MOCAVI: An Efficient Causal Protocol for Cellular Networks

136 IJCSNS International Journal of Coputer Science and Network Security, VOL.8 No.1, January 2008 MOCAVI: An Efficient Causal Protocol for Cellular Networks Eduardo Lopez Doinguez, Saul E. Poares Hernandez and Gustavo Rodriguez Goez Coputer Science Departent National Institute of Astrophysics, Optics and Electronics (INAOE), Luis Enrique Erro #1, 72840, Tonantzintla, Puebla, Mexico Suary A cellular network consists of two ain coponents: base stations (BS) and obile hosts (). It is through base stations that obile hosts can counicate. In order to reduce the causal overhead and the coputational cost over obile hosts, ost of the existing protocols for cellular networks ensure causal order at BSs. However, these protocols introduce unnecessary inhibition of delivery of essages since the causal ordering is carried out according to the causal view of the BSs and not in absolute accordance with the causal view of the s. In this paper, we present MOCAVI, an efficient protocol that ensures causal ordering according to the causal view of obile hosts, through which we avoid the unnecessary inhibition of essage delivery while aintaining a low overhead and coputational cost. Key words: Causal ordering, obile causal view, cellular networks, iediate dependency relation. 1. Introduction In recent years, cellular networks have experienced several exciting innovations and will continue to represent a rapidly growing sector in the near future. The evolution of cellular networks establishes a trend to use portable coputing devices, such as sart phones and personal digital assistants (PDAs). In conjunction with wireless counication technologies, cellular networks enable users to access the internet at anytie and anywhere in the world. The goal is to provide users with access to desktop applications, applications specially suited for obile users, and ultiedia applications. However, cellular networks involve new characteristics and constraints, such as changeable physical network connections, liited processing and storage capabilities in obile devices, as well as liited bandwidth on wireless counication channels. Many protocols have been proposed for cellular networks in different research areas such as causally ordered essage delivery [2-9], utual exclusion [13], and checkpoint protocols [14]. In this paper, we consider the proble of causal order essage delivery aong obile hosts in the context of group counication. Soe protocols [2-9] have been proposed to ipleent causal essage ordering over cellular networks. In order to reduce coputational costs and counication loads on obile hosts, ost of these protocols store relevant data structures in the base stations (BS), and they are executed by the BSs on behalf of the obile hosts (). These ethods give rise to two ain probles. First, the causal order seen by the BSs differ fro the causal order seen by the s. Secondly, they introduces unnecessary inhibition of essage delivery. This unnecessary inhibition is due to the serialization of essages at the BSs level. The serialization of essages appears since a base station is unable to detect utual concurrency between essages occurring at different s in its cell. In this paper, we propose a new protocol called MOCAVI, which ensures the causal ordering according to the causal view that the obile hosts perceive during the syste execution, avoiding unnecessary inhibition of essage delivery while aintaining a low overhead and coputational cost. To achieve this, we differentiate two counication levels according to the connection type (wired and wireless): intra-base counication level and inter-base counication level. At the intra-base counication level (wireless connection) we only send as causal overhead, between a BS and the s attached to it, a vector of bits Φ of size n (Φ(n), where n is the nuber of participants in the group). At the inter-base counication level (wired connection) we only send as causal overhead, between BSs, inforation about essages that are related through iediate dependence [11]. As we will show, the vector Φ(n) used at the intrabase counication level is sufficient to ensure causal essage ordering as seen by the s of the syste. The rest of this paper is organized as follows. Section 2 presents the syste odel, background, and definitions. A description of the proposed protocol in this work is provided in Section 3. Next, in Section 4 we copare our protocol with other works in two aspects: essage overhead and unnecessary inhibition in essage delivery. Finally, conclusions are presented in Section 5. Manuscript received January 5, 2007 Manuscript revised January 20, 2007

IJCSNS International Journal of Coputer Science and Network Security, VOL.8 No.1, January 2008 137 2. Preliinaries 2.1 The Syste Model A cellular network consists of two kinds of entities: obile support stations or base stations and obile hosts. A base station (BS) has the necessary infrastructure to support and counicate with obile hosts. The BS counicates with obile hosts through wireless counication channels. The geographic area covered by a base station is called cell, figure 1. A obile host () is a host that can ove while retaining its network connection. At any given tie, a is assued to be within a cell of at ost one BS, which is called its local BS. A can counicate with other s and BSs only through its local BS. We assue in this paper that the wireless counication channels between s and BSs are FIFO and reliable. The base stations are connected aong theselves using wired channels. The BSs and the wired channels constitute the static network. We assue that the wired channels are reliable and take an arbitrary but finite aount of tie to deliver essages. Due to syste asynchrony and unpredictable counication delays, the sent essages on cellular network can arrive in a different order as they were sent. Cell BS BS Cell Wired network Cell Figure 1. Cellular network architecture In a cellular network, a obile host can ove fro one BS to another. In this case, a hand-procedure (not presented in this paper) is perfored to transfer the counication responsibilities of to the new BS. BS BS Cell With respect to the logical specification in our work, the application under consideration is coposed of a set of obile hosts P = {i, j, n} organized into a group that counicates by reliable broadcast asynchronous essage passing. We consider a finite set of essages M, where each essage Î M is identified by a tuple = (p,t), where pîp is the sender of, denoted by Src(), and t is the sequential ordered logical clock for essages of p when is broadcasted. The set of destinations of a essage is always P. 2.2 Background and Definitions Causal ordering delivery is based on the causal precedence relation defined by Laport [10]. The happened-before relation establishes, over a set of events, possible precedence dependencies without using physical clocks. It is a partial order defined as follows: Definition 1. The causal relation is the least partial order relation on a set of events satisfying the following properties: If a and b are events belonging to the sae process and a was originated before b, then a b. If a is the send essage of a process and b is the reception of the sae essage in another process, then a b. If a b and b c, then a c. By using Definition 1 we can cay that a pair of events are concurrent related a b only if Ø (a b Ú b a). The precedence relation on essages denoted by is induced by the precedence relation on events, and is defined by: Û send() send( ) The Iediate Dependency Relation. The Iediate Dependency Relation (IDR) foralized in [11] is the propagation threshold of the control inforation regarding the essages sent in the causal past that ust be transitted to ensure a causal delivery. We denote it by, and its foral definition is the following: Definition 2. Iediate Dependency Relation (IDR): Û[ ( ) Ù " Î M, Ø( )] Thus, a essage directly precedes a essage, iff no other essage belonging to M exists (M is the set of essages of the syste), such that belongs at the sae tie to the causal future of and to the causal past of.

138 IJCSNS International Journal of Coputer Science and Network Security, VOL.8 No.1, January 2008 This relationship is iportant because if the delivery of essages respects the order of the diffusion for all pairs of essages in an IDR, then the delivery respects the causal order for all essages. This property is forally defined for the broadcast case as follows: Property 1: If ", Î M, Þ " p Î P : delivery(p,) deliver(p, ) then Þ "p Î P : delivery(p,,) delivery(p, ) Causal inforation that includes the essages iediately preceding a given essage is sufficient to ensure a causal delivery of such essage. Transission tie of essage ( d() ) We analyze the necessary tie for transitting a essage by a obile host p i to another obile host p j. Both obile hosts within the cell are covered by the base station BS r. First, the obile host p i sends a essage to its local base station BS r over a wireless counication channel. The local base station BS r receives the essage at a tie t. Before the transission of essage to obile host p j, the base station BS r attached control inforation to essage in a tie period called processing_tiebs r (). Finally, BS r sends the essage at tie t to obile host p j through a wireless counication channel, figure 2. BS r p i p j t Figure 2. Transission tie of a essage into its local cell. Thus, we can divide the necessary tie to transit a essage into three parts. uplink_tie(): transission tie in wireless counication channels for a essage fro the obile hosts to its base station. processing_tie(): period of tie necessary used by a base station to attach control inforation to the received essage. t d() downlink_tie(): transission tie in wireless counication channels for a essage fro the base station to a obile host. Therefore, the total transission tie of a essage is equal to: d()= uplink_tie() + processing_tie() + downlink_tie() + e In our case, we consider a possible error in the variation tie represented by the variable e. 3. The Causal View Protocol Protocol overview Fro the point of view of the physical architecture, we consider two counication levels in a obile syste: Intra-base and Inter-base. The Intra-base counication level is fored by a wireless network integrated by a base station and obile hosts. In this level, the base station provides counication services to obile hosts in its cell. The inter-base counication level is fored by a wired network constituted by several base stations. On the other hand, fro a logical point of view, we consider only one counication level. This counication level is fored by the view that obile hosts have during the syste execution. In our work, we propose a protocol that carries out a causal ordering according to the causal view that the obile hosts perceives during the syste execution. In our case, the base stations are in charge of carrying out the causal delivery of essages according to the order in which essages were observed by the obile hosts, thus avoiding the serialization of the essages iplicitly established by the causal view of the base station. The obile host uses a bit vector Φ i, to establish the iediate dependency relation aong essages. The nuber of bit vectors at a obile host is equal to the nuber of base stations involved in syste. In our protocol, each bit vector logically represents the obile host of a cell. The size of Φ i is equal to the nuber of obile hosts that are within the cell of the base station i. A bit of Φ i is equal to 1 if a essage sent by a obile host of the base station i has an iediate dependency relation (definition 2) with the next essage to send. The bit vectors are the only control inforation attached to essages sent in the wireless counication channel

IJCSNS International Journal of Coputer Science and Network Security, VOL.8 No.1, January 2008 139 which deterine the iediate dependency relation between essages. The base stations keep control inforation of essages causally sent in the cellular network. Through this control inforation and the bit vectors attached to essages by the s, the base stations can deterine precedence iediate dependencies between essages sent by s on different BSs. 3.1 Data Structures Each base station has the following data structures: VT(p) is the vector tie. For each obile host p there is an eleent VT(p)[j], where j is a obile host identifier. The size of VT is equal to the nuber of obile hosts in the group. VT(p) contains the local view that a obile host p has of the eleents of the syste. In particular, eleent VT(p)[j] represents the greatest eleent nuber of the identifier j and seen in causal order by p. It is through the VT(p) structure that we are able to guarantee the causal delivery of eleents. A structure to keep control inforation CI(p) of essages sent. The structure CI(p) is a set of entries (k, t, d,, ip). Each entry in CI(p) denotes a essage that is not ensured by participant p of being delivered in a causal order. The entry (k, t, d,, ip) represents a diffusion by participant k at a logical local tieclock t = VT(p)[k], where d is equal to the nuber of essages sent by the base station, is a variable of type tie, and ip is a boolean variable, which is used to indicate if the essage represented by the entry (k, t, d,, ip) iediately precede a received essage. An integer counter sent_essages that is increented each tie a essage is sent by the base station. The structure of a essage sent in the wired counication channels is a quintuplet ( i, t, BS k, data, H()), where i is the obile host identifier, t is the essage identifier, BS k is the base station identifier, data is the inforation in question, and H() is coposed of a set of eleents h r (), H()={ h r (), h s (), h w ()}, where w is equal to the nuber of base stations in the group. Each eleent h r () of H() is fored by a set of entries (k, t), which represent essages that that have an IDR with. Structure H() is created at the oent of diffusion of a essage by a base station. Data structures aintained at the obile host are: An integer counters received_essages, which is increented each tie that a essage is received by the obile host p. A bit vector Φ r, for each base station r in the counication group. The size of Φ r is equal to the nuber of obile hosts that are within the cell of the base station r. The bits put to 1 in Φ r indicate the iediate dependency relation that the transitted essage has with the essages sent by obile hosts in the BS r. For exaple, the bit of Φ r (p)[j] = 1, indicates that a sent essage by obile host j in the cell covered by the base station r iediately precedes the next essage to send by obile host p. The structure of a essage sent in the wireless counication channels has the following for: (i,t,data,received_essages,{φ r (p),φ s (p)...φ w (p)}, where i is the obile host identifier, t is the essage identifier, received_essages is a counter that is increented each tie a essage is received by the obile host i, and Φ r (p),φ s (p)..φ w (p) are bit vectors that logically represent to the obile host of the cells covered by the base stations r, s, and w, respectively. In our work, a essage transitted by a obile host is denoted by i. When a essage i is sent by the base station to local obile hosts, the essage is denoted by i, and a essage i sent by the base station to another base station is denoted by i. 3.2 Specification of the protocol Table 1. Initially 1. /* Data structures aintained at base station p */ 2. VT(p)[j] = 0 " j:1 n. 3. CI(p)[j] Æ " j:1 w 4. IDR_bits(p) /* vector of bits of size n */ 5. IDR_bits(p)[j] = 0 " j: 1 n. 6. /* Data structures aintained at obile host */ 7. Φ r(p)[j] = 0; j = 1 n ; r = 1 w 8. received_essages = 0 /* account of received essages */ 9. 10. let update_ci( H() ) { // update the control inforation at BS 11. For each h r() Î H() 12. " (x,y) Î h r() if ( x i ) then 13. if $ (k,t,d,, ip) Î CI(p) k = x and t y and = 0 then

140 IJCSNS International Journal of Coputer Science and Network Security, VOL.8 No.1, January 2008 14. (k, t, d,, ip) (k, t, d, = current_tie, ip) 15. Endif 16. Endfor 17. For each (k,t,d,,ip) Î CI(p) /* Delete soe entries of CI */ 18. if ( + d() current_tie ) then 19. CI(p) CI(p) / (k,t,d,,ip) 20. Endfor 21. } Table 2. Diffusion of essage by obile host p 1. /* building of essage */ 2. id_essage = id_ essage +1 3. /* º(i=id_host, t= id_ essage, received_essages, data, {Φ r(p), Φ s(p).φ w(p)}) */ 4. Difussion:send() /*sent of essage to local base station p*/ Table 3 Reception of essage at base station BS k={p i, p j..p n} 1. /* (i, t, received_essages, data,{φ r(p), Φ s(p).φ w(p)})*/ 2. if i Î BS k then 3. if not ( t =VT(p)[i] +1) then 4. wait 5. Else 6. delevery() 7. VT(p)[i] = VT(p)[i] +1 8. /* bit vectors to atach the sent essage to local obile hosts*/ 9. For each Φ r(p) Î r = s,t, w 10. For all Φ r(p)[j] = = 1; j = 1,2..n 11. if $ (k,t,d,,predecesor) Î CI(p) k = j and d received_essages and predecesor = false then 12. IDR_Bits r(p)[j] = Φ r(p)[j] 13. (k,t,d,, predecesor) (k,t,d,,predecesor=true) 14. else 15. IDR_Bits r(p)[j] = 0 16. Endif 17. Endfor 18. Endfor 19. ' (i,t =sent_essages+1,data,{idr_bits r(p),idr_bits s(p) IDR_Bits w(p)}) 20. Difussion : send( ) /* sent of essage to local obile hosts */ 21. For each Φ r(p) Î r = s,t, w // foring H() 22. For all Φ r(p)[j] = = 1; j = 1,2..n 23. " (k,t,d,,predecesor) Î CI(p) 24. if (( k = j ) and ( d received_essages))then 25. h r() h r() È ( k, t ) 26. endif 27. Endfor 28. Endfor 29. ( i, t, BS k, datos, H()) 30. Difussion : send( ) /* sent of essage to other 31. Endif /* End of if, line 3 */ 32. Else /* i Ï BS k */ Mobile hosts*/ 33. /* (i, t, BS k,datos, H()) */ 34. if not ( t =VT(p)[i] +1 and " (s,x)î H(): x VT(p)[s] ) then 35. Wait 36. Else 37. delivery() 38. VT(p)[i] = VT(p)[i] +1 39. /* essage to sent by BS to local obile hosts */ 40. For each h r() Î H() 41. " (x,y) Î h r() 42. if $(k,t,d,, predecesor)î CI(p) x=k and y = t and predecessor=false then 43. IDR_Bits l(p)[k] = 1 44. (k,t,d,, predecesor) (k,t,d,, predecesor=true) 45. Else 46. IDR_Bits l(p)[k] = 0 47. endif 48. Endfor 49. ' ( i, t =sent_essages+1,bs, datos, {IDR_Bits r(p), IDR_Bits s(p),. IDR_Bits w(p)}) 50. Difussion : send() /* sent of essage to local obile hosts */ 51. Endif 52. Endif 53. sent_essages= sent_essages + 1 54. update_ci(h() ) 55. CI(p) CI(p) È { (i,t, sent_essages, = 0, predecesor=fase)} Table 4. Reception of essage by obile host p. 1. /* ( i, t, BS k, datos, {IDR_Bits l(p), IDR_Bits l+1 (p),.. IDR_Bits (p)}) */ 2. If not ( t = received_essages + 1) then 3. Wait 4. Else 5. Delivery( ) 6. received_essages = received_essages + 1 7. For each IDR_Bits l(p) Î l = s,u, w 8. For all IDR_Bits l(p)[j] = =1; j = 1,2 n : j i 9. if (Φ l(p)[j] = =1) then 10. Φ l(p)[j] = 0 11. Endif 12. Endfor 13. Endfor 14. Φ k(p)[i] = 1 15. Endif

IJCSNS International Journal of Coputer Science and Network Security, VOL.8 No.1, January 2008 141 3.3 Scenario Exaple Consider the group of obile hosts g = {h 1, h 2, h 3, h 4 } and the diffusion of essage 3 to other obile hosts, where h 1 and h 2 are present in the cell served by BS 1, and h 3, and h 4 are present in the cell served by BS 2, see figure 3. Before the delivery of 3 to BS 1, CI(BS 1 )=(h 1,1,2,0,false), CI(BS 2 )=(h 1,1,2,0,false), VT(BS 1 )=(1,0,1,0) and VT(BS 2 )= (1,0,1,0). These values are deduced fro our MOCAVI protocol shown in tables 1-4. In figure 3, we show transitted essages during the execution of our MOCAVI protocol. Diffusion of essage 3 by h 2 at BS 1 Lines 2-4, table 2. The value of id_essage is increented by one. The variable id_essage identifies the essage sent by h 2. Diffusion of essage 3 =(h 2,1,2,data,10,00), send( 3 ). Delivery of essage 3 to its local BS 1 Lines 2-31, table 3. Each tie that a BS receives a essage fro a local obile host. The BS only verifies that the received essage satisfies the FIFO delivery condition. In this case, essage 3 =(h 2,1,2,data,Φ 1 =10, Φ 2 =00) satisfies the delivery condition (Line 3) because t=1 and VT(BS 1 )[ h 2 ] = 0. Thus, the condition t=vt(bs 1 )[h 2 ] +1 is satisfied. Now, essage 3 is delivered and the vector is increased by one in VT(BS 1 )[h 2 ], resulting in VT(BS 1 )=(1,1,1,0), lines 6-7. The bit put to 1 in Φ 1 indicates that a essage sent by h 1 served by BS 1 iediately precedes 3. Later on, the BS 1 ust send the essage 3 to its local obile hosts and to the others obile hosts in the base station BS 2, see figure 3. h 2 h 1 BS 1 BS 2 h 3 h 4 1 1 1 1 2 2 2 4 Figure 3. A scenario of group counication fored by four obile hosts. 3 4 3 3 3 5 4 5 5 Lines 9-20. Sending by BS 1 of essage 3 to the local obile hosts. BS 1 builds the bit vectors attached to 3. In this case, the essage to send is 3 º (i=h 2, t =3, data, IDR_Bits 1 =10, IDR_Bits 2=00). Diffusion of essage 3 by BS 1 to base station BS 2 Lines 21-30. Sending by BS 1 of essage 3 to base station BS 2. BS 1 identifies the essages that have an iediate dependency relation with 3 through of the bit vectors Φ r received attached to it and the control inforation stored in the structure CI(BS 1 ). In Φ 1 the bit equals to 1 indicates that h 1 has sent a essage that iediately precedes to 3. In order to identify the essage that iediately precedes to 3, BS 1 verifies if an entry (k,t,d) of obile host h 1 already exists in CI(BS 1 ) with a d inor or equal to the variable received_essages of 3. In this case, there is an entry storage at CI(BS 1 ) about h 1 with d =2 and the condition d received_essages is satisfied. This entry is the control inforation of essage 2. Thus, the only control inforation attached to 3 in order to ensure a causal order relates to 2, which is the only essage in an iediate dependency relationship with 3, see figure 3. Therefore, the essage to send by BS 1 to BS 2 is 3 =(h 2,1, BS 1,data, (h 1,1)), Line 29. Diffusion of essage 4 by h 4 at BS 2 Lines 2-4, table 2. The value of id_essage is increented by one. The variable id_essage identifies the essage sent by h 4. Diffusion of essage 4 =(h 4,1,2,data,10,00), send( 4 ). Delivery of essage 4 to its local BS 2 Lines 2-31, table 3. The BS 2 verifies that only the received essage satisfies the FIFO delivery condition. In this case, essage 4 =(h 4,1,2,data,10,00) satisfies the delivery condition (Line 3). Now essage 4 is delivered and the vector is increased by one in VT(BS 2 )[h 4 ], resulting in VT(BS 2 )=(1,1,1,1), Line 6-7. Later on, the BS 2 ust send the essage 4 to its local obile hosts and to base station BS 1. Lines 9-20. Sending by BS 2 of essage 4 to the local obile hosts. In this case, the essage to send is 4 =(h 4,3,data, IDR_Bits 1 =10, IDR_Bits 2 =00). Diffusion of essage 4 by BS 2 to base station BS 1 Lines 21-30. In Φ 1 the bit equal to 1 indicates that h 1 has sent a essage that iediately precedes to 4. In order to identify the essage that iediately precedes to 4, BS 1 verifies if an entry (k,t,d) of obile host h 1 already exists in CI(BS 1 ) with a d inor or equal to the variable received_essages of 4. In this case, there is an entry

142 IJCSNS International Journal of Coputer Science and Network Security, VOL.8 No.1, January 2008 storage at CI(BS 2 ) about h 1 with d =2, and d received_essages is satisfied. Thus, the only control inforation attached to 4 in order to ensure a causal order relates to 2, which is the only essage that has an iediate dependency relationship with 3, see figure 3. Line 29, Therefore, the essage to send by BS 2 to BS 1 is 4 =(h 4,1, BS 2,data, (h 1,1)). Line 30, Diffusion of 4, send( 4 ). Delivery of essage 3 to BS 2 Lines 33-55, table 3. Each tie a BS receives a essage fro a obile host within cell different to cover by it. The BS verifies that the received essage satisfies the FIFO and causal delivery condition. In this case, essage 3 =(h 2,1, BS 1,data, (h 1,1)) satisfies both conditions (Line 34) because t=1 and VT(BS 2 )[ h 2 ] = 0, and the conditions t=vt(bs 1 )[h 2 ]+1 and " (s,x)îh():x VT(p)[s] are satisfied. Now essage 3 is delivered and the vector is increased by one in VT(BS 2 )[h 2 ], resulting in VT(BS 2 )=(1,1,1,1). Later on (lines 40-50), the BS 2 ust send essage 3 to its local obile hosts. The essage to send by BS 2 to local obile hosts is 3 =(h 2,4, BS 1,data, 00,00), Line 49. Delivery of essage 3 to obile host h 3 Lines 1-10, table 4. Each tie that a obile host receives a essage, the only verifies that the received essage satisfies the FIFO delivery condition. In this case, essage 3 =(h 2,4, BS 1,data, 00,00) satisfies the delivery condition (Line 3) because t =4 and t = 3 + 1. Later on, h 3 updates its bit vectors, Line 2-8. After updating the data structures at h 3, the bit vectors are Φ 1 =01, and Φ 2 =01. In the bit vectors Φ 1 and Φ 2, the bits equals to 1 indicate that last essages received by h 3 were sent by h 2 and h 4, respectively. Diffusion of essage 5 by h 3 at BS 2 Lines 2-4, table 2. The value of id_essage is increented by one, id_essage=2. Line 4, Diffusion of essage 5 =(h 3,2,4,data,01,01), send( 5 ). Delivery of essage 5 to its local BS 2 Lines 2-31, table 3. In this case, essage 5 =(h 3,2,4,data, Φ 1 =01,Φ 2 =01) satisfies the FIFO delivery condition (Line 3). Now essage 5 is delivered, and the vector is increased by one in VT(BS 2 )[h 3 ], resulting in VT(BS 2 )=(1,1,2,1). Later on, the BS 2 ust send essage 5 to its local obile hosts and to base station BS 1. Lines 9-20. Sending by BS 2 of essage 5 to the local obile hosts. The essage to send is 5 =(h 3,5, BS 2,data,01,01). Line 20, Diffusion of essage 5, send( 5 ). Diffusion of essage 5 by BS 2 to base station BS 1 Lines 21-30. In Φ 1 and Φ 2 the bits set to 1 indicate that the essages sent 3 and 4 by h 2 and h 4, respectively, iediately precede to 5. Thus, the only control inforation attached to 5 in order to ensure a causal order relates to 3 and 4, which are the only essages that have an iediate dependency relation with 5, see figure 3. Line 29, Therefore, the essage to send by BS 2 to BS 1 is 5 =(h 3,2,BS 2,data,{(h 2,1),(h 4,1)}). Line 30, Diffusion of 5, send( 5 ). Delivery of essage 5 to BS 1 Lines 33-55, table 3. The BS 1 verifies that the received essage satisfies the FIFO and causal delivery condition, Line 34. In this case, essage 5 =(h 3,2,BS 2,data, {(h 2,1), (h 4,1)}) satisfies only the FIFO delivery condition (Line 34) because t=2 and VT(BS 1 )[h 3 ]=1 and the condition t=vt(bs 1 )[h 3 ]+1 is satisfied. Because the essage 4 hasn t been received by obile hosts within the cell covered by BS 1, the causal delivery condition (Line 34, 1 VT(BS 1 )[h 4 ]=0) is not satisfied; therefore, essage 5 cannot be delivered causally and it is delayed (Line 35). Delivery of essage 4 to BS 1 Lines 33-55, table 3. The BS 1 verifies that the received essage satisfies the FIFO and causal delivery condition. In this case, essage 4 =(h 4,1, BS 2,data, (h 1,1)) satisfies both conditions (Line 34). Message 4 is delivered, and the vector is increased by one in VT(BS 1 )[h 4 ], resulting in VT(BS 1 )=(1,1,1,1). Later on, the BS 1 ust send essage 4 to its local obile hosts. The essage to send by BS 1 to local obile hosts is 4 =(h 4,4,BS 2,data,00,00), Line 49. Delivery of essage 4 to obile host h 1 Lines 1-10, table 4. The obile host h 1 updates its bit vectors with the reception of essage 4 =(h 4,1,BS 2,data, 00,00), Lines 2-8. The bit vectors after updating the data structures at h 1 are Φ 1 =01, and Φ 2 =01. Line 10, the variable received_essages is increented by one, received_essages= 4. Delivery of essage 4 to obile host h 2 Lines 1-10, table 4. The bit vectors after updating the data structures at h 2 are Φ 1 =01 and Φ 2 =01. Line 10, The account of received essages is increented by one, received_essages= 4.

IJCSNS International Journal of Coputer Science and Network Security, VOL.8 No.1, January 2008 143 Delivery of essage 5 in causal ordering at BS 1 Lines 33-55, table 3. Finally, the BS 1 after the causal delivery of essage 4 verifies if essage 5 satisfies the causal delivery condition, Line 34. Now, essage 5 =(h 3,2,BS 2,data,{(h 2,1), (h 4,1)}) satisfies the causal delivery condition (Line 34) because essage 4 has been received by obile hosts within the cell covered by BS 1. The causal delivery condition (Line 34, 1 VT(BS 1 )[h 4 ]=1) is satisfied, and therefore essage 5 can be delivered causally (Line 37). Later on, the BS 2 ust send essage 5 to its local obile hosts. The essage to send by BS 1 to local obile hosts is 5 =(h 3,5,data, 01,01), Line 49. 4. Coparisons We copare our algorith versus the related work in two aspects: essage overhead and unnecessary inhibition in the essage delivery (see Table 5). 4.1 Message overhead In order to ensure the causal delivery of essages, all algoriths need to add control inforation to the header of each essage. This control inforation is overhead that will increase the bandwidth used. However, the aount of overhead added to the essages by each one of these algoriths is considerably different. Table 5. Coparison between causal algoriths for cellular networks (where n = nuber of s and =nuber of BSs) Protocol Overhead (wireless network) Overhead (wired network) Counication Unnecessary type delivery inhibition AV-1 0 O(n 2 ) Unicast No AV-2 0 O( 2 ) Unicast Yes AV-3 0 O( 2 * k 2 ) Unicast Yes YHH 0 O(n * ) Unicast Yes Mobi Causal O( å = i 1 li ) O( å = i 1 Hence, the control inforation size attached to essages send over the wired network of the algoriths AV-2, AV-3 [2], YHH [3], and Mobi_Causal [9] is O( 2 ), O( 2 k 2 ), O(n * ), and O( å i = 1 li ) respectively, where k is a predeterined integer paraeter, and l i represents the li ) Unicast NO LH 0 O() Multicast Yes PRS O(n) O(n) Group counication KHC 0 O() Multicast Yes MOCAVI Φ(n) O(s): 1 s n Group counication No No nuber of essages sent by base station i. In these algoriths, each essage is intended for a single destination site (obile host), whereas algoriths LH [4], PRS [8], KHC [5], and our proposed protocol MOCAVI allows a essage to be destined for n sites, see table 5. The lowest essage overhead, O(), is proposed in LH, and KHC [5]. However, these algoriths can unnecessarily delay the delivery of a essage since they preserve the causal ordering at a base station level. In our proposal, the size of control inforation differs fro the intra-base counication level and inter-base level. For the intra-base level, we send a constant overhead of n bits per essage. And for inter-base level (counication aong BSs) is given by the cardinality of H(), which can fluctuate in our case between 1 and n (0 H() n), where n is equal to the nuber of obile hosts in the group. This is because H() only has inforation about the ost recent essages that iediately precede a essage. In the best case, dealing with the serial case, we note that the essage overhead is H() =1, and in the case of concurrent essages, the worst case is H() =n. We notice that in our protocol, as for the inial causal algorith in [11], the likelihood that the worst case will occur approaches zero as the nuber of participants in the group grows. Copared with other works that are exclusively based on vectors clocks [2-9], our worst case denotes for the the constant overhead that ust always be attached per essage. 4.2 Unnecessary delivery inhibition Before we copare the probability of unnecessary delivery inhibition aong all protocols, we illustrate the phenoenon of unnecessary inhibition with an exaple. Consider the exaple shown in figure 4. In this scenario, the obile host h 2 sends essage 1 to its local base station BS 2. After delivering 1, the base station BS 2 sends essage 1 to base station BS 1. Another essage 2 is sent by h 3 to BS 2. After delivering 2, the base station BS 2 sends essage 2 to BS 1. As we can see, 2 has been sent before the delivery of 1 at h 3, and therefore, essages 1 and 2 are concurrent. In this case, essage 2 is received before 1 at BS 1. Soe protocols that carry out a causal ordering at a base station level can inhibit the delivery of 2 until 1 has been delivered to BS 1. This is because the essages are delivered according to the causal view of base station BS 2. For BS 2 essage 1 happened before 2 ( 1 2 ). See figure 4. On the other hand, the protocols that perfor a causal ordering according to the causal view of the obile host avoid the phenoenon of unnecessary inhibition.

144 IJCSNS International Journal of Coputer Science and Network Security, VOL.8 No.1, January 2008 h 1 BS 1 BS 2 h 2 h 3 concurrents 1 Figure 4. An exaple of unnecessary inhibition. Algorith AV-2 has the highest probability of unnecessary inhibition since it only aintains the causal ordering aong base stations [3], see table 5. AV-3 reduces the probability of unnecessary inhibition by dividing the physical cells in logical cells k and aintaining the causal order aong logical cells. In contrast, algoriths PRS and Mobi_Causal ensure causal ordering explicitly according to s. Hence, inhibition never occurs. However, these protocols have a essage overhead O(n) and O( å i = 1 li ) over the wireless and wired counication channels, respectively, table 5. Another drawback of Mobi_causal is the non bounded growth of inforation control storage on each obile host in order to achieve the causal ordering. In our approach, causal ordering is carried out by base stations in accordance with the causal view that the obile hosts have during the syste execution, avoiding the unnecessary delivery inhibition. Our algorith has a essage overhead of n bits, one bit by each obile host in the counication group. 5. Conclusions 2 Base station point of view 1 2 An efficient causal ordering protocol, MOCAVI, for cellular networks has been presented. MOCAVI perfors the causal ordering according to the causal view that the obile host perceives during the syste execution, eliinating with this the inhibition effect in the essage delivery. MOCAVI aintains a low overhead attached to the transitted essages in the wireless counication channels. Moreover, our protocol is efficient since the aount of coputation perfored by obile hosts is low and the control inforation (overhead) attached to the sent essages in the wired counication channels is dynaically adapted to the behavior of the syste. [3] L. H. Yen, T.L. Huang, and S.Y. Huang, A protocol for causally ordered essage delivery in obile coputing systes, ACM/Baltzer Mobile Networks and Applications, vol. 2, no.4, 365-372, 1997. [4] C.P. Li and T.L. Huang, A obile support station based causal ulticast algorith in obile coputing environent, Proc. 11 th Int l Conf. info. Networking, vol. 2, 9C-1.1-9C-1.10, 1997. [5] K. H. Chi, L.H. Yen, C.C. Tseng, and T.L. Huang, A Causal Multicast Protocol for Cellular networks, IEICE TRANS. INF. & SYST., vol. E83-D. no. 12, 2065-2073,2000. [6] P. Chandra, and A. Kshekalyani, Causal Multicast in Mobile Networks, Proc. The IEEE Coputer Societyapos 12 th Annual International Syposiu on Volue, Issue, 213 220, 4-8 Oct. 2004. [7] R. Praskash and Mukesh Singhal, Dependency sequences and hierarchical clocks: efficient alternatives to vector clocks for obile coputing systes, Wireless Networks, (3):349--360, 1997. [8] R. Praskash, M. Raynal.and Mukesh Singhal, An Efficient Causal ordering Algorith for Mobile Coputing Environents, Proceedings of the 16th International Conference on Distributed Coputing Systes, p. 744, 1996. [9] C. Benzaid and N. Badache, Mobi_Causal: A protocol for Causal Message Ordering in Mobile Coputing Systes, Mobile coputing and counications Review, vol. 9, 19-28,2005. [10] L. Laport, Tie Clocks and the Ordering of Messages in Distributed Systes, Counications ACM 21(7), pp. 558-565, 1978. [11] S. Poares Hernández, J. Fanchon, K. Drira, The Inediate Dependency Relation: An Optial Way to Ensure Causal Group Counication, annual Review of Scalable Coputing, Vol. 6, Series on Scalable Coputing. Ed. Y.C. Kwong, World Scientific, pp. 61-79, 2004. [12] C. Skawratananond, N. Mittal, and V. K. Garg, A Lightweight Algorith for Causal Message Ordering in Mobile Coputing Systes, In Proc. of 12th ISCA Intl. Conf. on Parallel and Distributed Coputing Systes (PDCS), 245-250, Florida, USA, 1999. [13] B.R. Badrinath, A. Acharya and T. Iielinsky, Structuring Distributed Algoriths for Mobile Hosts, Conf. on Distributed Coputing Systes, June 1994. [14] C.Yi Lin, S. Chi Wang and S. Yen Kuo, An Efficient Tie-Based Checkpointing Protocol for Mobile Coputing Systes over Mobile IP, Mobile Networks and Application, 687-697, 2003. h References [1] ETSI, European Telecounications Standards institute GSM recoendations. [2] S. Alagar and S. Venkatesan, Causally Ordered Message Delivery in Mobile Systes, In Proc.Workshop on Mobile Coputing Systes and Applications, 169-174, 1994.