Data Broadcast on a Multi-System Heterogeneous Overlayed Wireless Network *

JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 24, 819-840 (2008) Data Broadcast on a Mult-System Heterogeneous Overlayed Wreless Network * Department of Computer Scence Natonal Chao Tung Unversty Hsnchu, 300 Tawan E-mal: {jlhuang; jnln}@cs.nctu.edu.tw A mult-system heterogeneous overlayed wreless network wth multple wreless access technologes s deemed a key part of 4G networks. In addton, data broadcast s a promsng technque to mprove the bandwdth utlzaton and to conserve the power consumpton n a moble computng envronment. However, most of the pror studes n data broadcast only deal wth ssues n a sngle-system wreless network (.e., n a network wth one or multple broadcast channel(s)), and therefore, these pror approaches cannot be drectly used n a mult-system heterogeneous overlayed wreless network. In vew of ths, we propose n ths paper a two-phase algorthm, named algorthm Layered-Cuttng, to address the problem of broadcast program generaton n a mult-system heterogeneous overlayed wreless network. Specfcally, n nter-network data allocaton phase, algorthm Layered-Cuttng allocates a set of data tems to each subnetwork. Then, n ntra-network data allocaton phase, algorthm Layered-Cuttng generates one broadcast program for each subnetwork accordng to the number of channels n the subnetwork and the propertes (ncludng data access probabltes and object szes) of the data tems allocated to the subnetwork. To evaluate the performance of algorthm Layered- Cuttng, several experments are conducted. The expermental results show that algorthm Layered-Cuttng s able to effcently generate broadcast programs of hgh qualty for a mult-system heterogeneous overlayed wreless network. Keywords: data broadcast, heterogeneous overlayed network, moble computng, moble data management, ubqutous computng 1. INTRODUCTION A mult-system heterogeneous wreless network wth multple wreless access technologes s deemed a key part of 4G networks [1, 2]. A 4G network can be conceptually vsualzed as a collecton of multple ndependent access subnetworks. Ths vson leverages the relatve merts of multple cellular access systems, wth sgnfcant heterogenety n ther ndvdual characterstcs such as coverage area, transmsson range and channel bandwdth. By usng multple, physcal or software-defned rado nterfaces, moble devces are able to swtch between these wreless access technologes to obtan better servce qualty. In ubqutous computng envronments, the servce provders should take advantage of the relatve merts of dfferent subnetworks to provde hgh qualty network access at anytme n anywhere. Receved June 23, 2006; revsed October 16, 2006; accepted January 3, 2007. Communcated by Chung-Sheng L. * The prelmnary verson has been publshed n the 7th IEEE Internatonal Conference on Parallel and Dstrbuted Computng, Applcatons and Technologes (PDCAT 06) 2006. 819

820 In order to provde power conservng and hgh scalable servces n a moble envronment, a data delvery archtecture n whch a server contnuously and repeatedly broadcasts data to a clent communty through a sngle broadcast channel was proposed n [3, 4]. Related research ssues about broadcast-based nformaton systems have attracted a consderable amount of studes, ncludng broadcast program generaton [3, 5], on-demand broadcast [6-8], data ndexng [9, 10], locaton-dependent data broadcastng [11, 12], dynamc data and channel allocaton [13, 14], and dependent data broadcastng [15-18]. Unfortunately, most of the pror studes n data broadcast only deal wth data ndexng, broadcast program generaton or other ssues n a sngle-system wreless network (.e., n one network wth one or multple broadcast channel(s)). Therefore, the approaches proposed by these studes cannot be drectly used n a mult-system heterogeneous overlayed wreless network. We argue that wth the development of 4G networks, desgnng a proper scheme to employ data broadcast on mult-system networks wll become an mportant ssue n the development of moble nformaton systems. In vew of ths, we propose a two-phase algorthm, named algorthm Layered-Cuttng, to address the problem of broadcast program generaton n a mult-system heterogeneous overlayed wreless network. Specfcally, algorthm Layered-Cuttng conssts of two phases: nter-network data allocaton and ntra-network data allocaton, and cooperates wth a desgnated tradtonal broadcast program generaton algorthm for a snglesystem network. For better readablty, the employed tradtonal broadcast program generaton algorthm for a sngle-system network s referred to as algorthm BPG-Sngle (standng for Broadcast Program Generaton for Sngle-system networks) n the rest of ths paper. In nter-network data allocaton phase, algorthm Layered-Cuttng allocates a set of data tems to each subnetwork. Snce broadcast program generaton algorthms are usually of hgh complexty, for better scalablty, the tmes of executng algorthm BPG- Sngle should be mnmzed. To acheve ths, algorthm Layered-Cuttng employs an overall average access tme estmaton method to estmate the qualty of dfferent data allocaton settngs, and determnes a data allocaton settng wth smaller estmated overall access tme as the result of nter-network data allocaton phase. After determnng a proper data allocaton settng n nter-network data allocaton phase, algorthm Layered- Cuttng steps nto ntra-network data allocaton phase to generate one broadcast program for each subnetwork accordng to the number of channels n the subnetwork and the propertes (ncludng data access probabltes and object szes) of the data tems allocated to the subnetwork. To evaluate the performance of algorthm Layered-Cuttng, several experments are conducted. The expermental results show that algorthm Layered- Cuttng s able to effcently generate broadcast programs of hgh qualty for a mult-system heterogeneous overlayed wreless network. To the best of our knowledge, there s no pror work consderng data broadcast on heterogeneous overlayed networks. Ths characterstc dstngushes ths paper from others. The rest of ths paper s organzed as follows. Frst, problem descrpton and formulaton are gven n secton 2. Then, the detals of algorthm Layered-Cuttng are shown n secton 3. Secton 4 shows the expermental results, and fnally, secton 5 concludes ths paper.

DATA BROADCAST ON MULTI-SYSTEM WIRELESS NETWORKS 821 2.1 System Model 2. PRELIMINARIES Consder a mult-system heterogeneous overlayed network N = {N 1, N 2,, N N } consstng of N subnetworks, and suppose that these subnetworks are ordered by the szes of ther coverage areas n ascendng order. To facltate the followng dscusson, we make the followng two assumptons. 1. The servce area of subnetwork N s totally covered by that of subnetwork N j f j >. 2. When beng able to connect to subnetwork N and subnetwork N j smultaneously, users prefer usng subnetwork N than usng subnetwork N j f j >. (a) General system model. (b) Example. Fg. 1. Mult-system heterogeneous wreless networks. Wth the above assumptons, a general system model of mult-system heterogeneous overlayed networks s shown n Fg. 1 (a), whle an example s shown n Fg. 1 (b). These two assumptons hold n many cases. As mentoned n [19], wreless networks wth larger coverage areas are usually of hgher connecton fee and of lower bandwdth than those wth smaller coverage areas. For example, the servce area of a GPRS network s larger than the servce area of a W-F network, and the servce area of a W-F network s usually totally covered by a GPRS network. In addton, when beng able to connect to these two networks, users usually prefer usng the W-F network rather than usng the GPRS network snce W-F networks are cheaper and of hgher bandwdth than GRPS networks. Interested reader can refer to [19] for the more descrptons of mult-system heterogeneous overlayed networks. 2.2 Problem Descrpton and Formulaton Suppose that n subnetwork N, the servce provder allocates C channels to provde the data broadcast servce and the bandwdth of each channel s B. Suppose that the database D contans D data tems, D 1, D 2,, D D. Also let the sze of D be s and let the

822 Symbol N A C B D s l p Cut BPG-Sngle Table 1. Descrptons of used symbols. Descrpton the th subnetwork sze of the servce area of the th subnetwork number of broadcast channels n subnetwork N Bandwdth of one broadcast channel n subnetwork N the th data tem sze of D tme to broadcast D access probablty of D the th cuttng pont the selected broadcast program generaton for sngle-system networks access probablty of data tem D be p. For better readablty, the descrptons of symbols used are lsted n Table 1. Two metrcs, access tme and tunng tme, are ntroduced n [4] to evaluate the performance of broadcast programs. The access tme s the tme elapsed from the moment a clent ssues a request to the moment all the relevant data are read. The tunng tme s the amount of tme spent by the clent lstenng on the broadcast channels, whch s a measurement of the power consumpton. In ths paper, we take the access tme as the measurement of the performance of broadcast programs. Note that n broadcast envronments, a user ssues a request does not mean that the moble devce has to explctly ssue a data request to the server. In fact, t means that the user ssues a data request to the moble devce, and the moble devce wll tune to the broadcast channel, wat for the appearance of the requred data tem and retreve the requred data tem from the broadcast channel. As mentoned n [20], n a sngle-system network wth one broadcast channel of bandwdth B, to mnmze the overall average access tme, nstances of each tem have to be equally spaced, and the broadcast frequency of data tem D should be proportonal to p, where l l s defned as the tme to broadcast D n the broadcast channel. That s, l s s equal to B where B s the bandwdth of the broadcast channel. Ths result s also called square-root rule. When square-root rule s satsfed, the lower bound of overall average access tme s 2 1 D topt. = p l. 2 (1) = 1 On the other hand, f the network contans multple channels, say ChannelNo broadcast channels, the lower bound of overall average access tme wll be t = (2) ChannelNo Mult Opt. Opt.. t

DATA BROADCAST ON MULTI-SYSTEM WIRELESS NETWORKS 823 In addton to derve the above theoretcal results, the authors n [20] propose a probablstc broadcast program generaton algorthm to generate broadcast programs n a sngle-channel envronment. They also extend the proposed algorthm to a mult-channel envronment. For ease of presentaton, we assume that all data tems have been reordered p accordng to ther values n descendng order n the rest of ths paper. l We now consder the cases n a mult-system heterogeneous overlayed wreless network. We frst observe the case that data tems D 1, D 2,, D D are broadcast n a multsystem heterogeneous overlayed wreless network consstng of two subnetworks, N 1 and N 2. Snce N 2 s of the largest servce area, all data tems have to be broadcast n N 2 n order to provde the hghest data avalablty. On the other hand, to mnmze the overall average access tme, N 1 wll only broadcast some data tems wth hgh broadcast frequentp ces (.e., hgh values). Therefore, we have to determne a cuttng pont Cut l 1 so that data tems from D 1 to D Cut1 are broadcast n N 1 and data tems from D 1 to D D (.e., all data tems) are broadcast n subnetwork N 2. Here we say that data tems from D 1 to D Cut1 are allocated to subnetwork N 1 and data tems from D 1 to D D are allocated to subnetwork N 2. Snce access tme s taken as the performance metrc, we should determne a proper value of Cut 1 to mnmze overall average access tme. We then extend the above observaton to a more general case wth N subnetworks. When we have to broadcast data tems D 1, D 2,, D D n a mult-system heterogeneous wreless network consstng of N subnetworks, N 1, N 2,, N N, we shall frst determne the values of N 1 cuttng ponts, Cut 1, Cut 2,, Cut N -1, where Cut Cut j when < j. Then, for = 1, 2,, N 1, data tems from D 1 to D Cut are allocated to subnetwork N. All data tems are allocated to subnetwork N N. Hence, we have the followng defnton. Defnton 1 A cuttng confguraton s defned as a settng of the values of Cut 1, Cut 2,, Cut N -1 so that (1) Cut Cut j f j and (2) 1 Cut D for all. Snce overall average access tme s taken as the performance metrc n ths paper, the determnaton of the values of these cuttng ponts has to be under the goal of mnmzng overall average access tme. Ths procedure s called nter-network data allocaton, and the flowchart of nter-network data allocaton s shown n Fg. 2. Each subnetwork s assgned some data tems after nter-network data allocaton. Then, for each subnetwork, we should determne how to broadcast the assgned data tems by all broadcast channels of ths subnetwork. That s, to generate a broadcast program for each subnetwork. Such procedure s called ntra-network data allocaton. Fortunately, the problem of ntra-network data allocaton s equvalent to the problem of broadcast program generaton n a sngle-system network wth multple broadcast channels whch has been wdely studed n many pror studes [5, 21, 22]. Hence, we wll focus on nter-network data allocaton n the rest of ths paper and employ one pror broadcast program generaton algorthm n a sngle-system network wth multple broadcast channels to deal wth ntra-network data allocaton for each subnetwork. As a consequence, the problem of broadcast program generaton on heterogeneous overlayed wreless networks can be formulated as follows.

824 Fg. 2. Flowchart of nter-network data allocaton. Defnton 2 Gven a mult-system heterogeneous wreless network N = {N 1, N 2,, N N }, the number of allocated channels C n each subnetwork N, the number of data tems, and the access probabltes and szes of all data tems, for each subnetwork N, we shall determne: 1. whch data tems wll be broadcast n subnetwork N (.e., a proper cuttng confguraton), and 2. how these data tems are broadcast n subnetwork N (.e., one proper broadcast program for each subnetwork). 2.3 A Brute Force Algorthm for Optmal Solutons Snce the process n ntra-network data allocaton s equvalent to generatng broadcast programs n a sngle-system network, we frst select a broadcast program generaton algorthm for a sngle-system network, and such algorthm s referred to as algorthm BPG-Sngle for ease of presentaton. Note that algorthm BPG-Sngle can be any broadcast program generaton algorthm (e.g., algorthm VF K [5]) as long as t can generate broadcast programs for multple broadcast channels n a sngle-system network. We here desgn a brute force algorthm, named algorthm Brute-Force, to obtan optmal solutons by evaluatng all possble cuttng confguratons and selectng the best cuttng confguraton and the correspondng broadcast programs for all subnetworks (.e., wth the smallest overall average access tme) as the result. When evaluatng one cuttng confguraton, we should generate one broadcast program for each subnetwork by executng algorthm BPG-Sngle once so that the average access tme of the subnetwork s mnmzed. Then, the overall average access tme of the whole mult-system network s determned as the weghted summaton of the average access tme of each subnetwork. Suppose that the data access probabltes of all data tems observed by subnetwork N j are j j j 1 p, p, K, p D. The weght of a subnetwork s defned as below. 1 2 Defnton 3 The weght of subnetwork N j s defned as the probablty that a data 1 j Please refer to Appendx for the method to determne the values of p.

DATA BROADCAST ON MULTI-SYSTEM WIRELESS NETWORKS 825 request s served by subnetwork N j. Therefore, the weght of subnetwork N j s equal to D j p. = 1 After all cuttng confguratons have been evaluated, the best cuttng confguraton (.e., wth the smallest overall average access tme) and the correspondng broadcast programs for all subnetworks are selected as the result of the algorthm. The algorthmc form of algorthm Brute-Force s as follows. Algorthm Brute-Force 1: Mark all possble confguratons as UNEVALUATED 2: BEST NULL /* BEST s the confguraton of smallest overall average access tme up-to-now */ 3: whle there are some unevaluated cuttng confguratons do 4: Pck one unevaluated cuttng confguraton, say CURRENT 5: for ( = 1 to N ) do 6: Execute algorthm BPG-Sngle on subnetwork N wth cuttng confguraton CURRENT 7: end for 8: Calculate the overall average access tme of CURRENT 9: f (the overall average access tme of CURRENT s smaller than that of BEST) then 10: BEST CURRENT 11: end f 12: Mark CURRENT as EVALUATED 13: end whle 14: return BEST Snce evaluatng all possble cuttng confguratons, algorthm Brute-Force wll evaluate O( D N -1 ) cuttng confguratons. In each evaluaton, algorthm BPG-Sngle s executed N tmes to generate broadcast programs for all subnetworks. Let O(BPG Sngle ) be the tme complexty of algorthm BPG-Sngle. The tme complexty of evaluatng one cuttng confguraton s N O(BPG Sngle ). Therefore, the tme complexty of algorthm Brute-Force s O( D N -1 ) N O(BPG Sngle ) = O( D N N ) O(BPG Sngle ). 3. BROADCAST PROGRAM GENERATION ON A MULTI-SYSTEM HETEROGENEOUS OVERLAYED WIRELESS NETWORK Although beng able to obtan the optmal cuttng confguraton and the correspondng broadcast programs for all subnetworks, the tme complexty of algorthm Brute-Force s qute hgh. Ths result makes algorthm Brute-Force not sutable for practcal use, and hence, motvates us to desgn a more effcent algorthm, named algorthm Layered-Cuttng n ths secton to determne a suboptmal cuttng confguraton and the correspondng broadcast programs for all subnetworks. 3.1 Overvew of Algorthm Layered-Cuttng Obvously, the reasons that the tme complexty of algorthm Brute-Force s so hgh are as follows.

826 1. Algorthm Brute-Force entangles the nter-network and ntra-network data allocaton together. Snce beng executed several tmes when a cuttng confguraton s evaluated, algorthm BPG-Sngle wll be executed many tmes wthn one executon of algorthm Brute-Force. Owng to the fact that broadcast program generaton algorthms n a sngle-system network (e.g., algorthm BPG-Sngle) are usually of hgh tme complexty, the tme complexty of algorthm Brute-Force s nherently hgh. 2. Algorthm Brute-Force searches all possble cuttng confguratons, and therefore, does not scale well. To address the above two problems, the desgn ratonales of algorthm Layered- Cuttng are as follows. 1. Reduce the number of tmes of executng algorthm BPG-Sngle. That s, to reduce the number of tmes of executons of the employed broadcast program generaton algorthm n a sngle-system network. 2. Reduce the sze of search space by searchng only the confguratons of hgh probabltes to be the optmal confguraton nstead of searchng all possble cuttng confguratons. Bascally, algorthm Layered-Cuttng s a two-phase algorthm consstng of nternetwork data allocaton phase and ntra-network data allocaton phase. The objectve of nter-network data allocaton phase s to determne a proper cuttng confguraton so that the overall average access tme of the whole mult-system network s mnmzed. Then, n ntra-network data allocaton phase, algorthm Layered-Cuttng wll generate one broadcast program for each subnetwork accordng to the resultant cuttng confguraton. Dfferent from algorthm Brute-Force, algorthm Layered-Cuttng does not execute algorthm BPG-Sngle n nter-network data allocaton phase, snce the goal of nter-network data allocaton phase s only to generate a proper cuttng confguraton. In ntra-network data allocaton phase, algorthm Layered-Cuttng wll execute algorthm BPG-Sngle only N tmes to generate one broadcast program for each subnetwork. In addton, nstead of evaluatng all possble cuttng confguraton (algorthm Brute-Force does t), algorthm Layered-Cuttng only evaluates some cuttng confguratons wth hgh probablty to be optmal. Wth the above two characterstcs, algorthm Layered-Cuttng s able to obtan suboptmal cuttng confguratons effcently. 3.2 Phase One: Inter-Network Data Allocaton Phase Accordng to ratonale one, we should reduce the number of tmes of executng algorthm BPG-Sngle. Snce the objectve of nter-network data allocaton phase s only to determne a proper cuttng confguraton to mnmze overall average access tme, knowng the broadcast programs of all subnetworks s not necessary n nter-network data allocaton phase. Therefore, when evaluatng a cuttng confguraton, we use Eqs. (1) and (2) to obtan the lower bound of overall average access tme of each subnetwork and take the weghted summaton of these lower bounds as the lower bound of the whole multsystem network. Smlar to algorthm Brute-Force, the weght of a subnetwork s the

DATA BROADCAST ON MULTI-SYSTEM WIRELESS NETWORKS 827 probablty that a data request s served by the subnetwork. By employng Eqs. (1) and (2), algorthm Layered-Cuttng can use the lower bounds of the overall average access tme of cuttng confguratons as the estmated overall average access tme wthout executng algorthm BPG-Sngle. Bascally, algorthm Layered-Cuttng s an teratve algorthm whch merges several subnetworks and determnes the value of one cuttng pont n each teraton. The procedure to merge subnetworks s shown n secton 3.2.1. Then, the teratve procedure of algorthm Layered-Cuttng s descrbed n secton 3.2.2 whle the procedure to determne the values of cuttng ponts s gven n secton 3.2.3. 3.2.1 Mergng subnetworks To facltate the desgn of algorthm Layered-Cuttng, we frst consder the effect of mergng some subnetworks nto a logcal subnetwork. Suppose that the data access probabltes of all data tems observed by the combnaton of subnetworks N 1, N 2,, N j are 1~ j 1~ j 1~ j 2 p1, p2, K, p D. We then merge the combnaton of N 1, N 2,, N j nto a logcal sngle-system subnetwork, denoted as N 1~j, wth servce area of sze A j and one logcal broadcast channel of bandwdth B 1~j, where B 1~j s determned as follows. Consder a subnetwork N, 1 j, whch has C broadcast channels and each s of bandwdth B. The weght of logcal subnetwork N 1~j s defned as below. Defnton 4 The weght of logcal subnetwork N 1~k s defned as the probablty that a data request s served by one of subnetworks N 1, N 2,, N N. Therefore, the weght of D 1~ k logcal subnetwork N 1~k s equal to p. = 1 In addton, the aggregate bandwdth of subnetwork N s C B. Snce the szes of servce areas of subnetwork N and logcal subnetwork N 1~j are A and A j, respectvely, the contrbuton of subnetwork N on bandwdth of logcal subnetwork N 1~j can be estmated by unformly spreadng the bandwdth from servce area wth sze A to servce area wth sze A j. Therefore, B 1~j s defned as the summaton of the contrbutons of subnetwork N 1, N 2,, N j. As a result, B 1~j can be formulated as j = 1 A C B. A j Therefore, the lower bound of the overall average access tme of subnetwork N 1~j 1~ j 1~ j 1~ j 2 can be obtaned by Eq. (1) wth data access probabltes p1, p2, K, p D. Fnally, the lower bound of overall average access tme of the combnaton of subnetworks N 1, N 2,, N j can be approxmated by the lower bound of the overall average access tme of subnetwork N 1~j. 3.2.2 Layered cuttng The objectve of nter-network data allocaton phase s to determne a proper cuttng 2 Please refer to Appendx for the method to determne the values of 1~ j p detals.

828 confguraton (.e., determne the values of Cut 1, Cut 2,, Cut N -1 ) to mnmze overall average access tme of the whole mult-system network. Bascally, nter-network data allocaton phase of algorthm Layered-Cuttng s an teratve algorthm and determnes the value of Cut N -j n the jth teraton. In the frst teraton, we have a mult-system network wth N subnetworks. Snce subnetwork N N s of the largest servce area, all data requests wll be served by the combnaton of subnet- 1~ N works N 1, N 2,, N N. Hence, we have p = p for each data tem D. We then merge subnetworks N 1, N 2,, N N -1 nto logcal subnetwork N 1~ N -1 wth servce area of sze A N -1 and a broadcast channel of bandwdth B 1~ N -1. As a result, determnng the value of Cut N -1 n a mult-system network wth N subnetworks s transformed nto determnng the value of Cut N -1 n a mult-system network wth two networks (.e., logcal subnetwork N 1~(j-1) and subnetwork N j ). We then desgn a heurstc, named procedure Test-and- Prune, to determne the value of the cuttng pont between logcal subnetwork N 1~(j-1) and subnetwork N j. For ease of presentaton, we defer the descrpton of procedure Testand-Prune to secton 3.2.3 and assume that value of Cut N -1 can be obtaned rght now. We then determne the access probabltes observed by logcal subnetwork N 1~ N -1 (.e., 1~ N p 1 N ) and by subnetwork N N (.e., 1~ N 1 N p ). After p and p have been calculated, algorthm Layered-Cuttng fnshes the frst teraton and starts the second teraton. In essence, the process of the jth teraton s smlar to that of the frst teraton. In the jth teraton, only subnetworks N 1, N 2,, N N -j+1 are consdered. Frst, subnetworks N 1, N 2,, N N -j are merged nto logcal subnetwork N 1~ N -j. The value of Cut N -j s then 1~ N j+ 1 determned by procedure Test-and-Prune accordng to p whch has been deter- 1~ N j N j 1 mned n the (j 1)th teraton. Fnally, the values of p and p + are calculated. Internetwork data allocaton phase of algorthm Layered-Cuttng repeats the above steps untl the value of Cut 1 has been determned. That s, after teratng N 1 tmes, algorthm Layered-Cuttng termnates nter-network data allocaton phase and steps nto ntra-network data allocaton phase. The algorthmc form of the procedure of nter-network data allocaton phase n algorthm Layered-Cuttng s as follows. Procedure Inter-Network-Data-Allocaton p 1: Reorder all data tems accordng to ther values n descendng order l 1~ N 2: Let p be p for each data tem D 3: for (j = 1 to N 1) do 4: Merge subnetworks N 1, N 2,, N N -j nto a logcal subnetwork N 1~ N -j 5: Employ procedure Test-and-Prune wth left = 1 and rght = Cut N -j+1 to determne the value of Cut N -j accordng to 1~ p j + 1 1~ N j 6: Calculate p for each data tem D /* For next teraton */ N j 1 7: Calculate p + N j 1 for each data tem D /* p + wll be used n ntra-network data allocaton phase */ 8: end for 9: return Cut 1, Cut 2,, Cut N -1

DATA BROADCAST ON MULTI-SYSTEM WIRELESS NETWORKS 829 3.2.3 Determnng values of cuttng ponts After descrbng the process of nter-network data allocaton phase n algorthm Layered-Cuttng, we now descrbe how to determne the values of cuttng ponts n ths subsecton. Note that the determnaton method, called procedure Test-and-Prune, s used n algorthm Layered-Cuttng descrbed n secton 3.2.2. Fg. 3. Layered Cuttng n the jth teraton. We now consder the example of the jth teraton, and the example s shown n Fg. 3. In the jth teraton, we have to determne the value of Cut N -j, where 1 Cut N -j Cut N -j+1, so that the overall average access tme of logcal subnetwork N 1~ N -j and subnetwork N N -j+1 s mnmzed. 3 To facltate the followng dscusson, when Cut N -j s set to p, we denote the lower bound of the overall average access tme of logcal subnetwork N 1~( N -j) obtaned by Eq. (1) as LB 1~( N -j) (p). Also let LB N -j+1 (p) be the lower bound of subnetwork N N -j+1 calculated by Eq. (1) or Eq. (2) as LB N -j+1 (p). 4 As mentoned n secton 3.2.1, the lower bound of overall average access tme of the combnaton of subnetworks N 1, N 2,, N k can be approxmated by the lower bound of the overall average access tme of subnetwork N 1~k. Hence, the overall average access tme of logcal subnetwork N 1~ N -j and subnetwork N 1~ N -j+1 when Cut N -j = p can be determned as LB Cut N -j (p) = w 1~ N -j (p) LB 1~( N -j) (p) + w N -j+1 (p) LB N -j+1 (p), where w 1~ N -j (p) and w N -j+1 (p) are the weghts of logcal subnetwork N 1~ N -j and subnetwork N N -j+1, respectvely, when Cut N -j = p. To obtan the optmal value of Cut N -j, t s ntutve to scan all possble values of the cuttng pont and to select the best one as the value of Cut N -j. However, ths method s unscalable snce the number of data tems s usually large. In vew of ths, we desgn an effcent heurstc, named procedure Test-and-Prune, to determne a proper value of a cuttng pont n a test-and-prune manner. For better scalablty, the objectve of procedure Test-and-Prune s to fnd a local optmal value, nstead of the optmal value, of Cut N -j. Hence, we have the followng defnton. Defnton 5 A value of the cuttng pont, say p, s sad local optmal f LB Cut N -j (p 1) > LB Cut N -j (p), and LB Cut N -j (p + 1) > LB Cut{ N -j (p). 3 The value of Cut N s defned as D. 4 Eq. (1) s desgned for a sngle-system network wth one broadcast channel whle Eq. (2) s for a sngle-system network wth multple broadcast channels.

830 Defnton 6 A value of the cuttng pont, say q, s sad to be better than another value of the cuttng pont, say p, f LB Cut N -j (q) < LB Cut N -j (p). The process of procedure Test-and-Prune s as follows. Frst, varables left and rght are set, respectvely, to the smallest and the largest possble values of Cut N -j, and varable mddle s set to rght + left. Procedure Test-and-Prune checks whether settng Cut 2 N -j to mddle s local optmal. If so, procedure Test-and-Prune stops and suggests mddle as the value of Cut N -j. Otherwse, procedure Test-and-Prune checks the superortes of settng Cut N -j to mddle 1, mddle and mddle + 1. If settng Cut N -j to mddle 1 s better than settng Cut N -j to mddle and mddle + 1, values from mddle to Cut N -j+1 are pruned and rght s set to mddle 1. Otherwse, when settng Cut N -j to mddle + 1 s better than settng Cut N -j to mddle 1 and mddle, values from 1 to p are pruned and left s set to mddle + 1. The above procedure repeats untl a local optmal value of Cut N -j s found. The algorthmc form of procedure Test-and-Prune s as follows. Procedure Test-and-Prune(mn, max) Parameters: mn: the smallest possble value of the cuttng pont max: the largest possble value of the cuttng pont 1: left mn 2: rght max 3: mddle rght + left 2 4: whle (mddle s not better than mddle 1 and mddle + 1) do 5: f (mddle 1 s better than mddle and mddle + 1) then 6: rght mddle 1 7: else /* mddle + 1 s better than mddle 1 and mddle */ 8: mddle mddle + 1 9: end f 10: mddle 11: end whle 12: return mddle rght + left 2 Due to the behavor of procedure Test-and-Prune, the worst case tme complexty of procedure Test-and-Prune s O(log(rght left 1)) = O(log(rght left)). Fnally, we use the followng example to llustrate the behavor of procedure Test-and-Prune. (a) (b) (c) (d) Fg. 4. Procedure Test-and-Prune n the jth teraton.

DATA BROADCAST ON MULTI-SYSTEM WIRELESS NETWORKS 831 Example 1: Consder the example shown n Fg. 4 (a) that procedure Test-and-Prune s nvoked to determne the value of Cut N -j. Intally, left = 1, rght = Cut N -j+1, and mddle s set to rght + left. Procedure Test-and-Prune then tests whether settng Cut 2 N -j to mddle s better than settng Cut N -j to mddle 1 and mddle + 1. Suppose that mddle + 1 s better than mddle. Then, as shown n Fg. 4 (b), values from 1 to mddle are pruned. In addton, left s set to mddle + 1 and mddle s set to rght + left. 2 Suppose that n the case shown n Fg. 4 (b), mddle 1 s better than mddle and mddle + 1. Values from mddle to rght are pruned, and rght s set to mddle 1. Then mddle s set to rght + left, and the status s shown n Fg. 4 (c). In the case shown n 2 Fg. 4 (c), suppose that mddle s better than mddle 1 and mddle + 1. Therefore, as shown n Fg. 4 (d), mddle s local optmal and s reported as the suggested value of Cut N -j. 3.3 Phase Two: Intra-Network Data Allocaton Phase The objectve of ntra-network data allocaton phase s to determne the broadcast programs of all subnetworks accordng to the resultant cuttng confguraton. It s ntutve that generatng the broadcast program of subnetwork N j s equvalent to executng algorthm BPG-Sngle on subnetwork N j wth data access probabltes p j 1, p j 2, K, p j D. The algorthmc of ntra-network data allocaton phase n algorthm Layered-Cuttng s as follows. Procedure Intra-Network-Data-Allocaton 1: for (j = 1 to N ) do 2: Execute algorthm BPG-Sngle on subnetwork N j accordng to p for each data j tem D to generate the broadcast program of subnetwork N j /* The value of p for each data tem D has already been calculated n procedure Inter-Network-Data- Allocaton */ 3: end for 4: return The broadcast programs of all subnetworks Fnally, the process of algorthm Layered-Cuttng s to execute the procedures n nter-network data allocaton and ntra-network data allocaton sequentally, and the algorthmc form of algorthm Layered-Cuttng s as follows. Algorthm Layered-Cuttng 1: Execute procedure Inter-Network-Data Allocaton 2: Execute procedure Intra-Network-Data Allocaton 3: return The broadcast programs of all subnetworks returned by procedure Intra-Network-Data Allocaton 3.4 Tme Complexty Analyss The worst case occurs when Cut = D for = 1, 2,, N 1. In the worst case, j

832 procedure Test-and-Prune wll be executed N 1 tmes wth parameters left = 1 and rght = D n nter-network data allocaton phase. Snce the tme complexty of procedure Test-and-Prune s O(log D 1) = O(log D ), the tme complexty of nter-network data allocaton phase s O(( N 1)log D ) = O( N log D ). In ntra-network data allocaton phase, algorthm BPG-Sngle s executed to generate the broadcast programs of all subnetworks. Hence, algorthm BPG-Sngle wll be executed N tmes, and the tme complexty of ntra-network data allocaton phase s O( N ) O(BPG Sngle ). Fnally, the worst case tme complexty of algorthm Layered-Cuttng can be determned as the the summaton of the tme complextes of nter-network and ntra-network data allocaton phases, and s equal to O( N (log D + O(BPG Sngle ))). 4. PERFORMANCE EVALUATION Accordng to the complexty analyss n secton 3, algorthm Layered-Cuttng s more effcent than algorthm Brute-Force at the cost of generatng results worse than algorthm Brute-Force. Hence, we conduct several experments to evaluate the performance of both algorthms and expermental results (ncludng the executon tme and the qualty of results) are shown n the followng subsectons. 4.1 Smulaton Model To evaluaton the performance of algorthm Layered-Cuttng, we mplement both algorthm Layered-Cuttng and algorthm Brute-Force usng C++. Smlar to [13], we assume that the access probabltes of all data tems follow a Zpf dstrbuton wth parameter θ. That s, the data access probablty of data tem D s equal to p = = 1 θ () D ( 1 θ ) j 1 j. The default value of θ s set to be 0.8 wth a reference to the analyss of real Web traces [23, 24]. Smlar to [25], we assume that there are 1,000 data tems and the data szes are assumed to follow a normal dstrbuton wth mean 1 KBbytes. In the model of subnetworks, we assume there are N subnetworks n the mult-system heterogeneous overlayed network, and the servce provder allocates three channels n each subnetwork for broadcastng data tems. We also assume that subnetwork N s able to cover the whole servce area of the mult-system network and the rate between the szes of the servce areas of subnetwork and subnetwork + 1 s equal to 0.8. That s, A = 0.8 for all 1 N 1. In addton, the rato between the bandwdth of one A + 1 B broadcast channel n subnetwork and that n subnetwork + 1 s set to 2 (.e., B = 2), + 1 and B N s set to 10Kbytes [25]. We use the broadcast program generaton algorthm proposed n [20] as algorthm BPG-Sngle. That s, the algorthm proposed n [20] s used to generate broadcast programs for all subnetworks n ntra-network data allocaton phase. For better readablty, the default values of system parameters are lsted n Table 2.

DATA BROADCAST ON MULTI-SYSTEM WIRELESS NETWORKS 833 Parameter Table 2. System parameters. Default value Number of subnetworks ( N ) 5 Number of broadcast channels n subnetwork N (C ) 3 Number of data tems( D ) 1000 Dstrbuton of data tem sze (s ) normal wth mean 1 KBytes Dstrbuton of data access probabltes (p ) Zpf wth θ = 0.8 Broadcast program generaton for each subnetwork (algorthm BPG-Sngle) The algorthm proposed n [20] Number of Subnetworks Number of Subnetworks (a) Average access tme. (b) Executon tme. Fg. 5. Impact of the number of subnetworks. 4.2 Impact of Number of Subnetworks Fg. 5 shows the qualty of solutons and executon tme of algorthm Brute-Force and algorthm Layered-Cuttng wth the number of subnetworks vared. In ths experment, the number of subnetworks s settng from two to sx. It s ntutve that ncreasng the number of subnetworks wll decrease the average access tme of the resultant broadcast programs snce the total bandwdth of the mult-network system ncreases. Owng to the reason that networks wth hgher bandwdth usually cover smaller servce area that those wth lower bandwdth, the decrement of average access tme decreases as the number of subnetworks ncreases. In ths subsecton, we only execute algorthm Brute-Force n the cases wth two and three subnetworks because the executon tme of algorthm Brute- Force n the case wth four subnetworks s too longer (beyond one hour). As observed n Fg. 5 (b), algorthm Brute-Force does not scale well. Such result conforms to the tme complexty analyss n secton 2.3. On the other hand, as shown n Fgs. 5 (a) and (b), algorthm Layered-Cuttng s able to obtan solutons close to optmal ones quckly. In ths experment, the degradaton of solutons of algorthm Layered-Cuttng over solutons of algorthm Brute-Force s smaller than 6%, and algorthm Layered- Cuttng can termnate wthn one second. Such result also conforms to the tme complexty of algorthm Layered-Cuttng shown n secton 3.4, and shows the advantage of algorthm Layered-Cuttng.

834 Number of Data Items Number of Data Items (a) Average access tme. (b) Executon tme. Fg. 6. Impact of the number of data tems. 4.3 Impact of Number of Data Items Ths experment nvestgates the mpact of the number of data tems by settng the number of data tems from 250 to 1250. The qualty of resultant broadcast programs of algorthm Brute-Force and algorthm Layered-Cuttng s shown n Fg. 6 (a). As observed, the solutons generated by algorthm Layered-Cuttng s much close to those generated by algorthm Brute-Force (.e., optmal solutons) even the number of data tems s set to 1250. In ths experment, the degradaton of solutons of algorthm Layered-Cuttng over solutons of algorthm Brute-Force s smaller than 4%. Fg. 6 (b) shows the executon tme of both algorthms wth the number of data tems vared. It s ntutve that the executon tme ncreases as the number of data tems ncreases. Accordng to the analyss n secton 2.3, the tme complexty of algorthm Brute-Force s much senstve on the number of data tems than algorthm Layered- Cuttng. Such analytcal result can be observed n Fg. 6 (b). The executon tme of algorthm Brute-Force ncreases drastcally as the number of data tems ncreases. Under the same case, the executon tme of algorthm Layered-Cuttng only ncreases smoothly and can be termnated wthn one second. Ths result shows that algorthm Layered-Cuttng s much scalable than algorthm Brute-Force. 4.4 Impact of Skewness of Data Access Probabltes We now measure the mpact of skewness of data access probabltes on the qualty of resultant broadcast programs and executon tme of both algorthms. The value of θ s set from zero to 1.25. Note that θ = 0 ndcates that the data access probablty of each data tem s equal. As shown n Fg. 7 (a), the average access tme of the resultant broadcast programs of both algorthms greatly decreases as the value of θ ncreases. It s because when data access probabltes are hghly skewed, several data tems are requested frequently. Therefore, one transmsson of one hot data tem s of hgh probablty to serve more data requests, thereby reducng overall average access tme. In ths experment, the degradaton of solutons of algorthm Layered-Cuttng over solutons of algorthm Brute-Force s around 3%. As observed n Fg. 7 (b), the change of skewness of access probabltes only slghtly affects the executon tme of both algorthms.

DATA BROADCAST ON MULTI-SYSTEM WIRELESS NETWORKS 835 Zpf Parameter Zpf Parameter (a) Average access tme. (b) Executon tme. Fg. 7. Impact of skewness of data access probabltes. Servce Area Rato (a) Average access tme. Fg. 8. Impact of servce area rato. Servce Area Rato (b) Executon tme. 4.5 Impact of Servce Area Rato Fg. 8 shows the qualty of the resultant broadcast programs and executon tme of both algorthms wth servce area rato vared. As observed n Fg. 8 (b), the change of skewness of access probabltes only slghtly affects the executon tme of both algorthms. Consderng Fg. 8 (a), t s obvous that ncreasng servce area rato wll decrease overall average access tme snce subnetworks of hgher bandwdth can cover larger servce area and serve more data requests when servce area rato becomes large. We also observe from Fg. 8 (a) that the degradaton of solutons of algorthm Layered- Cuttng over solutons of algorthm Brute-Force ncreases from 0.2% to 8.3% as servce area rato ncreases from 0.5 to 0.9. It s due to the fact that algorthm Layered-Cuttng s greedy-based and may mss some solutons wth hgher qualty, and such effect becomes sgnfcant n the cases wth large servce area rato. Fortunately, the qualty of broadcast programs of algorthm Layered-Cuttng s stll close to those of algorthm Brute-Force even when servce area rato s set to 0.9. In addton, snce beng more faster than algorthm Brute-Force, algorthm Layered-Cuttng s more sutable for practcal use than algorthm Brute-Force.

836 5. CONCLUSION AND FUTURE WORK A mult-system network consstng of multple subnetworks s deemed to be able to provde better servces by combnng the relatve merts of heterogeneous communcaton technologes. In addton, data broadcast s a promsng technque to develop hgh scalablty and energy-conserved moble nformaton systems. In ths paper, we employed data broadcast n a mult-system heterogeneous overlayed wreless network and proposed a two-phase algorthm, named algorthm Layered-Cuttng, to address the problem of broadcast program generaton n a mult-system heterogeneous overlayed wreless networks. The expermental results showed that algorthm Layered-Cuttng s able to effcently generate broadcast programs of hgh qualty for a mult-system heterogeneous overlayed wreless network. Our future work s as follows. Snce n practce, the servce area of one subnetwork usually only partally overlap wth that of another, we wll consder n the future these cases and try to extend algorthm Layered-Cuttng for such envronments. One possble j 1~ j approach s to extend the formulae of p and p to measure the load of each subnetwork where subnetworks may partally overlap one another. By applyng the revsed formulae, algorthm Layered-Cuttng can drectly solve the problem of broadcast program generaton. Moreover, we wll also try to develop a dedcated broadcast program generaton algorthm for such envronments. In addton, we wll also take users preferences on choosng subnetworks nto consderaton to make our algorthm more practcable. APPENDIX j Determnng the Values of p and p 1~ j Consder the case that the whole mult-system network receves f data requests and these data requests are assumed to be located n the servce area of the whole mult-system network unformly. We can expect there are p f data requests for D. Let f k 1~k and f be the numbers of data requests for D served by subnetwork N k and by logcal subnetwork N 1~ k, respectvely. Intally, the values of all cuttng ponts are undetermned. Snce all requests of all data tems must be served by the logcal subnetwork N 1~ N, we have 1~ N p = p. Consder the case that the value of Cut N -1 has been determned. The whole system can be vewed as logcal subnetwork N 1~ N -1 and subnetwork N N. For a data request for D, the data request wll be served by the logc subnetwork N 1~ N -1 only when when (1) 1 Cut N -1 and (2) the user ssung ths request s located n the servce area of the logcal subnetwork N 1~ N -1. Therefore, all data requests for D, > Cut N -1, are served by subnetwork N N. Suppose that all data requests are unformly spread n the servce area of the A N 1 mult-system network (.e., the servce area of subnetwork N N ). Then, data re- A N quests for D, 1 Cut N -1 are served by logcal subnetwork N 1~ N -1 and the rest data requests are served by subnetwork N N. As a consequence, we have

DATA BROADCAST ON MULTI-SYSTEM WIRELESS NETWORKS 837 N f A 1 p f, f 1 Cut N 1 = A N p f, otherwse N 1, and A = 0, otherwse N 1 1~ N 1 p f, f 1 Cut N 1 A N f. By the defntons of j 1~ j p and p, we have p N N f D N f m= 1 m =, and p 1~ N 1 1~ N 1 f = D 1~ N 1 f m= 1 m. N 1~ N 1 N Therefore, after the value of Cut N -1 has been determned, f, f, p and 1~ N 1 p can be obtaned accordngly. Now, consder the case of determnng Cut j. Accordng to the process of algorthm Layered-Cuttng, when determnng Cut j, the server have already determned the values 1~ j+ of Cut j+1,, Cut N -1 and the values of f 1 Aj, 1 Cut j+1. Smlarly, data re- A j + 1 1~ j+ quests from f 1, 1 Cut j, are served by logcal subnetwork N 1~j and the rest data requests are served by subnetwork N j+1. As a consequence, we have j+ 1 f Aj 1~ j+ 1 1 f, f 1 Cut j A, 1~ j+ 1 f, otherwse = j+ 1 and 1~ j f A 1~ j+ 1 f, f 1 Cutj. 0, otherwse j = A j+ 1 By the defntons of j 1~ j p and p, we have p j+ 1 j+ 1 f D j+ 1 f m= 1 m =, and

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840 Ju-Nan Ln ( ) receved hs B.S. degree n Computer Scence and Informaton Engneerng Department n Natonal Chao Tung Unversty n 2005. Currently, he s a graduate student n Insttute of Network Engneerng n Natonal Chao Tung Unversty. Hs research nterests nclude wreless sensor networks, and pervasve computng.