a mobile radii0 network architecture with dynamically c

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A Mobile Radii0 Network Architecture with Dynamically C

Topology Using Virtual Siubnets

Ja c o b Sharony

Hnzcl t ine Corporat ion

Greenlawn, NY 11740

sharony@hazel t inc .com

Abstract

An a r c h i t ec t u r e a d a p t a b l e t o d y n a m i c t o p o l o g y c ha n ! ge s i n m u l t i -

h o p m o b i l e r a d i o n e t w o r k s i s d e s cr i b ed . T h e a r c h i t s c t u r e p a r t i -

t i o n s a m o b i l e n e t w o r k i n t o l o g ic a ll y i n d e p e n d e n l s u b n e t w o r k s .

N e t w o r k n o d e s a,re m e m b e r s of p h ys ica l a n d v i rtu rx l siibriets a n d

m a y c h a n g e t h e i r a f i l i a t i o n w it h t h e s e s u bn e t s d u e t o t h e i rmo -

b i l i t y . Ea ch n o d e as a l lo ca ted an a d d res s b a sedo ii

a ts cu r ren ts u b n e t a f i l i a t i o n . We o b s e r a e ~ esp ec ia l l y i n large r ie lwo rks

with random t o p o l o g y - t ha t p a r t i t i o n i n g of t h e n e t u io r k m a y r e-

s u l t in s ig n i f i ca n t ly mo re b a la n ced lo a d th a n i ri o n e l a r ge multi-

h o p n e t w o r k, an a t t r i b u t e t h a t c a n s i g n i f i c a n t l y i m ,p i .o ve t h e n e t -

w o r k’ s p e r f o r m a n c e . T h e a r c h i t ec t u r e is h i ,yh ly fa u l t - to le ra n t ,

ha s a r e l a t i v e l y s i m p l e l o c a t i o n u p d a t i n g a n d t r a c k i n g s c h e m e ,

a n d by v i r t u e of i t s l o a d b a l a n c i n g f e a t u r e , t y p i c n l l y a c h i e v e s

a n e two rk wi th r e l a t iv e l y h i g h t h r o u g h p u t a r id l o w d e l a y . T h e

a d d r e s s i n g m e t h o d , l o g ic al t o p o l o g y , m o b i l i t y m a n a g e m e n t a n d

r o u t i n g p r o c e d u r e a r e d e s c r i b e d , u n d n e t w o r k p e r f o r m a n c e i s

e v a l u a t e d .

1 Introduction

Mobile radio networks are expected to play a n impor tant role in

future commercial and military applications, especially where

a wired backbone network is not accessible or does not exist.

1hese networks are suitable in situations where inst ant infras-

tru ctu re is needed and no central system ad ministIration (like

base stmationsn a cellular sys tem ) is available. Typi cal appli-

cations for this type of peer-to-peer networks include: mobile

computing in remote areas, tactical communications, law en-

forcement operations and disaster recovery situations. A peer-

to-peer mobile radio network consists of a collection of mobile

packet radio nodes that create a network on demand without

administrative support and may communicate with each other

via intermedi ate nodes in a multi-hop mode, i.e., every node is

a router. A critical issue in these networks is their ability to

adapt well to dynamic topology changes ca.used by movementof nodes relative to other nodes in the network. Aclaptation to

topology changes requires changes both in channel assignment

and routing.

Previous work on mobile radio networks with dynamically

changing topology concentra.ted primarily on channel access

and routing s chemes in arb itrar y physical topologies [I ]-. [6]. To

improve network performance and reliability, several methods

of topology contro l (by adjusting transmission ranges) were pro-

posed [ 7 ] - [ l o ] . More recently, a multi-cluster architecture for

/ ,

multi-hop mobille radio networks supp orti ng multimedia traffic

was proposed [ I l l .

Th e motivation behind our approach is that n e t w o r k p a r -

t i t i o n i n g can improve critical functions such as media access,

routing, mobility management and virtual circuit set-u p, while

rcducing sigrialiog/control overhead. It can be observed in this

type of network that partitioning may result also in lower con-

gestion compared to one large network.‘l’his pape r discusses a n architecture based on a specific logi-

ca l topology superimposed over a physical topology (determined

by transmission coverage of network nod es); the architecture se-

l ec t ,~inks to be activated (logical links) out of a pool of physical

links. Our main concern is finding an efficient logical topology

and a suitable routing procedure which result in high perfor-

mance and reliability.

Th e paper describes an archi tect ure suitable for mobile ra-

dio networks wliich is adaptable to dynamic topology changes

due to node mobility. In this architecture, network nodes are

grouped into two types of clusters (sub nets ): p.hysica1 and vir-

tual, and may dynamically change their a.ffiliation with these

subn ets due to their mobility. Each node is allocated an address

based on its current sub net affiliation. We consider networks

th at have several t,ens to several thousands mobile nodes. It

is assumed that there exists a channel access protocol which

resolves content.ions and/ or interference in the network (e.g.,

Th e rest of t:he paper is organized as follows. Section 2 de-

scribes the addressing method. Section 3 describes the network

logical topology, explaining the formation of physical and vir-

tual subnets. Section 4 discusses mobility management and

Section 5 considers the routing procedure. Section 6 discusses

performance issues, and conclusions are given in Section 7.

i121, i131).

2 Addresising method

In this method, network nodes are allocated addresses depend-

ing on their cur rent physical connectivity. Assurne th at t he net-work is segmented into p physical subnets (the distinction be-

tween physical and virtual will be clarified shortly; for the mo-

ment assume that physical subnets cover a local area) each con-

taining up to q mobile nodes. We describe the pool of addresses

over an alphabet of size m = max(p, q ) containing the numbers

0 , 1 , 2 , . . .m - 1. Each node in th e network is given a word (ad-

dress) of length two, where the list significant digit (LSD) is a

digit in base-q and the most significant digit ( MS D ) is a digit

in base-p. Therefore, the to tal number of words (and nodes)

807-7803-3250-4/96$5.00O1996 IEEE

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mailto:[email protected]



Figure 1: Physical and virtual subnets in a mobile radio net-

work.

possible is N = p q . Each node in this topology is affiliated

with nodes whose address differs only in one digit; that is, node

~ 1 . ~ 0s affiliated with nodes Z I . Z ~ , 5 X; 5 q - , z ; # 2 0 ,

and with nodes 3c;.zo, 0 5 xi 5 p - 1,xi # 2 1 . Thus , every

node is affiliated with p + q - 2 other nodes; we say that each

node has p + q - logical neighbors. Next we group every q

nodes that differ only in their LSD into an MSD group, and

every p nodes that differ only in their MSD into an LSD group.

Note that there are altogether p + q groups, and each node is a

member of one LSD group and one MSD group. These groups

are the basic building blocks of the network as described in th e

next section.

3 Logical topologyEach node in the network is affiliated with a physical subnet

(M S D group) and a virtual subnet (LSD group). Nodes which

are members of a physical subnet are within close proximity in

a local geograp hic area. Nodes which are members of a vir-

tual subnet form a regional network (i.e., beyond a local area).

Figure 1 depicts a mobile radio network with physical subnets

(in shaded areas ) and virtual sub nets (e.g., in solid and dashed

lines). Note th at all nodes within a physical subne t have the

same MSD while all nodes within a virtual subnet have the

same LSD. It is assumed for the moment that nodes of a given

physical sub net ca n reach (e.g., by adjusting the ir transmission

power or by using a directional antenna) nodes of neighboring

physical subn ets. Later we deal with the case when this as-

sumpt ion does not hold (i.e., when a node is disconnected from

its virtual s ubnet).

A node becomes a member of a physical subnet by acquiring

the first available addres s (wit h the lowest LSD) in that subnet,

e.g., if a node joins physical sub net 1 2 and there ar e already

1 0 members in this subnet it will use the address 12 . 10 since

LSD’s 0-9 are occupied already. Once a node becomes affili-

ated with a specific physical sub net , automati cally it becomes

a member of a virtual s ubnet defined by th e LS D in its address;

referring to the above example, the node will be a member in

virtual subnet 10 . As long as the node remains in the vicin-

ity of physical subnet 1 2 (i.e., within “hearing” distance from

its members) it will keep its current address. Any node in the

network is updat ed with the curre nt addresses used in its phys-

ical and virtual subnets (by its logical neighbors). This can be

accomplished, e.g., by an advertising process where each node

notifies its logical neighbors of its current address using a ded-icated management channel. Therefore, a node which desires

to join a specific physical subnet would contac t a member(s) of

this physical sub net t o find ou t which address it can acquire,

and then would advertise its newly acquired address to all of

its logical neighbors. Note tha t if a node cann ot reach any of

its logical neighbors in its virtual subnet,, it will use an other

virtual subnet via one of its logical neighbors in its physical

subne t. This case will be further discussed in Section 5 dealing

with routing.

Observe tha t th ere is no logical connection between t he vir-

tual subnets, however, since they are “overlaid” on the same

region they might interfere with each other. Thik interference

is eliminated b y the channel access scheme in use. One way,

for example, is to ope rate each virtua l sub net on a different fre-

quency channel(s); when the number of frequency channels is

less tha n the number of virtual su bnet s some form of time shar-

ing can be used. Note t ha t a less acute problem exists between

neighboring physical subnets which have a limited degree of

overlapping since each one of them covers a limited area. Thus,

one can take advantage of spatia l reuse, where only neighboring

(overlapping) subnets use different frequency channels.

4 Mobility management

A mobile node which changed its subnet affiliation will notify

all the nodes in its new physical an d virtual subne ts (i.e., its

current logical neighbors) of its newly acquired address. This

notification process can take place, e.g., during the establish-

ment of links with its logical neighbors or by broadcasting in

its physical and virtual s ubnets . I n general, a source node does

not know the current address of a desired destination node.

The source node can determine this address by inquiring in its

physical (virtu al) subne t, since one of the nodes there is affil-

iated with the destination node virtual (physical) subne t. To

clarify, let source node S and destination node D addresses be

SISOan d Dl.Do, respectively, and deno te by IS1 the cardinal-

ity (number of members) of physical subnet SI. onsider two

different cases for finding node D’s address; first, if ]Si( o,

node S would inquire in its physical subnet SI about node D

and receives node D’ s address from node 5’1 .Do (which was no-

tified earlier by node D , via virtual subnet Do, regarding its

current addres s). Second, if IS11 < D O ,node S would inquire

in virtual subnet SO bout node D and receives node D’ s ad-

dress from nodeD1

.SOwhich is affiliated with node D physicalsubnet. Note that node S does not know a-priori which of the

above cases is valid, nevertheless, i t inquires about node D first

in its physical subnet and if it does not get a response it inquires

in its virtual subnet (at least one of node S logical neighbors

knows node D ’s address). Alternatively (instead of inquiring

about node D’s address), node S can broadcast its packets for

node D in its physical and virtual subnets, at least one node

(which is a logical neighbor of node D ) will be able to forward

the packets to their destination.

Figure 2 describes a simplified location updating and track-

808



loc-track

FH -fixed host {3.3)

{LN-FH} - logical neighbors of the fixed host{3.0,3.1,3.2,0.3,1.3,2.3)

{LN-FIM} - logical neighbors of both the fixed and mobile hosts {1.3,3.1)

{LN-MH} - logical neighbors of the mobile host {1.0,1.2,1.3,0.1,21,3.1}

MH - mobile host {1.1)

example: 3.3- .1- 1.I

Figure 2: Location up dating and tracking scheme.

ing scheme. After moving to a new location a mobile host

(MH) notifies its logical neighbors by sending a location up-

date (loc-update). A fixed host (FH) which desires to com-

municate with M H will inquire at its logical neighbors about

MH by sending a location inquiry (loc-inquiry). At least one of

FH’s logical neighbors is also MH’s logical neighbor, thus, one

of their m utua l logical neighbors will provide FB with MH’s

address by sending loc-track. After tracking down MH’s ad-

dress, FH sends its d ata t o MH via one of their mutual logical

neighbors. Figure 2 shows also through a specific example in a

16-node network ( p = p = 4 ) the nodes involved in the above

process. Note tha t this location updati ng and tracking scheme

involves only p + q - nodes which is much less than N ; hi s

results in reduced signaling/control overhead. For example, in

a 400-node network with p = 16, q = 25, the location updat-

ing/tracking process involves less than 10% of the nodes in the

network. Therefore] in the case of multi-hop su bnet s a flooding

scheme can be used (assuming a contentionless access scheme,

e.g., TDMA -FDM A) in the corresponding physical an d virtual

subnets, to broad cast t he loc-update a nd loc-inquiry messages

without overloading the whole network.

5 Routing

Several routing schemes ar e possible; we describe a shortest

path routing procedure which is self-routing. We assume first

the case of one-hop physical/virtual subnets. In this procedure

routes traverse one digit at a time in fixed order, e.g., from the

LSD to the MSD. For example, when the source-node address is

12.15 and the destination-node address is 9 . 1 7 , this procedure

would use the path 12.15i2.17 --i 9.17. Generally, the

route from source-node address u1 .UO o destin at on-node ad-

dress 7 ~ 1 . 7 ~ 0would traverse the path ~ 1 . ~ 0 1 . ~ 0 ~ 1 . ~ 0

(see Figure 3 ) . Th e length of the path equals the number of

different digits in the addresses of the source and destination

nodes, i.e., at most two hops. In the above proce’dure there is

a unique path between any two nodes.

In general, the network is composed of multi-hop subnets

which means th at more th an two hops are necessary from source

to destination. In this case the routing is performed in two

phases. In the first phase (Phas e I) routing is performed only

II

Figure 3 : Shortest path routing for the case of one-hop physi-

cal/virtual sub nets ; physical - virtual.

in the physical subn ets (exchanging local traffic). Here pack-

ets are routed (e.g., using shortest path) within the physical

subnet of the :source node from the source node via interme-

diate nodes to a node having the same LS D as the destina-

tion node. In the second phase (P hase 11) packets are routed

in the virtual subnet, where packets reached to the last node

in the first phase are routed from this node to the destina-

tion node via inter medi ate nodes within t’he virtual su bnet de-

fined by the LiSD of the dest inati on nod e. Preferabl y, during

Phase I transmission power is limited to cover only the local

area of the corresponding physical subnet; this would allow

frequency reuse due to spatial separation. In Phase I1 (when

virtual subnets are formed) transmission coverage is adjusted

(e.g., by using a directional antenna) to reach remote phys-

ical subnets. Referring to Figure 1, the route from source

node 12.15 to destination n ode 9.17 would traverse the p ath

12.15 + 2.10 + 2.17 + 1.17 + .17 -+ .17, with

two hops in physical subnet 1 2 and three hops in virtual sub-

net 17. Note though, that in case a node cannot reach any of

its logical neighbors in its virtual subnet (i.e., when the virtual

subnet is not connected) it will have to use a different virtual

subnet via one of its logical neighbors in its ]physical sub net.

For example, say that node A.B would like to communicate

with node C.L); using shortest path routing the path would

usually traverse via physical subnet A to node A.D and then

via virtual sub’net D to node C.D. However, if node A.D is

not connected to virtual subnet D it will connect to another

node (say A.E)t via physical subnet A and then via virtual sub-

net E to node C .E and finally to the destination node C.D via

physical subnet C as indicated in the following,

A.B -i . ---i A.Di. . -+ A .Ei+ C.E . . .* 7.0

alternatively, the fault-tolerant routing scheme described bellow

can be used to overcome situations of disconnected subne ts.

Finally, we mention here ano ther self-routing scheme (called

Long-path routing) which results in high fault tolerance (see

Subsection 6.2). In this procedure the longest path has three

hops (assuming one-hop physical/virtual su bnet s). Referring

to Figure 4, he route from ~ 1 . ~ 0o vl.zt0 would traverse the

path ~ 1 . ~ 0+ u1 .u ;i~ l . u ;-- 1 . ~ 0Figure 4(a)), or

~ 1 . ~ 0 :.uo u:.vo * I.WO (Figure 4 (b ) ) , where

0 5 U ; 5 y - 1 , u ; # uo an d 0 5 U ; 5 p - 1 , u ; # u1 . Note

809



Figure 4: Long-path routing for the case of one-hop physi-

cal/virt,iial snhnet s; ( a ) physical ~ virtual - physical, (b ) viri,ual

- physical - virt,ual.

that, each route traverses alt,ernately physical and virt,iial sill>-

nets. It can be shown th at between each source-dest#inationpairthere are p + (I- 2 disjoint paths, i.e., paths that do not share

links or nodes (e.g., for p = (I = fl he number of disjoint

paths is O(f l)) . Each of these paths corresponds to one of

the p + Q - 2 logical rieighbors of the source riode. Note that, a

pat,h is uniquely specified oncr a logical neighbor was srlected

by t h e source node. To route a packet from a source node to

a destination riode, the source node selects (say at random)

on e of tlie p + q - 2 disjoint, paths. In case of it path failure,

th e source node can select (say raridonily) one of th e remaining

disjoint paths .

6 Performance

Network perf orm mm in terms of throughput and fault toler

ance is evaluated. We compare the throughput of th e network

to that of a one large multi-hop network

6.1 Throughput

We assume i , l i a t i i i each multi-hop subnet ii link activation

T D M A - F D M h (multiple frequency channels per subnet are

possible) access scheme is usecl where each l ink is activatecl

at, lra st~ nce during each t,irne frame. We furtlier a.ssume t ha t

the above shortest-path routing is used (i.e.. any p ath traverses

a t most, two subnets . on e physical an d on e virtual). T h e anal-

ysis in this siibsection is t,riie fo i - any roiit.ing procedurr w t t h s n

th e mult,i-hop subnets. I n t,he following aualvsis we i i s r t,hrse

notations:

R - bit rate of each transmitting node.

cy - portion of time frame usecl i n Phase I (for int,ra-sribriet

traffic).

T - n u m b e r of time-slots rised in one large multi-hop network.

TI number of time-clots u se c l in Phase I.

'1)L - n i i m b r r of t,inie-slot,s i s e d in I'hase I

I , ~ total number of links activated in one large multi-hop net-

work.

L1 total number of liiiks activated in th e physical subnets

during Phase I .

L2 ~ total n umber of links act,ivated in th e virtual su bnets dur-

in g Phase 11.

7' - load of link i in on ? large mnlti-hop network, i.e., t,he num-ber of times link i is traversed by all possible N ( N - 1)

path s in t,he networ k.

r / iload of link J in its physical subnet., i.e., t,lie number of

times link is travers ed by all possible y (q ~ 1) paths in

its physical subnet.

71; ~~ load of link k in its virtual subnet, i.e., the number of

times link k is traversrd by all possible p ( p - 1) paths in

it,s virtual subne t.

maxi mum link-load in one large multi-hop network (i.e.,

maxl(q ' ) ) .

711 maximum link-load during Phase I (i .e.. maxJ (qi) ),

772 ~ masirnuin link-load during Pha se I1 (i.e.?maxk(y;))

It is assumed that traffic is homogeneous, where each node

in the network sends X packets/s ec t,o any of t,lie other N - 1

nodes. 'ro simplify t h e presentation, w e use an M / M / 1 queue-

ing model to drscribe t,he behavior of each act,ivat,ed ink; there-

fore, the average delay of a packet traversing link IC is given by

bk = F-, where l / p is t,he average packet length in bits,

c k is the link capacity in bitslsec and q k is the link load. Note

that if a more accurat,c model for th e link behavior is used it.

will only result in a different expression for 612. Using Little's

formula and suninling over all the activated links iri the net-

work, the average queueing delay across t hr net,work is givcn

by

Kote that tlie capacity of the links is inversely proportional

t.0 th e riurnber of time slots ( in t h e corresponding phase) which

depends on t 8 h enurnbrr of freqiiency channels used. The maxi-

mnm traffic between any t,wo nodes d uring p hase I is X I =*similarly. th e max imum t,raffic twt,wprn any two nodes d uring

phase I1 is A-, =w.I 'h r re fo re , the maximum t.raffic be-

twren a n y tw o nodes in t,hc network is

Th e normalized network throughput is giveii by

A - Y ( N - 1)r = X(A - 1)- ~ ( 3 )I LR Ti11i~ r l ; ~ 2 ~

Kote t ,h a t r / ~ an d 712 depend on the logical t,opology and t,he

routing procedure usecl within the subnets.

810



Figure 5: 16-node network with a well controlled 1 opology.

We ar e interested in comparing th e tliroughput prrformance

of the proposed architecture and that of a one large multi-hop

radio network. First, we find th e t,hronghput of the one large

network. In a similar way to the above, the queueing delay

across one large multi-hop network is given by

thus , the thro ughput of one large multi-hop netwo rk is given

by

N ( N - )

7-17r' = (5)

Th e throughput values for the proposed architectwe ( 3 ) an d

for one large multi-hop network (5 ) depend strongly on the

physical an d logical topologies, routing procedur e a n( i he num-

ber of frequencies. We observe d ~ especially in larg'e networks

with random topology (a characteristic of ad-hoc splxadic net-

works) - that the maximum link traffic-load in one large net-

work is significantly higher than the maximum link traffic-load

i n the su bnets, i.e., 11 >> p q l , q q 2 . Therefore, partitioning of the

network may reduce congestion in the network which in effpct

can improve th e performance, e.g., results in higher throu ghp ut,

lower delay. Note t ha t ther e is a penalty associated with large

transmission radii resulting in reduced link capacitips (because

more time-slots are needed). However, since th e link loading

ma.y be significantly reduced, the total effect may result in in-

creased th rou gh put . Also, while one large rnulti-hclp network

cannot take advantage of many frequencies (if available) be-

cause of spatial reuse, the current architecture can (t o separat>e

t h e overlayed virtual subnets), which also results ill increased

tlrroiighpii t .

Th e following ex ample of a 16-node network illustrates the

st,ren gth of the proposed arc hitectu re. Figure 5 depicts a net-

work with a well coiit,rollcd topology of maximum degree six

composed of equilateral triangles. According to thc proposed

architecture the network may be partitioned into four physicaland four virtual subnets (11 = y = 4 ) . Figure 6 ai181 Figure 7

show the links activated in tjhe physical and v irtual s ubn ets,

respectivcly.

Using TDMX-FDMA ink-activabion assignrnent~ nd short-

est path routing, we find the throughput prrformaric-r fo r oiic

large multi-hop network and for a rictwork using f o u r virtual

subiiets (depicted in Figurr 8). For this particulai- example,

one c a n scc t,hat fo r a given number of frequencies tlic pro-

posed architecture always has a better thro ughp ut performance

than the one large multi-hop network. Note that not more

Figure 6: Links activated in the physical sub nets .

Figure 7: Links activated in the virtiial subnets

than three frequencies are required to achieve the maximum

throngliput of the one large network, i.e., adding more frequen-

cies will not increase the thr ough put. This is because of th e

limited transmission range of the nodes, taking advantage of

spatial reuse. Ilowever, in the proposed network it is pos-

sible to further increase the throughput by adding more fre-

quencies (up to eight frequencies). Qbserv'e th at t he average

arid rnaxinium link loading in the one large multi-hop network

is 8 . 33 an d 1 6 , respectively, while for the network using four

virtual subnets the corresponding values axe identical - 8.0,

i.e., the network has a balanced load. The average and maxi-

mum number of hops in the one large network is 2 .29 and 6 . 0 ,

respectively, while for the network using four virtual subnets

th e corresponding values ar e 2 . 13 and 4.0.

6 .2 Fault -tollerance

To evaluat,e the fault-t,olerance of th e architecture we use two

rnetrics, n o d e c o n n e c t i v i t y an d l i n k c o n n e c t i v i t y . We define

16-node network

--I.0

Number of frequency channels

Figurr 8 Throughput performance for one large multi-hop net-

work and for a network using four virtual subnets.

81 1



architecture is highly fault-to lerant, has a relatively simple lo-

cation upd ating a nd tracking sche me, and by virtu e of its load

balancing feature, typically achieves a network with relatively

high throug hput and low delay. Network performance in terms

of throughput and fault-toleiance was evaluated

there are six disjoint paths betweennodes 1.3 and 3.2

1 3 ---> 1 0 --->3 0 -> 3 2

1 3- -> 1 1 - ->3 1 -> 32

1 3 - > 1 2 - > 3 21 3 --> 0 3 --->0 2 -> 3 2

1 3 --->2 3 --22 2 -> 3 2

1 3 - - > 3 3 - > 3 2References

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Figur e 9 Examp le node-disjoint p ath s in a 16-node mobile

radio network using Long-path routing.[2] I Cidon and M Sidi, “Distributed assignment algorithms

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n o d e c o n n e c t i v i t y - K as the minimum number of faulty nodes

th at creates a disconnected network. Assuming one-hop sub-

nets, each node in the logical topology is connected directly to

p + q - 2 other nodes, thus, the node connectivity of the n et-

work is 6 = p + q - 2. For example, consider a 1024-no de

network composed of 32 subnets of 32 nodes each, then any 61

nodes can be faulty before the network becomes disconnected.

Define th e network l i n k c o n n e c t i v i t y - CT as the minimum num-

ber of node-disjoint paths between any source-destination pair

(i.e., paths that do not share links or pass through the same

node). Th e link connectivity of the topology is CT = 2 for path-

lengths of not more th an two hops. If we allow path-lengths to

be u p to three hops (using Long-path r outing, see Figure 4 ) , it

can be shown tha t t he link connectivity reaches its maximum

value of = p + q - . Referring to the above example, there

are at least 62 node-disjoint paths, i.e., alternative paths be-

tween any source-destination pair with path-lengths of at most

thre e hops. Since the network has high node connectivity an d

high link connectivity it is therefore very reliable. A possible

technology th at can benefit fro m this is wireless A TM, where

a virtual path established between a given source-destination

pair has many alternative disjoint routes which can be used in

case of node or link failures due to mobility, interference etc.

Figure 9 depicts an example of a 16-node network ( p = q = 4)

having six node-disjoint paths between a pair of nodes when

using Long-path routing.

7 Conclusions

An architecture comprising a logical topology of physical and

virtual subnets, and corresponding addressing, mobilit,y man-

agement an d routing schemes were described. T his architecture

is applicable to mobile radio networks and acco mmod ates dy-namic topology changes due to relative movement of network

nodes. Th e architecture partitions a mobile network into log-

ically independent sub networks. Network nodes are members

of physical and virtual subnets and may change their affilia-

tion with these subnets due to thrir mobility. Each node is

allocated an addres s based on its current subn et affiliation. We

observed - especially in large networks with random t,opology -

tha t partitioning of th e network may result in significantly m ore

balanced load than in one large multi-hop network, an attribute

th at can significantly improve the net,work’s performance. Th e

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