M=00, K vares, expected maxmum floodng cost. 7 v

12 Fgure 3.5. Experment #3: L-BSBC algorthm, K/M rato stablty n average floodng cost when M changes...74 Fgure 3.6. Experment #3: L-BSBC algorthm, K/M rato stablty n maxmum floodng cost when M changes...74 Fgure 3.7. Experment #3: G-BSBC algorthm, K/M stablty n average floodng cost when M changes Fgure 3.8. Experment #3: G-BSBC algorthm, K/M rato stablty n maxmum floodng cost when M changes...75 Fgure 3.9 : Offsets between dfferent M-curves Fgure 3.0 : Damond strategy (N,r)=(5,6) for Fnte Floodng Horzon (FHF)...78 Fgure 3.. : Nodes that have routng nformaton about the center node after the L- BSBC algorthm converges Fgure 3.. SPLA formaton of centrods and regons for destnaton = Fgure 3.3. TPLA formaton of centrods and regons for destnaton = Fgure 3.4: M=00, K vares. LEADERS vs BSBC: Expected floodng cost n the worst case....9 Fgure 3.5. M=00, K vares. LEADERS vs BSBC: Expected floodng cost n the average case...93 Fgure 3.6. M=00, K vares. LEADERS vs BSBC: Capacty Rato obtaned for the same worst case floodng cost v

13 Chapter. Introducton The recent advances n wreless communcatons technologes combned wth the ntroducton of small portable computng devces have created the demand of realzng the ubqutous networkng dream: "Seamless communcaton and network access anytme and anywhere". In order to fulfll these ncreasngly rsng expectatons, extensve work nowadays focuses on the ntegraton of moble computers wthn the fxed network nfrastructure of the Internet. The extenson of the Internet to moble domans and hosts s mplemented by the Moble IP technology. Moble IP s ntended to enable nodes to move from one IP subnet to another ether ths subnet s n a form of a wreless LAN or an Ethernet segment. One can thnk of Moble IP as solvng the "macro" moblty management problem, snce moblty n ths case s happenng n the granularty of IP subnets. It s less well suted for more "mcro" moblty management applcatons lke the handoff amongst wreless transcevers, each of whch covers only a very small geographc area. Supportng ths form of host moblty requres address management and protocol nteroperablty enhancements, but core network functons such as hop-by-hop routng stll presently rely upon pre-exstng routng protocols operatng wthn the fxed network. The concept of moble ad-hoc networkng tres to extend moblty wthn autonomous, moble, wreless domans. In contrast to the exstng cellular networks, there s no centralzed admnstraton of each wreless doman (e.g. by the use of base statons), but rather the set of moble hosts form by themselves the network routng nfrastructure

14 n an ad hoc fashon. Each node partcpates n an ad-hoc routng protocol that allows t to dscover "mult-hop" paths through the network to any other node. Moble ad-hoc networks are deally suted for mltary and other tactcal applcatons such as emergency rescue or exploraton mssons, where an establshed (e.g. cellular) nfrastructure s unavalable or unrelable. But apart from the emergency stuatons, there are a lot of emergng ubqutous computng technologes that naturally ft n the "nfrastructureless" networkng model: On-the-fly conferencng applcatons, networkng ntellgent devces, wearable computng and smart sensor networks, are commercal applcatons of ubqutous computng that are to be deployed n the near future. There are no assumptons or lmtatons on the sze of the wreless domans n adhoc networks. Ths means that ad-hoc networks may consst of hundreds or thousands of nodes. The sheer number of nodes that one mght fnd n a ubqutous computng network or a smart moble sensor network underscores the need for a level of scalablty not commonly present n most approaches to network routng and management. An mportant queston that needs to be addressed n MANETs concerns how scalablty s acheved : Snce a MANET may consst of many portable devces that are characterzed by processng and memory sze lmtatons, n practce t wll not be possble for a host to keep routng nformaton for all the nodes n a large network. Some exstng routng protocols (DSR [4], AODV [0]) pnpont the need for cachng routng nformaton about some destnatons and floodng the network n case a source node s cache does not have the route to a specfc destnaton. However they do not address the queston of whch destnatons to cache nformaton about. In the case of small to

15 medum szed networks ths queston s not so mportant, snce the floodng cost for fndng a destnaton s not very large. However, n a large MANET a bad choce of destnatons to cache may result n floodng a great porton of the network ust for route dscovery. If ths route traffc adds up to the already exstng data traffc then there s a huge congeston problem n the network. Thus, as the MANET becomes larger, the dentty of destnatons a host keeps n ts cache becomes a crtcal ssue. Ths ssue becomes even more crtcal f we consder the wreless nature of MANETs whch s generally characterzed by severe bandwdth restrctons for data transmsson. Ths thess attempts to address the scalablty ssue descrbed above. We ntroduce a framework and strateges to quantfy the concept of cachng nformaton about destnatons. The observaton that a source host can augment ts cache s routng table by usng the caches of other closely stuated hosts forms the bass of our approach. We propose algorthms that determne a host s cached nformaton by takng nto account the host s memory capacty, the network sze and the number and dentty of the destnatons ths host needs to cache nformaton about. The man obectve s to mnmze the floodng cost per route dscovery by keepng the most "expensve" destnatons n the host s cache. In the subsequent sectons, we wll defne the noton of MANETs and the ssues nvolved n ther desgn, and wll revew and compare routng algorthms that have been mplemented so far n the context of large MANETs. At the end of the chapter we wll pont out the need for route cachng when the network gets bg, and propose a way to do that n order to acheve scalablty. In chapter we wll defne the framework upon whch we try to quantfy the noton of cachng destnatons. A NxN torrod mesh wll be 3

16 ntroduced, where nodes are consdered to be hosts wth small memory capacty. Each node wll try to address all other nodes n the network wth equal probablty. Optmal cachng strateges are found for ths case and at the end of the chapter there wll be a performance evaluaton of each of the strateges employed. In chapter 3 we wll consder the more nterestng and realstc case of each node addressng only a subset of the mesh network. We wll see that the resultng cachng algorthms n ths case are more general and they do not depend on the mesh structure of the network, renderng them more applcable to the case of a MANET. Manly two classes of algorthms were nvented. The frst class, takes nto account the avalable cache capacty per host but does not mpose any floodng constrants for the non-cached destnatons after the algorthm s run. The second class adopts a dfferent vew by relaxng on the floodng cost optmalty and takng nto account a maxmum floodng constrant n addton to the cache sze. At the end of the chapter there wll be a performance evaluaton of the algorthms and dscusson on the trade-offs governng them. The fnal chapter wll consst of a summary wth conclusons and dscusson.. Moble Ad-hoc networks (M.A.NETs) A moble, ad hoc network (MANET) s a collecton of wreless moble hosts formng a network wthout the ad of any establshed nfrastructure or centralzed admnstraton. A MANET may be consdered an autonomous system of moble nodes. Such networks have dynamc, sometmes rapdly-changng, random, multhop topologes whch are lkely composed of relatvely bandwdth-constraned wreless lnks. MANETs have several salent characterstcs that have to be taken nto account when consderng ther desgn and deployment: 4

17 Dynamc topologes: Nodes are free to move arbtrarly; thus, the network topology (whch s typcally multhop) may change randomly and rapdly at unpredctable tmes, and may consst of both bdrectonal and undrectonal lnks. Bandwdth-constraned, varable capacty lnks: Wreless lnks typcally have sgnfcantly lower capacty than ther hardwred counterparts. In addton, the realzed throughput of wreless communcatons (after accountng for the effects of multple access, fadng, nose, and nterference condtons) s often much less than a rado s maxmum transmsson rate. Energy-constraned operaton: Some or all of the nodes n a MANET may rely on batteres or other exhaustble means for ther energy. For these nodes, a fnte energy capacty may be the most sgnfcant performance constrant, and thus ts utlzaton should be vewed as a prmary network control parameter. Lmted physcal securty: Moble wreless networks are generally more prone to physcal securty threats than are fxed-cable nets. The ncreased possblty of eavesdroppng, spoofng, and denal-of-servce attacks should be carefully consdered. Exstng lnk securty technques are often appled wthn wreless networks to reduce securty threats. Whle the above characterstcs are common to any knd of wreless network, MANETs are further dstngushed by ther "Infrastructureless" property : There s no centralzed admnstraton or preexstng nfrastructure that takes care of the network management and exstence. Moble nodes are themselves responsble for establshng and mantanng connecton between them. In such an envronment, t s necessary for one 5

18 moble host, to enlst the ad of other hosts n forwardng a packet to ts destnaton, due to the lmted range of each moble host s wreless transmssons. Thus, robust and effcent operaton n moble wreless networks s supported by ncorporatng routng functonalty nto all the moble nodes, n contrast to fxed networks such as the Internet where only some nodes n the network perform the routng functon. It s obvous that the routng functon s of utmost mportance for the vablty of an ad-hoc network It s also a bg challenge snce all the characterstcs of the moblty and wreless channel prevously mentoned, must be taken nto account when desgnng such protocols. There has been extensve research and work n the feld of routng n MANETs. The routng protocols can be separated n two man classes, namely proactve or reactve, accordng to the way routes are created and mantaned..3 Proactve Routng Protocols Proactve routng protocols for moble ad-hoc networks are bult on the phlosophy of tradtonal routng protocols used n packet swtched networks. So before we descrbe some representatves of ths class we revew the two man ways of routng n wred networks namely "Lnk State" and "Dstance Vector" routng algorthms. In lnk state protocols each node mantans ts own vew of the network topology, ncludng lnk costs of all ts outgong lnks. To keep vews up to date, each node perodcally broadcasts the lnk costs of all ts neghbors to all the nodes n the network usng floodng. Ths s done whenever there s a change n lnk costs. As a node receves ths nformaton, t updates ts vew of the network topology and apples a shortest path algorthm (e.g. Dkstra's algorthm []) to choose the next hop to a destnaton. Asynchronous lnk cost updates may gve rse to short-lved routng loops; however they 6

19 dsappear by the tme update messages have propagated throughout the network []. A very popular lnk state routng protocol used n wred networks s OSPF (Open Shortest Path Frst)[]. In the Dstance Vector approach, for each destnaton, every node mantans a set of dstances or costs, (), where k ranges over the neghbors of. Node d k * k s treated as the next hop node for a data packet destned for, f d () mn{ d () } k * =. To keep these dstances up-to date, whenever there s any change of ths mnmum dstance because of lnk cost changes, the new mnmum dstance s reported to the neghbor nodes. If, as a result, a mnmum dstance to any neghbor changes, ths process s repeated untl the network reaches eventually a steady state. Ths technque s the classcal dstrbuted Bellman Ford algorthm (DBF) []. Compared to the lnk state method, t s comptatonally more effcent, easer to mplement and requres much less storage space. Besdes the advantages over lnk state, DBF suffers from the problem of short lved or long lved routng loops. The prmary cause for ths s that nodes make uncoordnated modfcatons to ther routng tables based on some nformaton whch could be ncorrect. Routng loops result n packets crculatng meanngless n the network consumng bandwdth and resources. Especally n the case of the low bandwdth wreless envronment we want to avod the creaton of such loops at any cost. Ths problem s allevated by employng nternodal coordnaton mechansms [4][5]. However these are complex methods and they mght be effectve when topologcal changes are rare. In the context of moble networks, a smpler approach to solve ths problem usng sequence numbers was followed n the DSDV algorthm, whch we wll revew later. k k 7

20 There s also a possblty of the "countng to nfnty" problem, where t takes a very large number of update messages to detect that a node s unreachable. Ths performance problem arses from the fact that DBF does not have an nherent mechansm to determne when a network node should stop ncrementng ts dstance to a gven destnaton []. On the other hand, Lnk State algorthms are free of the "countng to nfnty" problem. However they need to mantan the up-to-date verson of the entre network topology at every node, whch may consttute excessve storage and communcaton overhead n a hghly dynamc network. Also no lnk state algorthm mplemented so far has been able to totally elmnate the creaton of temporary routng loops. Dstance Vector and Lnk State algorthms have as a common characterstc that they are both shortest path approaches : They allow a host to fnd the next hop neghbor to reach the destnaton va the "shortest path". By "shortest path" we usually mean the number of hops; however other sutable cost measures such as lnk utlzaton or queung delay can also be used. Although the methods of dstance vector and lnk state are good deas and have been successfully used n many dynamc packet swtched networks, they cannot be used n ther natve form n MANETs. The floodng technques used n lnk state protocols create excessve traffc n a multhop rado network wth dynamc topology. On the other hand, the routng protocols based on DBF take a long tme to converge and the frequent topology changes n a wreless network wth moble nodes make the loopng problem of DBF unacceptable. 8

21 Proactve Routng protocols try to match the lnk state and dstance vector deas to the wreless envronment by takng the above lmtatons nto account and tryng to reduce or elmnate them. The two promnent protocols n the proactve class are the Destnaton Sequenced Dstance Vector Protocol (DSDV) [9] and the Wreless Routng Protocol (WRP) []..3. Destnaton Sequenced Dstance Vector Protocol (DSDV) The Destnaton Sequenced Dstance Vector protocol (DSDV) [9] has been specfcally targeted for moble networks. Its key advantage of DSDV over tradtonal dstance vector protocols s that t guarantees loop freedom. Ths protocol extends on the classcal DBF by taggng each dstance entry d k () by a sequence number (SN) that orgnated by the destnaton node. In ths way, nodes can quckly dstngush stale routes from the new ones and thus avod formaton of routng loops. To mantan the consstency of routng tables n a dynamcally varyng topology, each staton perodcally transmts updates mmedately when sgnfcantly new nformaton s avalable. Ths update must be made often enough to ensure that every moble computer can almost always locate any other moble computer of the collecton. Also ths update s n the form of ncremental packets that reflect only the changes and not the whole routng table of the node. So the data broadcast by each moble computer wll contan ts new ncremented sequence number and the followng nformaton for each new route : The destnaton s address, the number of hops requred to reach the destnaton and the sequence number of the nformaton receved regardng the destnaton, as orgnally stamped by the destnaton. 9

22 When a moble host receves new routng nformaton, that nformaton s compared to the nformaton already avalable from prevous routng nformaton packets. A route R s more favorable than R f R has a greater sequence number or f the two routes have equal sequence numbers but R has a lower metrc. The metrc used n the algorthm to determne shortest paths s the hop count. The metrcs for routes chosen from the newly broadcast nformaton are each ncremented by one hop. Newly recorded routes are scheduled for mmedate advertsement to the current moble host s neghbors. Routes receved n broadcasts are also advertsed by the recever when t subsequently broadcasts ts routng nformaton; the recever adds an ncrement to the metrc before advertsng the route, snce ncomng packets wll requre one more hop to reach the destnaton (namely the hop from the transmtter to the recever). A broken lnk s descrbed by an nfnte metrc (.e. any value greater than the maxmum allowed metrc). When a node A decdes that ts route to a destnaton D has broken, t advertses the route to D wth an nfnte metrc and a sequence number one greater than ts sequence number for the route that has broken (makng an odd sequence number). Ths causes any node B whch s routng packets through A to ncorporate the nfnte metrc route nto ts routng table untl node B hears a route to D wth a hgher sequence number. In addton to loop elmnaton t has been shown that DSDV avods the countng to nfnty problem as well..3. Wreless Routng Protocol (WRP) The Wreless Routng Protocol (WRP) s based on a broader class of dstrbuted shortest path algorthms that utlze nformaton regardng the length and the second-to- 0

23 last hop (predecessor) of the shortest path to each destnaton to elmnate the countng to nfnty problem of DBF. Each node mantans the shortest path spannng tree reported by ts neghbors. A node uses ths nformaton along wth the cost of adacent lnks to generate ts own shortest path spannng tree. An update message exchanged among neghbors conssts of a vector of entres that report updates to a sender s spannng tree; each update entry contans a destnaton dentfer, the dstance to the destnaton, and the second-to-last hop of the shortest path to the destnaton. The general class of PFAs elmnate the countng to nfnty problem but stll ncurs temporary loops n the paths specfed by the predecessor before they converge. Wthout proper precautons ths can lead to slow convergence or ncur substantal processng f a node s requred to update ts entre routng table for each nput event. WRP remedes ths by lmtng routng table updates to nclude only these entres affected by a network change..4 Reactve Routng Protocols As we saw n the prevous paragraph, proactve protocols try to keep the shortest path routes and routes are mantaned to all potental destnatons (possbly all nodes n the network) all the tme, whether or not all such routes are actually used. Route mantenance s obtaned by route update traffc, and ths can be a lot of overhead, especally for large networks. Reactve routng protocols or "on demand" routng protocols create and mantan routes only n an "as needed" bass. When a route s needed, a global route dscovery procedure s ntated to fnd the path for the specfc nformaton that has not been

24 cached. The route dscovery s usually done by employng classcal floodng mechansms..4. Dynamc Source Routng (DSR) The Dynamc Source Routng protocol (DSR) [4], uses source routng a technque where the source of a data packet determnes the complete sequence of nodes through whch to forward the packet. The source explctly lsts ths route n the packet s header and then transmts the packet over ts wreless network nterface to the frst hop dentfed n the source route. When a host receves the packet, f ths host s not the fnal destnaton of the packet, t strps from the packet header ts own address and smply transmts the packet to the next hop dentfed n the packet header. Ths process goes on untl the packet reaches ts destnaton. The two basc operatons supported by DSR are Route Dscovery and Route Mantenance. DSR bulds routes on demand by floodng the network n a controlled manner (for example by usng a Tme To Lve (TTL) feld n the packet header). In Route Dscovery, the source node sends a query n the form of a route request packet that carres the sequence of hops t passed through. Once a query reaches the destnaton, the destnaton reples wth a route reply packet that smply copes the route from the query packet and traverses t backwards. To reduce the cost and frequency of the Route Dscovery, each node has a route cache, where complete routes have been stored as learned from the reply packets. These routes are used by the data packets untl they fal as determned by the falure of attempted message transmssons. Route Mantenance procedure montors the operaton of the routes and nforms the sender of any routng errors. Error detecton s supported n the data lnk layer. If the

25 data lnk layers reports a transmsson problem for whch t cannot recover, ths host sends a route error packet to the orgnal sender of the packet. The route error packet contans the addresses of the hosts at both ends of the hop n error : the host that detected the error and the host to whch t was attemptng to transmt ths packet on ths hop. When a route error packet s receved by the source host, the hop n error s removed from ths host s route cache and all routes whch contan that hop are truncated at that pont. Then, a new route dscovery for the destnaton s ntated by the sender. DSR has a unque advantage by vrtue of source routng. The key advantage of source routng s that ntermedate nodes need not mantan up-to date routng nformaton n order to route the packets they forward, snce the packets themselves already contan all the routng decsons. Ths fact coupled wth the on demand nature of the protocol elmnates the need for the perodc route advertsement and neghbor detecton packets present n other protocols. Another nce feature of DSR s that snce the route s part of the packet tself, routng loops, ether short or long lved, cannot be formed, as they are mmedately detected and elmnated. Ths property opens up the protocol to a varety of useful optmzatons. For example, a flooded query can be quenched early by havng any non-destnaton host reply to the query f that host has a route to the ntended destnaton. A node can learn a route to a destnaton whle passng on route reply packets. Also routes can be mproved by havng nodes promscuously lsten to conversatons between other nodes n proxmty..4. Ad-Hoc On Demand Dstance Vector Protocol (AODV) AODV s an on-demand varaton of dstance vector protocols. It s essentally a combnaton of DSR and DSDV : It borrows the basc on demand mechansm of Route 3

26 Dscovery and Route Mantenance from DSR plus the use of hop-by-hop routng, sequence number and perodc beacons from DSDV. AODV uses sequence numbers mantaned at destnatons to determne freshness of routng nformaton. In AODV, a query flood s used to create a route, wth the destnaton respondng to the frst such query, much as n DSR. However, AODV mantans routes n a dstrbuted fashon, as routng table entres on all ntermedate nodes of the route. Routng table entres are tuples n the form of <destnaton, next hop, dstance>. Nodes propagatng query packets remember the earler hop taken by such a query packet. Ths hop s used to forward the reply packet back to the source. The reply packet, n turn, sets the routng table entres on the nodes n ts path. Dstrbutng routng tables n such a fashon makes them smaller than the case of DSR where each node must keep the whole path n ts cache. However, n order to mantan routes, AODV normally requres that each node perodcally transmt a HELLO message, wth a default rate of one per second. Falure to receve three consecutve HELLO messages from a neghbor s taken as an ndcaton that the lnk to the destnaton n queston s down. When a lnk goes down, any upstream node that has recently forwarded packets to a destnaton usng that lnk s notfed va an UNSOLICITED ROUTE REPLY contanng an nfnte metrc for that destnaton. Upon recept of such a ROUTE REPLY, a node must acqure a new route to the destnaton usng Route Dscovery as descrbed above. AODV mantans the addresses of the neghbors through whch packets destned for a gven destnaton were receved. A neghbor s consdered actve (for a destnaton) f t orgnates or relays at least one packet for that destnaton, wthn the past actve 4

27 tmeout perod. A routng table entry s actve f t s used by an actve neghbor. The path from a source to destnaton va the actve routng table entres s called an actve path. On a lnk falure, all routng table entres for whch the faled lnk s on the actve path, are erased. Ths s accomplshed by an error packet gong backwards to the actve neghbors, whch forward them to ther actve neghbors and so on. Ths technque effectvely erases the route backwards from the faled lnk. Much lke DSR, AODV advocates use of early quenchng of request packets,.e, any node havng a route to the destnaton can reply to a request. AODV also uses a technque called route expry, where a routng tale entry expres after a predetermned perod, after whch fresh route dscovery must be ntated. Nether DSR nor AODV guarantee shortest path. Ths s partcularly true f early quenchng s used. However, earler performance evaluaton shows that the lengths of the routes dscovered are usually very compettve wth the ones found n shortest path protocols [6]..4.3 Temporary Ordered routng Algorthm (TORA) The unque feature of TORA [6] s that t s a protocol desgned to mnmze reacton to topologcal changes. Ths s accomplshed by mantanng multple routes to a specfc destnaton, so that many topologcal changes need no reacton at all, unless all routes to a specfc destnaton are lost. In that case routes are re-establshed va a temporary ordered sequence of dffusng computatons, whch are essentally lnk reversals that eventually establsh a path to the destnaton. TORA does not mantan routes between a gven source/destnaton par at all tmes but creates new routes on demand. Route optmalty (shortest paths) s consdered 5

28 secondary mportance, and longer routes are often used to avod the overhead of dscoverng newer routes. Ths ablty to ntate and react nfrequently serves to mnmze the communcaton overhead at the expense of multple non-optmal (shortest path) routes to the destnaton. In order to select one of the multple routes two alternatves are suggested : choosng a neghbor randomly so that the loads are more or less evenly dstrbuted or choosng the "lowest" neghbor. TORA s based n part on algorthms that try to mantan the destnaton orented property of a drected acyclc graph [3]. A DAG s defned to be destnaton orented f there s always at least one path to a specfc destnaton. The DAG becomes destnaton dsorented when one or more lnk fals. In ths case by employng lnk reversals these algorthms ensure that the DAG wll become agan destnaton orented n a fnte tme. TORA uses the noton of node "heght" to mantan the destnaton orented DAG. Each node mantans a heght and exchanges ths value wth each neghbor. The sgnfcance of the heght s that a lnk s always drected from a "hgher" node to a "lower" node. The noton of "heght" and lnk reversals are destnaton specfc. Ths means that each node of the network runs a logcally separate copy of TORA for each destnaton. The route dscovery process for a specfc destnaton creates a destnaton orented graph for ths destnaton n a source ntated fashon: The source node broadcasts a QUERY packet contanng the address of the destnaton for whch t requres a route. Ths packet propagates through the network untl t reaches the destnaton or an ntermedate node havng a route to the destnaton. The recpent of the QUERY then broadcasts an UPDATE packet lstng ts heght wth respect to the destnaton. As ths packet propagates through the network, each node that receves the 6

29 UPDATE sets ts heght to a value greater than the heght of the neghbor from whch the update was receved. Ths has the effect of creatng a seres of drected lnks from the orgnal sender of the QUERY to the node that ntally generated the update. Route mantenance s acheved as follows : when a node dscovers that a route to a destnaton s no longer vald, t adusts ts heght so that t s a local maxmum wth respect to ts neghbors and transmts an UPDATE packet. Ths s effectvely a lnk reversal and t means that now all lnks emanatng from node are drected from towards ts neghbors (snce the neghbors have now lower heghts). Ths has as an effect all traffc enterng to flow back out of towards the neghbor nodes that had prevously been routng packets to the destnaton va. If the node has no neghbors of fnte heght wth respect to ths destnaton, then the node attempts to dscover a new route va the route dscovery process. Fnally, n the event of network parttons, the protocol s able to detect the partton and erase all nvald routes : when a node detects a network partton, t generates a CLEAR packet that resets routng state and removes nvald routes from the network..5 The scalablty ssue Most envsoned MANET networks (e.g. moble mltary networks or hghway networks) may be relatvely large (e.g. tens or hundreds of nodes per routng area). An nterestng queston would be how would proactve and reactve protocols compete n terms of scalablty. Even f there has not been a performance comparson between the two classes, we argue n favor of the reactve protocols when scalablty s consdered. As we saw n the prevous sectons, tradtonal routng protocols usng lnk state or dstance vector have been successfully used n the deployment of dynamcally fxed 7

30 packet swtched networks. However ther success does not nclude effcency wth respect to scalablty : When the number of network nodes becomes very large, routng loops, the countng to nfnty problem and very slow convergence tmes make the network performance unacceptable. Even f proactve protocols lke DSDV and WRP have elmnated or reduced the formaton of routng loops and the countng to nfnty problem, each one has stll ts own problems. DSDV requres selecton of the followng parameters : perodc update nterval, maxmum value of the settlng tme for a destnaton and the number of the update ntervals whch may transpre before a route s consdered "stale". Ths senstvty of parameter selecton s even more pronounced when we have a huge network. Another drawback of DSDV s that a node has to wat untl t receves the next update message orgnated by the destnaton n order to update ts dstance-table entry for that destnaton. Ths mplct destnaton-centered synchronzaton suffers from the same latency problems as smlar algorthms based on explct synchronzaton. Also DSDV uses both perodc and trggered updates for updatng routng nformaton, whch could cause excessve communcaton overhead. Of course such latency and excessve communcaton overhead become more severe when the network becomes bgger. In WRP, there s a sgnfcant amount of overhead assocated wth mantanng the shortest path spannng tree reported by each neghbor and reactons to falures may be far-reachng (.e every node whch ncludes the lnk n ts shortest path spannng tree must partcpate n the falure reacton). Ths hgh overhead does not seem to make ths protocol vable n the case of a large number of nodes. 8

31 Fnally and most mportantly, for a large number of moble nodes, both proactve protocols wll converge very slowly, snce shortest path convergence tme always depends on the network sze. Fortunately, fxed networks addressed the scalablty problem by utlzng herarchcal structures, and usng aggregaton : Only some specalzed nodes called routers or gateways perform the routng functon over clusters (LANs) of hosts that support ther own more effcent (and more expensve) routng protocols. Ths approach does not seem to ft n the case of MANETs and proactve algorthms used n them, snce each node must support a routng functonalty and we are requred to have a flat structure (every node has the same functonalty wth the rest). On the other hand, reactve protocols seem to be a more attractve soluton n terms of scalablty n MANETs. The property of creatng and mantanng routes on demand elmnates the need to keep constantly routng nformaton on every destnaton, and cachng the most expensve routes reduces communcaton overhead and latency a lot. However the problem of scalablty strkes back n a dfferent way. Each host s a portable devce whch usually has a lmted processng power and memory capacty and n general t wll not be able to keep routng nformaton for all the destnatons t has traffc for : If the destnaton s n the source node s cache and s up to date, then t s used to address the destnaton. If t s not, the node must flood the network to fnd nformaton about the destnaton. 9

32 .6 Intellgent Cachng Algorthms for On Demand Routng Protocols In all the reactve protocols dscussed, the authors pnpont the need for cachng of some desrable destnatons. However, there s no formulaton or crtera as to whch destnatons each node must cache. The protocols have been smulated ether under the assumpton that each node can cache ALL the destnatons t has traffc for, or by runnng the algorthms wth a few number of nodes where the ssue of whch destnatons to keep n the cache s not so crtcal. Of course these smplfyng assumptons may be accepted n order to see the protocol actually workng, and see how moblty affects the protocol performance, but the answer to the scalablty problem s not actually addressed. Our obectve s to fnd algorthms for ntellgent cachng of destnatons n each moble host. These algorthms run on top of on demand routng protocols renderng them ntellgent and vable for large network szes. The am of the ntellgent cachng algorthms s farly smple : For each source node at a specfc tme nstant, keep n the node s cache the destnatons that are consdered to be more expensve n terms of dscoverng them by floodng. Furthermore, f the destnaton paths that are NOT cached by a node are (optmally) placed n other nodes nearby, we can create the lluson of a large "vrtual" routng table that ncludes nformaton about all the destnatons, rather than the small one that s physcally attached to ths source node. Ths effect can be accomplshed by the use of the "early quenchng" mechansm : upon a route dscovery, when a nondestnaton node contans the destnaton n ts own routng table, t stops the floodng message propagaton and sends ts own nformaton to the source node wthout nterferng the destnaton. 0

33 There are two benefts of early quenchng that make ts use crtcal n large moble ad-hoc networks. The frst s sgnfcant floodng cost reducton : If early quenchng were not used and the destnaton s very far from the source node, the source would have to flood a great porton of the network n order to fnd the destnaton s path and n a large network of nodes ths floodng cost s unacceptable due to excessve congeston. The second beneft of early quenchng s hgher speed for retreval of a specfc destnaton path that s not cached by the host. Unlke AODV and TORA, DSR has some desrable characterstcs that may make t more sutable n a large network context. Routng loops are avoded, perodc advertsements for routes are no longer needed and the packets themselves already contan the route to the destnaton, thus takng off the load from the ntermedate nodes to make the routng decson. Furthermore routng tables are not dstrbuted as n the prevous cases, so t s easer to perform cachng of destnatons. However the source routng nature of DSR s ts potental doom as well, snce there s a scalablty problem : As the network becomes larger, control packets (whch collect node addresses from each node vsted) become larger and consttute a large proporton of the total traffc generated. Clearly ths has a negatve mpact due to the lmted avalable bandwdth. Early quenchng s the only way to make DSR a scalable protocol and enoy all ts benefts that were prevously mentoned. In ths way, routng messages are suppressed by ntermedate non-destnaton nodes before they become too large. Of course one could argue that early quenchng does not produce shortest routng paths. Actually ths s the prce all reactve protocols have to pay n order to favor from ther "on demand" behavor. Shortest path constrants are many tmes relaxed n favor of

34 multple path nformaton, or more robust paths accordng to the wreless channel s current state and strngent bandwdth requrements. As a matter of fact, n many comparatve studes performed [5][6], on demand protocols have exhbted compettve routes when compared to the shortest paths provded by proactve algorthms. We proceed n the next chapter by ntroducng a framework and methodology for ntellgent cachng algorthms runnng on top of a DSR-lke routng algorthm. Ths does not mean that AODV and TORA could not use smlar technques. We prefer usng DSR because the routng tables are not dstrbuted and the cachng algorthms are smpler and more straghtforward to understand and mplement n ths case.

35 Chapter. General Framework We now ntroduce a framework upon whch we try to quantfy the noton of destnaton address cachng n a network of nodes that form a NxN mesh network. Each node n ths mesh s consdered to be a host equpped wth a processor, a network nterface, and a memory (cache) that can hold nformaton for up to K destnatons. The nodes can only communcate drectly only n a horzontal or vertcal fashon, and there can be no message broadcastng along dagonals n a sngle step. Ths type of communcaton s often called "Manhattan Style", and the dstance assocated wth t, s called Manhattan Dstance Fgure.. : A 9x9 mesh The Manhattan Dstance between two nodes s defned as a hop count and s the mnmum number of nodes that form a path between them, ncludng the destnaton node. In order to elmnate dscrmnaton for nodes placed at the sdes of the mesh and 3

36 treat the mesh network n a unform manner, we also assume that the mesh s organzed as a torrod, that s the two farmost opposte sdes communcate drectly wth each other producng a "wrap-around" effect : the nodes stuated on the same lne and are at the farmost opposte sdes they have a dstance of one. For example n Fg.., nodes 3 and 4 have a dstance of, nodes and 3 a dstance of, 0 and 8 a dstance of (due to the wraparound effects), and nodes and 0 a dstance of 5. In ths confguraton, each node may wsh to address any other node n the network wth an equal probablty. The cache memory of each node can hold nformaton for only K out of the N nodes n the network. Destnatons that are not cached by the node are dscovered by floodng the network. The floodng cost between two nodes x and y wth respect to ther Manhattan Dstance d(x,y) s : d Cost(x,y) = f(d(x,y)) = + 4 = d + d + (.) = Ths s manly a damond of a dagonal equal to d+ nodes centered at the source node. A node s called "Aware" of a specfc destnaton f t has nfo n ts routng table about ths destnaton and "Unaware" f t doesn t. A destnaton s of course consdered Aware of tself. Each entry of the routng table of each node s kept n the form <destnaton,pathtodestnaton>, where PathToDestnaton s a mnmum path (sequence of nodes) to the destnaton. Furthermore, we assume that a moble ad-hoc routng protocol lke DSR s used n order to keep the routes consstent and takng care of the new route creatons upon a node's request. 4

37 . The Floodng Mechansm If a node wants to communcate wth a specfc destnaton and does not have routng nfo about t, then t must ntate a route dscovery and flood the network to fnd a path to the desred destnaton. Route dscovery s accomplshed n the followng way : The source node broadcasts a floodng message ("needle packet") contanng the destnaton address to all ts neghbor nodes. Each neghbor, f t has NOT routng nfo on the destnaton, t propagates the floodng message to all ts neghbors (4 of them) by appendng t s address to the needle message, else t stops the floodng message propagaton, appends the path that s found n ts cache to the needle message constructed so far and sends ths path back to the source node. Ths technque of a node respondng wth the routng path of ts own cache wthout nterferng the destnaton n the route dscovery process, s called "early quenchng" n the moble ad-hoc networks lterature, and we beleve that t s an ndspensable element for an ad-hoc network wth many hosts. There are two varatons of floodng that we wll take nto account n our study. Infnte horzon floodng (IHF) In Infnte horzon floodng, floodng s contnung endlessly, unless t s suppressed by nodes who have routng nfo on the destnaton. Fnte horzon floodng (FHF) In Fnte Horzon Floodng there s a mechansm that constrans the floodng generated by a node. Ths mechansm s usually mplemented by a TTL (Tme To Lve) feld on each floodng message, whch s ntalzed by the desred Horzon value and s decremented when t s forwarded by the next neghbour who does not have routng nfo on the destnaton. When the counter reaches zero, the floodng message s no longer forwarded and s dscarded. If a node startng wth a specfc horzon does not 5

38 fnd any nfo on the destnaton (that s, a destnaton aware node or the destnaton tself) t ncrements the horzon by a step (typcally by ), and retres to flood wth the hope to fnd nfo on the destnaton. Ths process goes on untl nfo about the destnaton s found..3 The problem at hand Early quenchng seems to be a good technque to cope wth small routng tables wth respect to a large network. However ths technque has by no means been quantfed n the lterature and s usually proposed as an optmzaton. Usng early quenchng, the dentty of the destnatons that are cached n each node s crtcal snce ths drectly affects the floodng cost n the network. Confnng the floodng cost as much as possble, s our prmary nterest. Ths can be accomplshed by fndng the best strategy of arrangng the routng nformaton at each node. In ths chapter, we assume the smplest case where each node may wsh to address any other node n the network wth an equal probablty. The cache memory of each node can hold nformaton for only K out of the N nodes n the network. So we want to fnd the best K destnaton entres to be kept n each node s cache, so that the floodng cost s mnmum. Of course there wll be dfferent thngs to take nto consderaton for the two types of floodng mentoned n the prevous paragraph : In IHF t s obvous that the nodes contanng routng nfo for a specfc destnaton, should surround n some way the ones who don t, so that the floodng wll eventually be stopped. Also the arrangement of the nodes wth routng nfo for a specfc destnaton should be symmetrc n some way. In ths way, the number of the entres of 6

39 the routng table K of each node wll be equal to the number of nodes wth routng nfo n the mesh network. In our elaboraton we consder two symmetrc strateges : Damonds strategy : Startng from the man dagonals of the mesh, routng nfo for a specfc destnaton s placed dagonally n the mesh and the dagonals have a fxed dstance r unts of each other. In ths way we have damond-lke regons, wth Aware nodes on the damond permeter and Unaware nodes n the nteror. Squares strategy : Startng from the mddle row and column of the mesh, routng nfo s placed on rows and columns whch have a fxed dstance r nodes of each other. In ths way, we have rectangle and square regons, wth Aware nodes on the permeters and Unaware nodes n the nterors. Note that the torrod structure of the mesh allows us to use the above strateges for any destnaton, no matter where ths destnaton's place s n the mesh. Thus the strateges assume that the destnaton s the center node of the mesh and buld ther damond or square structures around t. In FHF, The problem of how to arrange the Aware nodes n the mesh for a specfc destnaton s stll at hand. Questons arse lke : Should the structure be symmetrc or not? What s the optmal arrangement? have to be confronted. Of course the Aware nodes for a specfc destnaton need not be so many as n the IHF case, snce there s an nherent mechansm for suppressng the floodng eventually. However, the startng floodng horzon h, (whch s common for all Unaware nodes n the mesh) for a specfc arrangement (N,r) should be chosen n such a way so that the 7

40 average floodng cost n the mesh be mnmzed. Another consderaton that should be taken nto account s the followng : If for an ntal horzon no node wth routng nfo s found, what s the floodng step ncrement that would fnally yeld the mnmum average floodng cost?.4 The Infnte Floodng Horzon (IHF) problem In ths case we assume that the use of a symmetrc strategy lke damonds or squares s best. We want to fnd whch of these two routng polces yelds the mnmum floodng cost, for approxmately the same number of K Aware nodes n the mesh. To do ths, we frst fnd K and the average floodng cost Cavg for a gven N (number of nodes at each sde of the square mesh) and a gven r. r s the dstance between dagonals n the damonds strategy and the dstance between columns or rows n the squares strategy)..4. Damond Strategy For a fxed N, the parameter that changes s actually r, the dstance between dagonals. Here we have to dstngush between dstance that s measured n unts and n number of nodes. By sayng unts, we mean that two consecutve nodes on a dagonal have an r= unts, and the mdway between the two nodes s one unt. The unts are ntroduced because a damond routng polcy may have an r=3 for example where r ncludes two nodes on the dagonal plus the halfway dstance between the second and thrd node. In general, a damond-shaped grd n our NxN mesh may nclude three types of regons : 8

41 Regon A : Damonds havng sde equal to r. Regon B : Trangles of sde (n unts) b, b 0 N s =, where b = REM r, b = 0 r (.) Regon C : Truncated damonds of sde r where one corner has been truncated by the sdes of the NxN mesh. Fgure.. : Damonds strategy for N=5 and r = 7 Fgure. shows the regons A, B and C for the case N=5 and r=7, and what happens n case a node wthout routng nformaton n each of the regons floods the network. To dstngush between all the possble cases of (N,r), we have to take nto account the followng parameters : N N b = REM, D = QUOT r r (.3) If b 0, then our damond strategy s gong to have all the above types of regons, whereas f b = 0, the mesh s gong to have regons of type A and type B only. We wll 9

42 consder these two cases separately. For each case, we calculate the average floodng cost C and the capacty of each node, K. Fnally, we denote by : N : The number of regons of type, = { A, B, C} C : The floodng cost of regon of type, = { A, B, C} l : The permenter of regon of type, = { A, B, C} C l = : The probablty that an Unaware node s n regon of type N P { A, B C}, =, C avg = { A, B, C} N C P : Average Floodng Cost K : the number of aware nodes about the destnaton whch s equal to the number of cache routng table entres for each node. CASE A : b 0 r s even Floodng Cost Computaton: Type A : = D( D ) N A C A r = + r + l A = r P A CA l = N Type B : = 4 ( D + ) N B A 30

43 C B b = + l B = b + P B C = B / N l B Type C : N C = 4D C C r = + br b + 4 l C = r + b + P C C = C / N l C C avg = { A, B, C} N C P Node capacty : K = 4 DN + N ( r + ) D( D + ) + 3 r s odd b s odd Floodng Cost Computaton: Let L = b + Type A : = D( D ) N A C A r + = l A = r 3

44 P A CA l = N A Fgure.3. : r=5(odd) and b=5(odd). Type B : = 4 ( D + ) N B ( ) C B = L L + l B = L P B C = B / l N B Type C : N C = 4D C C r + = + Lr L( L ) l C = r C P = C C / N l C 3

45 C avg = { A, B, C} N C P Node capacty : N(d + ) (r + ) D ( r + ) D + 3, D even K = N(d + ) (r + ) D rd + 4, D odd b s even Floodng Cost Computaton: Let b L = Type A : = D( D ) N A C A r + = l A = r P A CA l = N Type B : = 4 ( D + ) N B A C = ( L +) B l B = L + P B C = B / N l B Type C : N C = 4D C C ( r + )( r + 3) = + rl L 4 33

46 C C CC = CC r, L r, L = l C = r P C CC l = N C C avg = { A, B, C} N C P Node capacty : N(d + ) (r + ) D ( r + ) D + 3, D even K = N(d + ) (r + ) D rd + 4, D odd CASE B : b = 0 r s even Floodng Cost Computaton: Type A : = D( D ) N A C A r = + r + l A = r P A CA l = N A Type B : N B = 4D C B r = + r + 34

47 l B = r + P B C = B / N l B C avg = { A, B, C} N C P Node capacty : K = 4DN rd D D + 3 Fgure.4. : b=0, r =4 (even) : We have only regons of type A and B. r s odd Floodng Cost : Let L = r Type A : = D( D ) N A C A = L + 4L + 35

48 l A = r P A CA l = N A Type B : N B = 4D C B ( ) = ( L + ) L + l B = ( L + ) P B CB / l = N B C avg = { A, B, C} N C P Node capacty : K = 4DN rd D D Square Strategy For a fxed N, the parameter that changes here s r, the dstance between rows or columns. Here we do not use unts but number of nodes to denote dstance. In general, a damond-shaped grd n our NxN mesh may nclude three types of regons : Regon A : Squares havng sde equal to r. Regon B : Rectangles at the mesh boundares that communcate wth each other va the mesh wrap-around. Regon C : The 4 corner squares that are formed for every choce of r. To dstngush between all the possble cases of (N,r), we have to take nto account the followng parameters : 36

49 N b = REM r N D = QUOT r Fgure.5. : The damond strategy. In ths case, r=, D =, b = 4 CASE A : b 0 Floodng Cost Computaton: Type A : N A = 4D C = ( r +) A l A = 4r P A CA l = N A Type B : N B = 8D C B N = Dr + r + ( ) 37