Optimal Time Slot Assignment for Mobile Ad Hoc Networks

Transcription

1 Optiml Time Slot Assignment for Mobile A Ho Networks Koushik Sinh Honeywell Tehnology Solutions Lb, Bnglore, Ini sinh kou@yhoo.om Abstrt. We present new pproh to fin ollision-free trnsmission sheule for mobile ho networks (MANETs) in TDM environment. A hexgonl ellulr struture is overli on the MANET n then the tul emn for the number of slots in eh ell is foun out. We ssume 2-ell buffering in whih the interferene mong ifferent mobile noes o not exten beyon ells more thn istne 2 prt. Bse on the instntneous ell emns, we propose optiml slot ssignment shemes for both homogeneous (ll ells hve the sme emn) n non-homogeneous ell emns by lever reuse of the time slots, without using ny interferene. The propose lgorithms exploit the hexgonl symmetry of the ells requiring O(log log m + md + n) time, where m is the number of mobile noes in the ho network, n n D being the number of ells n imeter of the ellulr grph. 1 Introution In time ivision multiplexe (TDM) environment, the existing solutions to time slot ssignment in MANET ttempt to ssign globlly unique time slot to eh noe in the network, usully through grph oloring tehniques [13, 14, 15], or by fining n pproprite set of prtitions of the set of noes n then ssigning unique time slot to eh of these prtitions [7, 10], so tht no two noes trnsmit uring the sme slot. The lgorithms esribe in [6, 7, 10] nee more slots (non-optiml ssignment) thn the optiml solution n lso the number of slots inreses rpily with inrese in the mximum noe egree of the network grph, lthough the verge noe egree my be very smll. [15] uses mximl inepenent set of the noes to generte self-orgnizing TDMA sheule. In this pper, we introue novel strtegy for ssigning time slots to the noes in n ho network bse on the lotion informtion of the iniviul noes. The propose solution signifintly improves slot utiliztion by n elegnt tehnique of re-using the time slots by suffiiently istnt noes, voiing ny ollision uring trnsmission. For this, we first prtition the eployment zone into regulr hexgonl ells, similr to the ellulr networks. Using the lotion informtion of the noes, the number of tive noes n hene, the tul emn of eh ell t tht instnt of time is ompute. We use this ell emn informtion to ssign time slots to eh mobile noe by lever re-use of the time slots whih exploits the hexgonl symmetry of the impose ellulr struture, n vois interferene mong the noes. The propose tehnique ensures n optiml ollision-free ssignment for every noe of the network in O(m) time, m A. Pl et l. (Es.): IWDC 2005, LNCS 3741, pp , Springer-Verlg Berlin Heielberg 2005

2 Optiml Time Slot Assignment for Mobile A Ho Networks 251 being the number of noes in the network. We term this problem of fining n optiml time slot ssignment sheule for the ho network s the Slot Assignment Problem (SAP). The slot ssignment lgorithm presente here supersees the existing lgorithm in [10, 13] with respet to optimlity, n require O(log log m + md + n) time to etermine n optiml, ollision-free slot ssignment sheule for the entire network, n being the number of ells in the overli ellulr grph n D being the imeter of the ho network. Mobility of the noes is lso onsiere by invoking the ssignment lgorithm whenever noe moves from one ell to n jent ell. Approprite protools for ientifying suh sitution through the use of speil ontrol slots n brosting the i of the leer of every ell to ll noes within tht ell uring these ontrol slots, hve been presente. 2 System Moel We ssume the pre-existene of prtitioning of the MANET eployment re into number of isjoint ells. The noes in the network re ssume to possess lotion informtion whih re either GPS enble or ble to use the network infrstruture to etermine their lotions reltive to the eployment zone [4, 9]. A mpping is use to onvert the geogrphil region to hexgonl gri ells [5, 8]. The noes nee to be synhronize in time. GPS n provie highly urte n synhronize globl time, besies urte lotion informtion. 3 Preliminries We first onsier the stti moel of the slot ssignment problem, where the number of slots require for eh ell is known priori. The vilble time spe is prtitione into equl length time slots n re numbere 0, 1, 2,...from the lower en. The interferene between two ssigne time slots is represente in the form of o-slot onstrints, ue to whih the sme slot is not llowe to be ssigne to ertin pirs of ells simultneously. We onsier 2-ell buffering slot ssignment problem (similr to 2-bn buffering in [1, 2, 3]) for hexgonl ellulr network overli on n ho network, in whih slot n be ressigne to ell more thn istne 2 wy. Following the nottions in [1, 2], let s 0, s 1 n s 2 be the minimum slot seprtions between ssigne slots in the sme ell, in ells t istnes one n two prt respetively. In our se of slot ssignment in TDM environment, s 0 = s 1 = s 2 =1.Aellulr grph is grph G =(V,E), where eh ell of the hexgonl gri is represente by noe n n ege exists between two noes if the orresponing ells re jent to eh other, i.e., they shre ommon ell bounry. Cells i n j re istne-k prt if the minimum number of hops it tkes to reh noe i from j in G is k. Allegesressumetobe symmetril. Figure 1 shows ell n its six jent ells. The igrm on the right moels this senrio s hexgonl ellulr grph of seven noes. The nottion N i (u) enotes the set of ll ells tht re t istne i from ell u.

3 252 K. Sinh b g b g f e f e Fig. 1. Conversion of hexgonl gri to hexgonl ellulr grph v u w Fig. 2. A hexgonl ellulr grph Definition 1. Suppose G =(V,E) is ellulr grph. A subgrph G =(V,E ) of G is si to be istne-k lique, if every pir of noes in G is onnete in G by pth of length t most k n V is mximl. Definition 2. A istne-2 lique of 7 noes in hexgonl ellulr network is efine s omplete istne-2 lique. The noe tht is t istne-1 from ll other noes in the omplete istne-2 lique is terme s its entrl noe or entrl ell n the remining noes re terme s its peripherl noes or peripherl ells. In 2-ell buffering environment, the o-slot interferene my exten up to ells t istne 2 prt. In view of this, we efine ellulr istne-2 lique s follows. Definition 3. A ellulr istne-2 lique G 2 =(V 2,E 2 ) is grph generte from omplete istne-2 lique G 1 by ing eges to G 1 between every pir of noes tht re t istne two in G 1. Figures 3() n 3(b) illustrte omplete istne-2 lique n the orresponing ellulr istne-2 lique. Cell 0 is the entrl noe of the grph. The she eges in the ellulr istne-2 lique re the eges joining the istne-2 neighbors. Definition 4. If G 1 is ellulr istne-2 lique with noe u s the entrl noe, then ellulr istne-2 lique G 2 is si to be jent to G 1 iff, i) u is peripherl noe of G 2, ii) the entrl noe of G 2 is lso peripherl noe of G 1, n iii) G 1 n G 2 hve totl of 4 noes in ommon, inluing the entrl noes of G 1 n G 2. 4 Minimum Slot Requirement for Cellulr Networks Let D (2) 7 (G) be the sum of emns of ll ells of ellulr istne-2 lique, G = (V,E), where the rinlity of V, V 7. Then, D (2) 7 (G) = w i,wherew i is the emn from the ell i. iɛg

4 Optiml Time Slot Assignment for Mobile A Ho Networks () A omplete istne-2 lique 4 (b) A ellulr istne-2 lique Fig. 3. A omplete istne-2 lique n the orresponing ellulr istne-2 lique Definition 5. A 7-noe ellulr istne-2 lique G or its subgrph is lle ritil blok, CB 7, whih is ompose of mximum of 7 ells, suh tht the sum of the emns of the ells in CB 7 is mximl over ll possible ellulr istne-2 liques in the network. We enote the emn of ritil blok by D (2) 7. Thus D (2) 7 =mx G D(2) 7 (G). Note tht there my be more thn one suh ellulr istne-2 lique. We first onsier the simpler se of homogenous ell emn, where ll ells hve the sme emn. 4.1 Homogeneous Cell Demn Let w represent the homogeneous emn for ll ells in the network. For w =1, the ritil blok emn D (2) 7 woul be 7 time slots. Referring to figure 4(), we see tht ue to struturl symmetry, ny istne-2 lique n be hosen s the ritil blok. Without ny loss of generlity, let the ellulr istne-2 lique befg be esignte s the 7-noe ritil blok, with noe g s the entrl noe. Consiering now the ellulr istne-2 lique gbpqr, entere t, we note tht, noe p n be ssigne the sme time slots s those of noes e n f, noe r n be ssigne the sme time slots s those of noes n f, while noe q n be ssigne the time slots s those of noes, e n f. Thus, we fin tht the emn of the ellulr istne-2 lique gbpqr n be stisfie ompletely by the time slots ssigne to the ritil blok. Figure 4(b) epits possible ssignment sheme for the ellulr grph of figure 4(). We now stte the following results. Lemm 1. For ny given unstisfie noe u, jent to one or more stisfie ellulr istne-2 liques, it is lwys possible to fin stisfie noe v t istne-3 from u suh tht the slot ssigne to v is unuse within istne two of u. We now exten the results of homogeneous emn with w =1to the generl se of w>1 by simply ssigning bloks of w onseutive slots to eh noe, inste of single slot, leing to the following result. Lemm 2. The optiml number of slots require for ellulr grph with homogeneous emn of w slots per ell is 7w time slots. For ll positive n negtive integer vlues (inluing 0) of m n n, we efine the opertion (m, n)mok s returning the slot numbers strting from m mo k to n mo k, (inluing both m n n). The lgorithm to hnle w slots per ell emn is presente below, whih uses only the optiml number of require slots.

5 K. Sinh [6] [0] [0] [1] [2] [3] [4] b p [2] [3] [4] [5] b p [6] [0] f k g q [5] k f [6] [0] [1] g q [2] j l e r s [0] j l [1] [2] [3] [4] [5] s e r i h u m t [3] i h [4] [5] [6] u m t [7] o n () Homogeneous emn of unit slot o n [0] [1] (b) An optiml ssignment sheme Fig. 4. Slot ssignment for ellulr grph with homogeneous unit emn Algorithm homogeneous slot ssignment Step 1 : Assign slot numbers (0,w 1) to the entrl ell of the ritil blok. Step 2 : Assign slot numbers (iw, (i +1)w 1) mo 7w, i 1 to the i th ell to the right of the entrl ell long prtiulr iretion, sy long the horizontl line s shown in figure 4(b). Tht is, we ssign the inresing orer slot numbers (0,w 1), (w, 2w 1),..., (6w, 7w 1) repetely to the ells to the right of the entrl ell long the horizontl iretion. Step 3 : Assign slot numbers ( iw, (i 1)w 1)) mo 7w, i 1 to the i th ell to the left of the entrl ell. Tht is, we ssign the eresing orer slot vlues (7w 1, 6w), (6w 1, 5w),..., (w 1, 0) repetely to the ells to the left of the entrl ell. Step 4 : For rows below the entrl ell, shift the (0,w 1) slot vlue 3 ells to the left n then repet steps 2 n 3 to obtin slot ssignment for eh suh row. Step 5 : For rows bove the entrl ell, shift the (0,w 1) slot vlue 3 ells to the right n then repet steps 2 n 3 for eh suh row. 4.2 Heterogenous Cell Demn We now onsier the generl se of SAP, where ells hve ifferent emns,i.e., w i,w j,i j, suh tht w i w j. The 7-noe ritil blok is insuffiient to etermine the optiml number of slots of the ellulr grph, s emonstrte below. Exmple 1. Consier the ellulr grph s shown in figure 5. The numbers in prentheses besie eh ell enotes the emn of the ell. The ellulr istne-2 lique bfihe hs emn of 62 slots. The subgrphs bgjief n bef hve emns of 61 n 62 time slots respetively. Thus, we see tht there re two nite ritil bloks in the network : either subgrph bfihe or subgrph bef. We rbitrrily hoose the subgrph bfihe s our 7-noe ritil blok. For the istne-2 lique bgjief jent to the ritil blok, ells g n j n hve their emns stisfie from the slots ssigne to the ells n. However, the emn of ell (w =12)

6 Optiml Time Slot Assignment for Mobile A Ho Networks 255 (5) b (10) (12) e f g (4) (20) (15) h(6) i (2) j Fig. 5. Heterogeneous emn - 7 noe CB fils to give minimum number of slots (20,24) b (25,34) (52,63) e f g (58,61) (0,19) (35,49) (21,21) h(52,57) i (50,51) j (20,20) Fig. 6. An ssignment sheme requiring 64 slots is greter thn the slots ssigne to its two istne-3 neighbors, n h of the 7-noe ritil blok. The emn sum of ells n h, w + w h =(4+6)<w =12. Hene, it is neessry to ssign slots in ition to those ssigne to the ritil blok to stisfy the emn of ell. Thus, we see tht for heterogeneous emn, in generl, the 7-noe ritil blok will not lwys give the optiml number of slots of the ellulr network. Figure 6 shows possible slot ssignment sheme for the grph in figure 5. The 2-tuple besie eh ell enotes the slots ssigne to tht ell - (m, n) inites the slots in the rnge m to n, both inlusive. The 7-noe ritil blok fils to give the optiml number of slots s it is possible for one of the noes jent to noe of the ritil blok but not prt of it, to hve emn tht exees the sum of the emns of its istne 3 neighbors in the ritil blok. From the ellulr grph we see tht for every peripherl noe of the ritil blok, there re three neighbors whih re t istne 3 from some other peripherl noe of the ritil blok. Consier for exmple the noe f in figure 5 with neighbors, g n j. Noe n ontribute to stisfying the emns of ll of these three noes while the noe n only stisfy the emns of j n g, n noe h n only stisfy the emns of n g. Hene, eh of these three neighbors is potentil soure of exess emn over tht of the D (2) 7, either iniviully or in ombintion with the others. This suggests tht it is neessry to inlue ll of these three noes in omputing the optiml number of slots. Using 8-noe or 9-noe ritil blok woul lso fil to obtin lower boun on the number of slots for the sme resons s for 7-noe ritil blok. So, we onsier 10-noe blok onsisting of 7-noe istne-2 lique n three other noes outsie this istne-2 lique whih re neighbors of peripherl noe of this istne-2 lique. We thus get the following result. Lemm 3. For ellulr network with heterogeneous emn vetor, to fin the optiml bnwith requirement of the network, it is neessry to onsier 10 noe ritil blok, s using ritil blok with fewer thn 10 noes woul not be suffiient to ompute the minimum slot requirement of the network. In orer to ompute the emn of the 10-noe ritil blok for whih the number of slots will be mximum mong ll suh 10-noe bloks, let C =(V,E) be

7 K. Sinh ellulr istne-2 lique. Let free u enote the number of slots of noe uɛc tht n be use by noe whih is t istne three from u n not prt of C, n use u (j) be the number of slots ssigne to uɛc tht re reuse by noe j ɛ C n t istne three from u. Noting tht N 3 (u) is the set of ll istne-3 neighbors of noe u, weefineresiul emn res j of noe jɛn 1 (i), iɛc,j ɛ C s, res j =mx(0,w j use u (j)). ForiɛC, the sum of resiul emns of uɛn 3(j) V N 1 (i) whih re not in C will be terme s the resiul sum of neighbors of i n is efine s Res i = res j. jɛn 1(i),j ɛ C We emonstrte the proeure for omputing the 10-noe ritil blok with the help of the following exmple. Exmple 2. Consier the ellulr grph shown in figure 7. Let befg be nite ritil blok. Without ny loss of generlity, we onsier the three neighbors x, y n z of noe. Initilly, free = w, free f = w f n free e = w e. The omputtion of Res woul be s follows, Step 1 : Assign slots to noe x using mximum number of slots from noe e, nthe rest, if ny, from the noe f. use e (x) =min(w x,free e ); free e = free e use e (x) use f (x) =min(w x use e (x),free f ); free f = free f use f (x) res x =mx(0,w x (use e (x)+use f (x))) Step 2 : Assign slots to noe z using mximum number of slots from noe, nthe rest, if ny, from the noe f. use (z) =min(w z,free ); free = free use (z) use f (z) =min(w z use (z),free f ); free f = free f use f (z) res z =mx(0,w z (use (z)+use f (z))) Step 3 : Assign slots to y using vilble number of slots from noes e, n f. res y =mx(0,w y (free + free e + free f )) Step 4 : Sum the resiul emns of x, y n z, i.e., Res = res x + res y + res z. u v b x f g y e z t Fig. 7. A 10 noe ritil blok

8 Optiml Time Slot Assignment for Mobile A Ho Networks 257 Let Res mx (C) =mx [Res i]. Referring to figure 7, let D (2) 10 (G) represent the emn of the 10-noe subgrph, G befgxyz, whered (2) 10 (G) = D(2) 7 (C) + iɛc Res mx (C). The emn of the 10-noe ritil blok, D (2) 10 is then efine s the emn of 10-noe subgrph tht hs the mximl D (2) 10 (G) in the network, i.e., D (2) 10 =mx G [D (2) 10 (G)] Let R C represent the set of noes tht re outsie C, but jent to some peripherl noe of C, orresponing to Res mx (C). We ll R C s the mximum resiul set of C. Theorem 1. The emn sum D (2) 10 is the optiml bnwith requirement of hexgonl ellulr network hving heterogeneous emn vetor. Proof. We estblishe from lemm 3 tht it is neessry to onsier t lest 10 noe ritil blok in orer to ompute the minimum slot requirement of ellulr network. We now prove tht the emn of 10-noe ritil blok is neessry n suffiient to ompute the optiml bnwith requirement of hexgonl ellulr network. Let CB 10 enote the 10-noe ritil blok in ellulr network. Suppose the subgrph befgxyz in figure 7 is our ritil blok. Let G = befg be the ellulr istne-2 lique of the 10-noe ritil blok. Let R G enote the mximum resiul set of G. Thus, R G = {x, y, z} in figure 7. We note tht our 10-noe subgrph for hexgonl ellulr network is tully ompose of two jent ellulr istne-2 liques. To estblish theorem 1, onsier n ssignment sheme whih proees in spirl, lyer by lyer fshion, strting with the 10-noe ritil blok. Lyer 0 is ompose only of CB 10, lyer 1 ompose of ll unssigne ellulr istne-2 liques jent to CB 10. Lyer 2 inlues ll unssigne istne-2 liques jent to the istne-2 liques in lyer 1, n so on. One the emn of CB 10 hs been stisfie, we first strt with the unssigne istne-2 lique in lyer 1 tht inlues ll the noes of R G n then move in n nti-lokwise spirl orer. Cll this istne-2 lique C 1.Now in figure 7, the noes, x, y n z of C 1 re lrey stisfie. For the remining three unssigne noes in C 1, the noes, f, g n e n be use to stisfy their emns. As the slots ssigne to CB 10 re from slot 0 to D (2) 10 1, if the remining three noes in C 1 were to require slots beyon D (2) 10 1, it woul imply tht D (2) 10 (C 1) > D (2) 10, whih is ontrition. For the remining istne-2 liques jent to CB 10,wesee tht for ny suh istne-2 lique, C, there n be mximum of three unssigne noes in C. The ssigne noes re prt of CB 10. To prove tht D (2) 10 slots re suffiient to stisfy their emns, we prtition the set of the remining istne-2 liques jent to CB 10 into two sets : 1. Set of istne-2 liques whih hs t lest one but not ll unssigne noes within istne 2 of the noes in R G. 2. Set of istne-2 liques whose unssigne noes re ll t istne 3 from ny noe in R G. We first onsier the senrio when there is t lest one unssigne noe within istne two of R G. Without ny loss of generlity, let u n v be two unssigne

9 258 K. Sinh noes of the istne-2 lique C = uvxgb within istne two of R G s shown in figure 7. Noe u is 2-hop n v is 1-hop wy from x. From figure 7 it is pprent tht ny suh C woul hve to be jent to CB 10.Now,D (2) 10 for ellulr network woul not be optiml if noe u or v woul require slots beyon tht require by CB 10. Suppose, without ny loss of generlity, u requires slots beyon tht ssigne to CB 10. This implies tht res u must be greter thn res y + res z, or else these two noes oul itionlly be use long with the noes n e from the subgrph befg of CB 10 to stisfy the emn of u.now,ifres u >res y + res z res u +res x >res x +res y +res z res u +res v +res x >res x +res y +res z This woul imply tht the noes u, v n x form the set R G of the istne-2 lique befg. In other wors, the lique befg n the three noes u, v n w woul form the 10-noe ritil blok, whih woul be ontrition to the originl ssumption tht the noes x, y n z form the set R G for the ellulr istne-2 lique G. Consiering now the seon senrio of istne-2 lique C suh tht ll its unssigne noes re no less thn istne 3 from ll noes of R G.IfC is jent to G, then the emn of ny unssigne noe uɛc n be stisfie using ll noes of R G, in ition to the noes in G tht re t istne three from u. If the slots from 0 to D (2) 10 1 were not suffiient to stisfy the emn of noe u, then rguing s before, if the resiue emn of n unssigne noe uɛc, res u is greter thn Res mx (G),then it implies tht, res u >res x + res y + res z, whih woul gin be ontrition to our originl ssumption tht R G = {x, y, z} represents the mximum resiue set of the istne-2 lique G. Thus, it is possible to stisfy the emns of ll istne-2 liques jent to CB 10, using the slots from 0 to D (2) Using similr ssignment proeure n rgument s bove, we n show tht the slots from 0 to D (2) 10 1 re suffiient to stisfy the emns of ll unssigne istne-2 liques in lyer 2 tht re jent to stisfie istne-2 liques in lyer 1. The proess n be repete for istne-2 liques in lyer 3, 4, 5,..., to obtin n ssignment sheme tht requires only slot vlues from 0 to D (2) Hene, D (2) 10 is the optiml require bnwith for ellulr network. Note tht the ellulr istne-2 lique of 10-noe ritil blok my not be 7-noe ritil blok, s my be seen from figure 8. In figure 8 we see tht the 7-noe ritil blok emn is 62 slots, while the 10-noe ritil blok emn is 65 slots. Subgrphs bfjie n bef both hve emns of 62 slots (orresponing to 7-noe ritil blok), while the subgrphs pqrstuvwxy n pqwvrstu both hve emns of 10- noe ritil blok. If, bfjie (bef) is hosen s the 7-noe ritil blok, then the emn of the 10-noe subgrph bfjiegk (befij) woul be 64 time slots. 5 b p 10 q 10 w 6 e f g u v r x i 2 j 1 k 1 1 t 4 s y 1 Fig. 8. A 10 noe ritil blok not forme by 7 noe ritil blok

10 Optiml Time Slot Assignment for Mobile A Ho Networks 259 The lgorithm for fining n optiml slot ssignment for ellulr network with heterogeneous emn, while stisfying the 2-ell buffering onstrint is s follows : Algorithm heterogeneous slot ssignment Step 1 : For eh ell i of the network, onstrut ellulr istne-2 lique, C with i s the entrl noe. Compute the emn sum, D (2) 7, of the ells belonging to C. Step 2 : For eh peripherl noe jɛc, ompute the resiul sum set, Res j. Step 3 : The mximum resiul sum set, R C orrespons then to the set of neighbors of peripherl noe kɛc suh tht Res k = Res mx (C) =mx [Res j].letg enote jɛc the 10-noe subgrph orresponing to entrl noe i of C. Then, G = C R C. Step 4 : Compute the emn of G, D (2) 10 (G) =D(2) 7 + Res mx(c). Step 5 : Repet step 1 to 4 to obtin the emn D (2) 10 (G) of ll 10-noe subgrphs in the network. The mximum of these emns is the 10-noe ritil blok emn. D (2) 10 =mx G [D(2) 10 (G)] Step 6 : Now rbitrrily hoose one of the 10-noe nite ritil bloks s the 10-noe ritil blok of the ellulr network. Step 7 : Stisfy the emn of the noes of CB 10 uner the 2-ell buffering onstrint. Step 8 : Stisfy the emns of ll istne-2 liques in lyer 1, jent to CB 10. Begin with the one forme by the noes of mximum resiul set of CB 10. Step 9 : Continue the proess of ssigning slots to istne-2 liques in lyer 2, lyer 3 n so on, in spirl, lyer by lyer fshion s esribe in theorem 1. 5 A Centrlize Optiml Slot Assignment Algorithm (COSA) We present in this setion entrlize slot llotion lgorithm for ssigning slots s per emn of eh ell in the ellulr network, while utilizing the minimum number of slots require for generting ollision-free trnsmission sheule tht stisfies the 2-ell buffering onstrint, s 0 = s 1 = s 2 =1. Eh MT is ssigne unique ientifier (i) from the set {1, 2, 3,...,m},wherem is the totl number of mobile terminls. Initilly, eh mobile terminl (MT) knows its positionl o-orintes. In orer to hnle mobility of the mobile terminls, eh ell keeps few slots for trnsmitting ontrol messges n some unuse slots for hnling new MTs joining the network n hn-off senrios. In generl, ell i omputes its emn w i s the sum of the number of mobile terminls in the ell, the number of slots llote for ontrol messges n n itionl few unuse slots. We ssume the number of unuse slots to be some frtion f of the number of mobile terminls urrently in the ell. If m i is the number of MTs urrently in ell i n slots re use for ontrol purpose, then the emn, w i of ell i is, w i = m i + +mx(1, fm i ), 0 f Algorithm COSA The steps of the lgorithm re s follows : Step 1 : Elet n MT s the network leer through some leer eletion protool [11, 12] n ll this MT s L.

11 260 K. Sinh Step 2 : L brosts the mpping to onvert the geogrphil region into hexgonl gri struture to ll the noes of the network. Eh noe, on reeiving this messge, ppens it with its own lotion o-orintes to be known to ll other noes. An MT i trnsmits its messge in i th slot to voi ollision uring this step. Step 3 : For eh ell i, ell leer L i is elete from the MTs resiing in ell i, bse on some metri suh s remining bttery power, lo, lotion, et. [12]. Step 4 : The emn of eh ell i, w i is ommunite by eh ell leer L i to the network leer L. L proues n optiml, ollision-free trnsmission sheule by exeuting either homogeneous slot ssignment or heterogeneous slot ssignment lgorithm. Step 5 : L brosts the slot ssignment sheule of the network to eh ell leer. The slot ssignment sheule etils the slots ssigne to eh ell i, whih h emne w i slots. One ell leer L i of ell i reeives the informtion bout the slots ssigne to it from L, it genertes trnsmission sheule for the MTs in the ell i n oes perioi lol brost of this sheule within the ell i. Due to spe onstrints, we briefly esribe the hnling of vrious ynmi situtions like joining/leving of mobile terminls n hn-off. New mobile terminl joining the network : When new MT joins the network in some ell i, it first wits to her ell sttus messge brost by the ell leer, L i n then tries to join the network by sening request to L i. A reomputtion of globl slot ssignment by L is require if not enough free slots exist in ell i. Mobile terminl leving ell or network: If ell (network) leer leves ell then new ell (network) leer is elete from the remining MTs (ell leers). Hn-off of mobile terminls : The proess of hn-off is trete in the sme wy s new MT u joining ell j, from ell i, with n itionl messge from L j to L i to inite the new ell in whih u n be foun. 5.2 Complexity Anlysis The leer eletion proess in step 1 of lgorithm COSA tkes O(log log m) time [11, 12]. Steps 2 n 5 eh tkes O(mD) time for roun-robin brost, ssuming i, i D n w i = O(m) forstep5oflgorithm COSA. Step3oflgorithm COSA tkes O time. Computtion of n optiml slot ssignment sheule by either lgorithm homogeneous slot ssignment or lgorithm heterogeneous slot ssignment tkes O(n) time, n being the number of ells in the ellulr network. Thus, step 4 tkes O(mD)+O(n) time. Hene the omplexity of our propose lgorithm COSA is O(log log m + md + n) time. 6 Conlusion We hve presente novel pproh to the problem of generting ollision-free trnsmission sheule for mobile terminls in mobile ho network. Our propose lgorithm overlys MANET with hexgonl ellulr gri struture n then genertes ollision-free trnsmission sheule with the minimum number of time slots, while stisfying the 2-ell buffering onstrint using low overhe. Due to the bsene of

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