Push and Pull Systems

Transcription

1 Push and Pull Systems 1 Chapter I Push and Pull Systems Petros Ncopoltds, Arstotle Unversty of Thessalonk, Greece Georgos I. Papadmtrou, Arstotle Unversty of Thessalonk, Greece Andreas S. Pomportss, Arstotle Unversty of Thessalonk, Greece Abstract Data broadcastng has emerged as an effcent way for the dssemnaton of nformaton over asymmetrc wreless envronments where the needs of the varous users of the data tems are usually overlappng. In such envronments, data broadcastng stands to be an effcent soluton snce the broadcast of a sngle nformaton tem s lkely to satsfy a possbly large number of users. Communcatons asymmetry s due to a number of facts, the most mportant beng equpment, network, and applcaton asymmetry. Ths chapter starts wth a dscusson of prelmnary ssues and termnology for asymmetrc envronments for data broadcastng. The chapter then dscusses broadcast schedule constructon for systems employng a sngle broadcast channel, schedule constructon for systems employng multple broadcast channels, and schedule constructon for systems that take nto account the effect of recepton errors. It then presents an

2 2 Ncopoltds, Papadmtrou, & Pomportss algorthm that tres to provde better support for clents whose access patterns devate a lot form the overall access pattern of the clent populaton. It also presents algorthms for envronments where tem requests by clents are dropped f not served n a certan tme perod. Bref comments on ssues that affect performance of the dscussed data broadcastng methods are also made. Introducton Push and pull data delvery systems are members of a famly of systems known as data broadcastng or nformaton dssemnaton systems. Such systems have emerged as effcent ways for the dssemnaton of nformaton over asymmetrc wreless envronments where the needs of the varous users of the data tems are usually overlappng. Examples of such applcatons are nformaton retreval ones, lke weather and traffc nformaton systems. For example, a traffc nformaton system n an arport could be of much beneft to watng passengers. A user comng to the arport wll want nformaton regardng departure of hs flght (e.g., exact tme of departure, possble delays, etc.). A broadcast server could delver such data for all flghts n the near future. Sometmes, demand for some flghts s lkely to be hgher than for others (ether due to more passengers for that flght or due to ths flght departng n the very near future). Thus, one can see that clent needs for data tems are usually overlappng and, consequently, data broadcastng stands to be an effcent soluton snce the broadcast of a sngle nformaton tem s lkely to satsfy a possbly large number of users. Communcatons asymmetry s due to a number of facts, the most mportant beng equpment, network, and applcaton asymmetry. Equpment asymmetry s caused by the fact that a broadcast server usually has transcevers that are not subject to power lmtatons, whereas clent transcevers are usually hndered due to fnte battery lfe. Moreover, t s desrable to keep the moble clents cost low, whch sometmes results n the lack of clent transmsson capablty. Network asymmetry s due to the fact that, n many cases, the avalable bandwdth for transmsson from the server to the clents (downlnk transmsson) s much more than that n the opposte drecton (uplnk transmsson). Furthermore, there exst extreme network asymmetry cases where the clents have no avalable uplnk channel (back channel). Even n the case of back-channel exstence, however, the latter s subject to becomng a bottleneck n the presence of a very large clent populaton. Applcaton asymmetry concerns the pattern of nformaton flow. Snce most nformaton retreval applcatons are of clent-server nature, the flow of traffc from the server to the clents s usually much hgher than that n the opposte drecton. Furthermore, applcaton asymmetry concerns the pattern of accessng the broadcast nformaton tems. Ths s because, n many cases, the majorty of the clents are nterested only n a subset of the server s nformaton tems. Thus, some tems tend to be a lot more popular than others and consequently, the envronment s characterzed by a skewed demand pattern. So far, two major approaches have appeared for desgnng broadcast schedules. These are the pull (also known as on-demand) and the push approaches. In pull systems, the

3 Push and Pull Systems 3 server broadcasts nformaton after requests made by the moble clents va the uplnk channel. The server queues up the ncomng requests and uses them to estmate the demand probablty per data tem. In push systems there s no nteracton between the server and the moble clents. The server s assumed to have an a pror estmate of the demand per nformaton tem and transmts tems accordng to ths estmate. Fnally, combnatons of push and pull lead to hybrd approaches. Hybrd systems dvde the avalable downlnk bandwdth nto two transmsson modes: the perodc broadcast mode, n whch the server pushes data perodcally to the clents, and the on-demand mode, whch s used to broadcast data explctly requested by the moble clents through the uplnk channel. Chapter Scope Ths chapter s organzed as follows: It starts by dscussng some prelmnary ssues and termnology that wll be used later durng the presentaton of the varous algorthms. It then dscusses broadcast schedule constructon for systems employng a sngle broadcast channel and then broadcast schedule constructon for systems employng multple broadcast channels. Next, t dscusses broadcast schedule constructon by takng nto account the effect of recepton errors. The secton after that presents an algorthm that tres to provde better support for clents whose access patterns devate a lot form the overall access pattern of the clent populaton. Followng ths, the case where tem requests by clents are dropped f not served n a certan tme perod s dscussed. The next secton brefly comments on ssues that affect performance of the dscussed data broadcastng methods. Fnally, the chapter ends wth a bref concludng summary. Prelmnares The Need for Schedulng As wll be seen later on, the major part of ths chapter s concerned wth the constructon of effcent broadcast schedules. A broadcast schedule s a sequence of data tem broadcasts by the broadcast server. It wll be made clear that the prmary goal of an effcent broadcast schedule s to mnmze the mean watng (response) tme at the clents. An obvous thought (albet nave after a thorough examnaton) would be that all a schedulng algorthm needs to do s to broadcast tems accordng to ther popularty among the clents. Ths subsecton wll explan that an effcent broadcast schedulng algorthm needs to take more nto account than ths fact. The followng example, whch resembles that whch appears n Acharya, Frankln, and Zdonk (1995), s llustratve. Consder a database of three equal-length data tems, A, B, and C, and a sngle clent. The clent accesses tems A, B, and C wth probabltes p A, p B, and p C, respectvely. The broadcast server s able to broadcast dfferent tems wth dfferent frequences so as to

4 4 Ncopoltds, Papadmtrou, & Pomportss provde more bandwdth to the popular pages than to the unpopular ones. Furthermore, we consder three schedules: The flat one, whch schedules pages cyclcally. Thus, all pages are broadcast wth the same frequency. The schedule wll be A, B, C, A, B, C The skewed1 one, n whch tem A s broadcast twce as often as tems B and C. Furthermore, subsequent broadcasts of page A are clustered together. Thus, the schedule wll be A, A, B, C, A, A, B, C The skewed2 one, dfferng from the above n such a way that nstances of the same tem are separated by equal gaps. Thus, the schedule wll be A, B, A, C, A, B, A, C For varous values of p A, p B, and p C, Fgure 1 shows the mean watng tme for a clent for each of the above three schedules. The mean watng tme s calculated by multplyng the probablty of access for each tem wth the assocated watng tme and summng up the results. It can be seen that for unform tem demand probabltes, the flat schedule performs best. Ths s to be expected snce the server broadcasts tems the way these are demanded by the clent. However, as tem demand probabltes begn to shft away from unform dstrbuton, the last two schedules perform better. A thrd remark s that the skewed program wth fxed gaps between nstances of the same tem always performs better than the other skewed schedule. Ths s attrbuted to the fact that f gaps between nstances of the same tem are fxed, then the mean watng tme for an tem request arrvng at a random tme s one half of the gap between successve nstances of the tem. On the other hand, f the skewed schedule wth nonfxed gaps between nstances of the same tem s used, gaps wll be of varable length. Thus, the probablty of an tem request beng made durng a large gap s greater than the probablty of one beng made durng a short gap. Therefore, an ncrease n the varance of gap length between nstances of the same tem tends to ncrease the mean watng tme. Mnmzaton of the mean watng tme s not the only possble target for an effcent schedulng algorthm. Another possble goal s to make a system energy effcent. Ths would be possble f clents are able to go to a mode wth lower energy consumpton ( sleep mode) and wake up only when the data tem that nterests them s about to be broadcast. Thus, the goal s to mnmze the tme a moble clent spends actvely lstenng to the communcatons medum (tunng tme). Mnmzaton of tunng tme obvously results n energy preservaton at the clent. Indexng methods (Imelnsk, Vswanathan, & Badrnath, 1994a, 1994b; Yee, Navathe, Omecnsk, & Jermane, 2002) Fgure 1. Mean watng tme for three dfferent schedules

5 Push and Pull Systems 5 enable clents to acheve energy effcency by multplexng ndex tems along wth data ones. Snce ndex tems nform about the tme of broadcast of subsequent data tems, clents need to be n actve mode only when they need to receve a data tem. A nave form of ndexng s to send an ndex tem once for every perod of the data broadcast. Ths, however, would not perform very well due to the fact that clents who mss an ndex have to wat the entre broadcast perod to receve the next ndex. A better soluton s (1, m) ndexng, whch s proposed by Imelnsk et al. (1994a), where the ndex s broadcast m tmes durng the perod of the broadcast schedule. The optmal value for m s provded by the authors n Imelnsk et al. (1994b). An enhancement of (1, m) ndexng s dstrbuted ndexng. Accordng to ths method, each ndex tem need not contan the entre ndex, but only nformaton regardng the data tems that succeed t. Envronment In all the algorthms presented n ths chapter, we assume an asymmetrc communcaton envronment comprsng a sngle broadcast server and N moble clents. Moreover, the broadcast server possesses a database that comprses M nformaton tems not necessarly of the same sze. As far as transmsson speed, tem sze, and tme are concerned, we do not consder pure numbers; rather, we assume that the smallest data tem s of unt sze and s transmtted over the server-clent lnk n a unt tme nterval. The sze of an tem, M s denoted by l. In an asymmetrc nformaton dssemnaton envronment, clents request nformaton tems from the broadcast server. The probablty that tem s requested (demand probablty for tem ) s denoted as d. As was mentoned above, due to overlappng demand patterns among dfferent clents, the demand pattern for data broadcastng applcatons s often characterzed by a certan amount of skew. In order to map ths fact nto the demand probabltes d, the Zpf dstrbuton s used. Although t shouldn t be used as the de facto workload for any wreless nformaton system, we brefly menton t here snce t s commonly used to carry out performance analyss n research. Mathematcally, t s expressed as follows: q q æö 1 æö 1 d = c, where c= 1/,, k Î[1.. M] ç èø å èø ç (1) k where θ s a parameter named access skew coeffcent. For ncreasng values of θ the Zpf dstrbuton produces ncreasngly skewed demand patterns and can thus model commonalty n clent demands for nformaton tems. For a sample database of 500 nformaton tems, the tem demand probabltes for varous values of θ are plotted n Fgure 2.

6 6 Ncopoltds, Papadmtrou, & Pomportss Broadcast Schedules and Clent Cache Management The goal pursued n most of the proposed data delvery approaches s twofold: 1. Determnaton of an effcent sequence for data tem transmsson (broadcast schedule) so that the overall mean access tme t at the clents s mnmzed. The overall mean access tme s essentally the mean watng tme observed by a clent for a requested nformaton tem. It can be computed when knowng the average watng tme t for every nformaton tem. Thus: t = M = 1 p t. 2. Management of clent local memory (cache management) n a way that effcently reduces performance degradaton when msmatches occur between a clent s demand pattern and the server s schedule. It has to be noted, however, that not all the methods presented below assume clents wth cache memory. Fgure 2. Plot of the Zpf dstrbuton for varous values of θ =0.3 =0.6 =0.9 =1.2 Demand probablty Item number

7 Push and Pull Systems 7 Statc and Dynamc Clent Demands In terms of clent demand pattern, there exst two types of envronments: statc and dynamc ones. Statc envronments are those n whch the way that clents access the server s nformaton tems does not change over tme. Thus, the demand probablty for all nformaton tems remans the same and the server does not need to adapt to new tem demand probabltes. By extendng the above reasonng, one mght defne envronments where demand probabltes change, wth the nature of changes beng known to the broadcast server, as statc envronments. Ths s because a fxed a pror model that dynamcally estmates the tmelness of the tme-senstve demand could easly be magned and thus always provdes the server wth the current tem demand probabltes. However, n many data broadcastng applcatons, overall clent demands are lkely to change wth tme wth the nature of changes beng a pror unknown. A possble example of such an applcaton wth dynamc overall clent demands could be the case of a museum possessng the necessary nfrastructure n order to delver to the users nformaton regardng the exhbts. Most museums contan several sectors, wth each sector contanng exhbts of a dfferent type (e.g., Egyptan, Greek, etc.). It would be desrable for vstors wthn a sector to be aded n ther tour by recevng nformaton regardng the contents of the sector. Upon the arrval of a group of vstors to a specfc sector, the demand for nformaton regardng the exhbts of ths sector wll grow. When the group leaves the sector, ths demand wll lower to reflect the demand of vstors remanng n the sector. It can be easly seen that n such a stuaton, demands for nformaton are characterzed by a certan amount of commonalty snce all users nsde a certan sector wll demand the same nformaton and thus the same data tem (or set of data tems). Moreover, overall clent demands are sure to be (a) dynamc snce the transton of a group of vstors to another sector wll produce a change n clent demands and (b) unknown a pror due to the fact that the amount of tme spent by groups of vstors nsde a sector s not known. Such envronments wth changng clent demand patterns, where the nature of occurrence of these changes s unknown to the broadcast server, are herenafter characterzed as dynamc. Assumptons Unless stated otherwse, the followng assumptons are made n the dscusson of the algorthms n ths chapter. 1. The communcaton medum s a broadcast channel, thus every transmtted nformaton tem s vsble to all clents. 2. In push systems, the broadcast server has by some means acqured knowledge regardng the overall demand probabltes of the varous nformaton tems. Furthermore, these probabltes do not change. These assumptons are lfted n the secton dscussng the adaptve push system. 3. All nformaton tems are self-dentfyng. Ths can be easly mplemented va header nformaton ncluson n the tems.

8 8 Ncopoltds, Papadmtrou, & Pomportss 4. Clents are contnuously lstenng to the broadcast; thus no power-savng procedures are performed. 5. There are no nterdependences between nformaton tems. 6. A broadcast nformaton tem s receved by clents only f wanted. 7. Values of nformaton tems do not change. 8. No back channel exsts. Ths s true only for the pure push methods. Pull and hybrd methods use a back channel. Schedule Constructon for a Sngle Channel Push Systems Some of the early work relevant to push data broadcastng used the flat approach (Bowen, 1992; German, Gopal, Lee, & Wenrb, 1987; Gfford, 1990), whch schedules all tems wth the same frequency. However, a very nterestng paper (Ammar & Wong, 1985) revealed the followng two facts, whch are also used by the push systems we wll descrbe later on. Specfcally, Ammar and Wong (1985, 1987) showed that n order to mnmze mean access tme, schedules must be perodc and: The varance of spacng between consecutve nstances of the same tem must be reduced. Items should be broadcast wth frequences proportonal to the square root of the probablty of beng demanded. It has to be mentoned that the push algorthms presented n ths secton can be easly appled to pull envronments by substtutng vector d contanng the demand probablty estmates for the varous tems wth a vector that contans the estmates of demand probabltes based on pendng requests for those tems. Broadcast Dsks A method that satsfes both the above-mentoned constrants s broadcast dsks (Acharya et al., 1995). Accordng to t, schedules are perodc and the spacng between consecutve nstances of the same tem s the same. Ths method defnes a dsk to be a subset of the server s database that contans nformaton tems havng close demand probabltes. It proposes a way of superposton of multple dsks spnnng at dfferent frequences on a sngle broadcast channel. Ths essentally results n the server nterleavng the transmssons of nformaton tems belongng on dfferent dsks so that (a) tems on the faster dsks are broadcast more often and (b) tems on the same dsk are

9 Push and Pull Systems 9 broadcast wth the same frequency. The most popular nformaton tems are placed on the faster dsks and, as a result, perodc schedules are produced, wth the most popular data beng broadcast more frequently. Fgure 3 shows a sample database of fve nformaton tems, I1, I2,..., I5, splt nto dsks D1, D2, and D3 spnnng at relatve frequences gven by f D1 = 2f D2 = 2f D3. It has to be noted that Acharya et al. (1995) assume statc clent demands and equlength nformaton tems. We assume that K dsks are used and that the server s database comprses M nformaton tems. Schedule constructon nvolves the followng steps: 1. Informaton tems are ordered n ascendng order of demand probabltes. 2. Items are splt nto the K dsks so that each dsk contans tems wth smlar demand probabltes. 3. The relatve frequences f, 1 K of the dsks are defned wth the only constrant of beng nteger multples of the frequency of the slower dsk. 4. Dsks are splt nto smaller unts named chunks. The splt s made such that dsk s splt nto max_chunks/f chunks, where max_chunks s the least common multple of f, 1 K. We denote as chunks() the chunks of dsk and note that chunks of dfferent dsks mght be of dfferent szes, as n general, a chunk mght comprse more than one nformaton tem. 5. The broadcast program s created by broadcastng a chunk of the frst dsk, followed by a chunk of the second, and so forth. In pseudocode, broadcast schedule constructon s expressed as follows: whle(1) for j:=1 to max_chunks for :=1 to K broadcast chunk (j mod chunks()) of dsk. Fgure 4 shows the resultng schedule for a database of sx nformaton tems broadcast va three dsks wth f D1 = 2f D2 = 4f D3. Notce that the algorthm causes unused slots to appear n the broadcast f t s not possble to evenly dvde a dsk nto the requred number of chunks. In our example, dsk D3 s dvded nto three chunks whereas t should be dvded Fgure 3. Dsks and schedule constructon

10 10 Ncopoltds, Papadmtrou, & Pomportss nto four. Thus, at the fourth tme a chunks from D3 s broadcast, the algorthm wll broadcast an empty tem rather than an tem between I4 and I6 so as to preserve fd1 = 4fD3. It can be seen that the resultng schedule perod (called a major cycle, nsde whch every database tem s transmtted at least once) comprses mnor cycles, each of whch contans one chunk from each dsk. Energy-Effcent Broadcast Dsks As already mentoned, broadcast dsks target reducton of overall mean access tme. An nterestng paper that bulds on the method of broadcast dsks s Yee et al. (2002). It proposes technques for schedulng data broadcasts that are favourable n terms of both response and tunng tme. Ths means that overall, clent requests wll be satsfed n a low tme, requrng at the same tme low energy consumpton by the clent. The contrbuton of Yee et al. s threefold: Determnaton of a method to assgn the M data tems to be broadcast to the varous dsks so that overall mean access tme s reduced. Determnaton of the number of dsks to use, K. Integraton of ndexng n order to provde energy effcency. Assgnment of the data tems to the K dsks has also been addressed n Yee, Omecnsk, and Navathe (2001), whch solves the problem by usng dynamc programmng. However, ths method has an O(KM2) computatonal complexty and may not be of practcal use n many stuatons. To ths end, a heurstc approxmator s used n Yee et al. (2002). In ths method, tem assgnment s made by orderng the M data tems n descendng order of popularty and fndng the best K-1 splttng ponts so that the resultng overall mean access tme s mnmzed. The algorthm tests each possble splttng pont s n each partton and accepts t f Cs, j < C, j, where C,j s the cost n terms of overall mean access Fgure 4. Broadcast schedule constructon

11 Push and Pull Systems 11 tme of mantanng a partton startng from tem and endng wth tem j, and s C, j = C, s + Cs+ 1, j s the cost n terms of overall access tme of splttng that partton at pont s. In order to fnd the optmal number of dsks, K, the algorthm that assgns tems to parttons s run for all values of K between 1 and M, and the one that yelds the lower overall mean access tme determnes the value of K to be used. Integraton of ndexng n the method of Yee et al. (2002) takes advantage of the fact that tems at each dsk are broadcast n a flat manner. Thus, t apples (1, m) ndexng to each partton. Parttons now contan ndex and data tems and are nterleaved nto a sngle channel. The only needed modfcaton to (1, m) ndexng s that each data tem contans an offset to the next ndex to appear, ether belongng to the same dsk of the data tem or to another dsk. Smulaton results n Yee et al. (2002) show the expected behavour of ncreasng performance gan over the flat scheme for ncreasng skewness n tem demands. When the ndex scheme s taken nto account, the followng observatons occur: Overall mean access tme s not better than that of a flat (1, m) ndexng scheme for low values of data skewness. The ndexed broadcast dsk method beats the flat (1, m) ndex scheme at medumand hgh-demand skewness. The tunng tme of the ndexed broadcast dsk schedule s sgnfcantly lower than that of the nonndexed one, wth obvous advantages for clent energy effcency. The Vadya-Hameed Method Broadcast schedule constructon n Vadya and Hameed (1996, 1999b) s based on the followng two arguments: Argument 1: Argument 2: Broadcast schedules wth mnmum overall mean access tme are produced when the ntervals between successve nstances of the same tem are equal (Ammar & Wong, 1985). The actual structure of the broadcast s determned by the so-called square-root rule: Under the assumpton of equally spaced nstances of each tem, the mnmum overall mean access tme occurs when the server broadcasts nformaton tems wth frequency proportonal to the factor: d l, where d s the demand probablty for tem and l s the tem s length. Ths s a generalzaton of the result presented by Ammar and Wong (1985) for fxed-length tems.

12 12 Ncopoltds, Papadmtrou, & Pomportss Thus, accordng to Argument 2, assumng that s s the constant spacng between the nstances of tem, the overall mean access tme s mnmzed when the followng relaton stands: l s µ, " Î [1.. M] (2) d where M s the number of canddate tems for broadcastng. The work n Vadya and Hameed (1996, 1999b) proposes an algorthm that s motvated by the arguments presented above. Specfcally, t schedules broadcastng whle tryng to equalze the space between successve nstances of the same tem, such that the followng equaton s acheved to the extent possble: s 2 d l = constant, [1.. M ]. (3) The algorthm operates as follows: Assumng that T s the current tme and R() the tme when tem was last broadcast, the broadcast scheduler selects to broadcast tem havng the largest value of the cost functon G: 2 d G( ) = ( T R( ) ), [1.. M ]. (4) l For tems that have not been prevously broadcast, R() s ntalzed to -1. If the maxmum value of G() s shared by two or more tems, the algorthm selects one of them arbtrarly. Upon the broadcast of tem at tme T, R() s updated so that R() = T. After the completon of the tem broadcast, the algorthm proceeds to select the next tem to broadcast. The algorthm descrbed above s of O(M) complexty. Computatonal cost reducton va bucketng. In order to reduce the computatonal cost of the method, a scheme known as bucketng s proposed (Vadya & Hameed, 1996, 1999b). Accordng to ths scheme, the server s M nformaton tems are splt nto K buckets, B 1, B 2,, B K. Bucket contans q tems. Obvously, q = M. We defne the followng: K = 1

13 Push and Pull Systems 13 d j B avg(b ) = q d j as the average demand probablty of tems n bucket B and j l B j (B ) = q lavg as the average length of tems n bucket B. It s shown (Vadya & Hameed, 1996, 1999b) that n order to mnmze overall mean access tme, for each tem j n each bucket B t must hold that: d 2 avg ( B ) s j = cons tan t, " Î[1.. K], and j Î B (5) l avg ( B ) Each bucket s organzed as a queue. Bucketng modfes the basc algorthm by workng only wth tems that are n the front of the bucket. Assumng that T s the current tme and R(B ) the tme when an tem from bucket B was last broadcast, the broadcast scheduler selects to use a bucket such that the cost functon G s maxmzed: 2 d (B ) ( (B )) avg(b ) G = T R, [1.. k]. l (6) avg(b ) For buckets that have not been prevously selected, R(B ) s ntalzed to -1. If two or more buckets share the maxmum value of G, the algorthm selects one of them arbtrarly. Upon the broadcast of the tem at the front of bucket B at tme T, R(B ) s updated so that R(B ) = T. After the completon of the tem at the front of bucket B, that tem s placed at the rear of B and the algorthm proceeds to select the next tem to broadcast. Usng the bucketng scheme, the push method (Vadya & Hameed, 1996, 1999b) reduces ts complexty to O(K). Snce tems n each bucket are broadcast wth the same frequency, t s obvous that the members of each bucket must have close l /d values for good results. Smple performance evaluaton. In what follows, we brefly evaluate the performance of the basc method by Vadya and Hameed (1996, 1999b). Fgure 5 plots the performance of the method. It can be seen that the method s able to take advantage of ncreased commonalty n tem demands for large values of θ and exhbt a low overall mean access tme. Several parameters that are nvolved n the performance comparson are explaned below. Clents are cacheless. Every clent s ntally set to access server nformaton tems n the nterval [1...Access Range], wth Access Range M. All tems outsde ths nterval have a

14 14 Ncopoltds, Papadmtrou, & Pomportss Fgure 5. Overall mean access tme n unt tems versus data skew coeffcent θ, for sngle channel broadcast zero demand probablty at the clent. Ths tem nterval conssts of an ntegral number of regons wth each regon contanng Regon Sze tems. The probabltes of regons are computed usng the Zpf dstrbuton. Items nsde the same regon have the same demand probablty. To smulate dfferences among the demands of dfferent clents, the parameters Dev and Ns are used. A Dev percentage of clents devate from the ntal overall clent demand. The demand patterns for such clents are generated as follows: wth probablty Ns, the demand probablty of each nformaton tem accessed by such a clent s swapped wth that of another tem selected unformly among all the tems n the server database. In the smulaton results of Fgure 5, Ns = 0.5. Furthermore, results n Vadya and Hameed (1996, 1999b) show that the performance of the bucketng method for a relatvely small number of buckets compared to the server database sze (10 buckets are used wth a database of sze 500 n Vadya & Hameed, 1999b) s qute close to that of the orgnal algorthm, mplyng that bucketng can sgnfcantly reduce the computatonal cost of the method.

15 Push and Pull Systems 15 An Adaptve Push System Both the push methods descrbed above, and also all others that have been proposed, are only practcal for statc envronments snce no means for updatng tem probabltes s provded. However, data broadcastng applcatons operate n dynamc envronments. The method n Ncopoltds, Papadmtrou, and Pomportss (2001, 2002) proposes a push-based system that s adaptve to dynamc clent demands. The system uses a learnng automaton at the broadcast server n order to provde adaptvty to the method of Vadya and Hameed (1996, 1999b) whle mantanng ts computatonal complexty. Usng smple feedback from the clents, the automaton contnuously adapts to the overall clent populaton demands n order to reflect the overall popularty of each data tem. It s shown va smulaton that, contrary to the Vadya and Hameed method, the adaptve system provdes superor performance n an envronment where clent demands change over tme, wth the nature of these changes beng unknown to the broadcast server. Learnng Automata Learnng automata (Narendra & Thathachar, 1989) are structures that possess the ablty to learn the characterstcs of a system s envronment. A learnng automaton mproves ts performance by nteractng wth ts random envronment. Its target s to effcently select among a set of A actons the optmal one, so that the average penalty gven by the envronment s mnmzed. Thus, there must exst a mechansm that notfes the automaton about the envronmental feedback to a specfc acton. A learnng automaton operates va a sequence of cycles, whch eventually lead to mnmzaton of average receved penalty. Each learnng automaton typcally uses a vector p(n) = {p 1 (n), p 2 (n),..., p A (n)} that represents the probablty dstrbuton for choosng one of the actons a 1, a 2,..., or a A at cycle n. Obvously: A å p ( n) = 1. (7) = 1 The core of a learnng automaton s the algorthm used to update the probablty vector. Also known as the renforcement scheme, ths algorthm uses after each a at cycle n the envronmental response β(n) trggered by ths acton n order to update the probablty dstrbuton vector p. After the updatng has taken place, the automaton selects the acton to perform at cycle n + 1 accordng to the updated probablty dstrbuton vector p(n + 1).

16 16 Ncopoltds, Papadmtrou, & Pomportss The Adaptve Schedulng Algorthm In what follows, we ntroduce the estmaton probablty vector p, whch stores the server s estmaton of the actual demand probablty vector d that contans the actual choce probabltes of the varous nformaton tems averaged over the entre clent populaton. The adaptve push system uses at the server a learnng automaton whose probablty dstrbuton vector contans the server s estmate p of the actual demand d of the overall clent populaton for each data tem ; d s the overall popularty of each tem at the clent populaton, meanng that t s the probablty that when an tem request s made by the clent populaton, ths wll be a request for tem. Obvously: M d = 1 = 1, where M s the number of nformaton tems n the database of the broadcast server. Accordng to the Vadya and Hameed (1999b) method, the server selects to broadcast tem havng the largest value of the cost functon G. The adaptve approach extends ths method: After broadcastng tem, the server wats for acknowledgment from all clents that were satsfed by ths tem broadcast. All clents that were watng for tem acknowledge ther recepton va a short feedback pulse. The sum of the receved pulse strength at the server wll be used by the automaton to update the probablty dstrbuton vector p. Nevertheless, the pulse strength of each clent s pulse at the server depends on ts dstance from the server and s not constant due to the moblty of the clents. Assumng 1 that the path loss s a n type loss wth a typcal n = 4, the feedback pulse of clents x located close to the broadcast server wll be extremely stronger than those of clents further away. To prevent the clents close to the server from favourng the automaton decson toward ther demands, there exsts a power-control mechansm on the returnng pulses. Thus, every tem can be broadcast ncludng nformaton about the sgnal strength used for the tem s transmsson. Assumng that nformaton on the sgnal strength at whch the tem was orgnally transmtted s A 0, and the sgnal strength measured at the tem recepton s A (obvously t wll stand that S S 0 ), clents wll set the strength of ther feedback pulse to A 0 /A. Thus, ths form of power control forces contrbuton of each clent s feedback pulse at the server to be the same rrespectve of the clent-server dstance. The probablty dstrbuton vector at the automaton at the server defnes the demand probablty estmate of the server for each nformaton tem. Va ths scheme, the automaton uses the ampltude of the receved pulse to update the server s estmate of nformaton tem probabltes. Thus, for the upcomng broadcast, the server chooses whch tem to transmt by takng nto account the updated values of the tem probablty estmates.

17 Push and Pull Systems 17 Probablty Updatng Scheme When the broadcast of an nformaton tem does not satsfy any clent, the server probablty estmates of the data tems do not change. Followng a useful broadcast of an tem, however, the probablty estmate of tem wll be ncreased. In general, after the server s kth broadcast, the followng probablty updatng scheme s used: p ( k + 1) = j p ( k) L(1 â( k))( p j j ( k) a), j p ( k + 1) = p ( k) + L(1 â( k)) j ( p j ( k) a). (8) L s a parameter that governs automaton convergence speed. Low values of L lead to more accurate estmatons. However, low values for L also reduce convergence speed. It holds that L, a (0,1) and p (k) (a,1), [1..M]. The role of parameter a s to prevent the probabltes of nonpopular tems from takng values very close to zero n order to ncrease adaptvty. Ths s because f the probablty estmate p of an tem becomes zero, then G() wll also take a value near zero. However, tem, even f unpopular, stll needs to be transmtted snce some clents may request t. Furthermore, the dynamc nature of demands s lkely to make ths tem more popular n the future. Upon recepton of the aggregate feedback pulse, ts ampltude s normalzed n the nterval [0,1]. β(k) stands for the normalzed envronmental response after the server s kth broadcast. A value of β(k) = 1 represents the case where no clent acknowledgment s receved. Thus, the lower the value of β(k), the more clents were satsfed by the server s broadcast at cycle k. Fgure 6. Convergence of automaton estmaton of the demand probabltes for tems 1 to 2

18 18 Ncopoltds, Papadmtrou, & Pomportss Usng the renforcement scheme of Equaton 8, the data tem probablty estmates converge near the actual demand probabltes for each tem. Ths makes ths approach attractve for dssemnaton applcatons wth dynamc clent demands. Ths convergence s schematcally shown n Fgure 6, whch plots the convergence of the tem probablty estmates toward the actual overall demand probabltes for data tems 1 and 2, n a smulaton of an envronment wth a pror unknown clent demands that change after some tme. It s evdent that convergence of the automaton tem probabltes estmates for tems 1 and 2 to the overall clent demand for these tems s acheved. The normalzaton procedure n the calculaton of β(k) suggests the exstence of a procedure to enable the server to possess an estmate of the number of clents under ts coverage. Ths s made possble by broadcastng a control packet that forces every clent to respond wth a power-controlled feedback pulse. The broadcast server wll use the sum of the receved pulses S to estmate the number of clents under ts coverage. Then, upon recepton of a pulse of ampltude Z after the server s kth broadcast, β(k) s calculated as Z/S. Ths estmaton process wll take place at regular tme ntervals wth the neglgble overhead of broadcastng a unt-length tem. More on the normalzaton procedure can be found n Ncopoltds et al. (2002). The probablty updatng scheme of Equaton 8 s of O(M) complexty. Therefore, the adaptve push method does not ncrease the computatonal complexty of the orgnal nonadaptve one by Vadya and Hameed. The bucketng descrbed n the latter method would not further reduce computatonal complexty n the adaptve one, as complexty would reman of O(M) due to the probablty updatng scheme. Smple Performance Evaluaton Smulaton results n Ncopoltds et al. (2001, 2002) show that the adaptve push system outperforms the nonadaptve one n Vadya and Hameed (1999b) n dynamc envronments. Ths s due to the fact that the adaptve system s able to learn the changng envronment and adapts ts operaton by takng nto account the actual demand probabltes. The nonadaptve push system, however, operates blndly by utlzng the same set of demand probabltes all of the tme. Ths superorty of the adaptve system for varous values of the access skew coeffcent θ s shown n Fgure 7. In these comparsons, the statc push system s server always broadcasts the entre range of ts tems assumng equprobable demand per tem. Ths s because such an approach s the best wthout knowledge of the nature of overall clent demands. The smulaton assumptons are the same wth those mentoned n the secton descrbng the nonadaptve method by Vadya and Hameed. Pull Systems In general, pull systems have the advantage of beng adaptable to dynamc clent demands due to the knowledge of the demand at the server through clent requests. However, they are not easly scalable to large numbers of clents. In such cases, requests carred over the back channel wll ether collde wth each other or saturate the server.

19 Push and Pull Systems 19 Fgure 7. Overall mean access tme n unt tems versus data skew coeffcent θ In ths secton we wll descrbe the work of Aksoy and Frankln (1998, 1999) as a representatve pull system. In that paper, t s reported that the man algorthms that have been proposed for pull-based data broadcastng are: Frst Come Frst Served (FCFS). Ths broadcasts nformaton tems n the order they were requested. Most Requests Frst (MRF).Ths schedules broadcasts by transmttng tems based on the number of ther pendng requests n descendng order. Most Requests Frst Lowest (MRFL). Ths s smlar to the prevous one; however, for two or more tems havng the same number of pendng requests, the algorthm frst transmts the tem havng the lowest access probablty. Longest Wat Frst (LWF). Ths transmts the tem havng the largest aggregate watng tme frst (the sum of watng tmes for all pendng requests for that tem). Smulaton results n Aksoy and Frankln (1998, 1999) show that LWF s the most preferable algorthm. However, t s not practcal for large systems snce at each step, t needs to calculate the aggregate watng tme for every pendng tem. The proposed method n Aksoy and Frankln (1998, 1999), RxW, provdes a method that s shown va smulatons to provde close performance to LWF whle havng a lower overhead. Unlke most other pull algorthms (and also push ones as well), RxW constructs the schedule based on the state of the request queue rather than the tem probabltes. Specfcally, the RxW algorthm dctates that the broadcast server mantans a lst that contans the R xw value for each tem that has pendng requests, where R s the number

20 20 Ncopoltds, Papadmtrou, & Pomportss of pendng requests for tem and W s the tme that has elapsed snce the oldest request for tem was made. In order to further reduce the overhead of RxW and to provde t wth scalablty to systems operatng on larger databases, the followng algorthms are proposed n Aksoy and Frankln (1998, 1999): A varant of RxW that reduces the calculatons needed per tem broadcast and stll manages to broadcast the nformaton tem havng the largest RxW value. Ths s acheved by reducng the tem range examned by the algorthm n ts search for the tem to broadcast. A heurstc verson of RxW that further reduces overhead by searchng, at each step t, not for the tem havng the largest RxW value, but nstead for the frst one that has an RxW value greater than or equal to axthresh(t), where Thresh(t) = (Thresh(t - 1) + PrevRxW)/2. PrevRxW s the RxW of the prevously broadcast tem and a s a parameter that can be tuned to provde a trade-off between scalablty to large databases and broadcast-schedule constructon optmalty. Specfcally, as a approaches 0, the heurstc algorthm reduces toward a constant tme approach to the selecton of the tem to broadcast, whereas as a ncreases to nfnte, the behavour heurstc algorthm approaches that of the orgnal RxW one. Hybrd Systems In hybrd methods clents can use a back channel to submt requests to the server for nformaton tems that are not cached n the clent and are not scheduled to appear n the broadcast n the near future. It can be easly seen that there must exst a polcy on effcent back channel usage as a large number of clent requests wll ether collde or saturate the server due to the latter s fnte processng power and request-storage capablty. To support a mxture of push and pull delvery, the broadcast server wll nterleave pushed tems wth pulled ones (tems that are broadcast n response to specfc clents requests). The percentage of bandwdth that can be allocated to pulled tems s a matter of study n Acharya, Frankln, and Zdonk (1997), Lee, Hu, and Lee (1999), and Stathatos, Roussopoulos, and Baras (1997). In Acharya et al. (1997), ths bandwdth percentage s controlled by a parameter named PullBW, takng values n [0...1]. When PullBW = 0, the system s a pure push one, whereas when PullBW = 1, the system becomes a pure pull one. When PullBW takes values n (0...1), the system employs a combnaton of push and pull and thus becomes a hybrd one. A refnement of ths method uses a threshold parameter, Thresh, that lmts back channel use by clents. Specfcally, clents pull tems (.e., submt explct requests) only f the requested tem wll appear n the broadcast later than the duraton of a 1-Thresh porton of the broadcast schedule s major cycle. Thus, ths method constrans a clent to usng the back channel only for nformaton tems whose mss would cost a lot. A complementary method to ncrease performance of the system s to exclude from the push schedule those pages that are most unlkely to be demanded by clents.

21 Push and Pull Systems 21 Thus, these pages can be accessed only on demand. Ths method has the obvous effect of reducng push bandwdth to the favour of pull bandwdth, wthout a sgnfcant performance penalty due to the very lmted popularty of the data tems excluded from the push schedule. However, f the pull bandwdth s not enough despte ts ncrease, performance can degrade snce clents wll not be able to access on demand the tems that were excluded from the push schedule. Smulaton results by Acharya et al. (1997) show that whle pure pull and pure push perform better than the hybrd method n underutlzed and overutlzed systems respectvely, the hybrd method provdes nearly unformly good overall mean access tmes n almost all cases and s thus of practcal use n a wde range of system loads. Although beng able to effcently combne push and pull, the hybrd method of Acharya et al. (1997) has the dsadvantage of not beng able to dynamcally adapt the rato of push to pull bandwdth to changng degrees of system utlzaton. A method that overcomes ths problem s proposed n Lee et al. (1999). Ths paper proposes an algorthm, whch, accordng to system workload, dynamcally (a) allocates bandwdth to push and pull modes and (b) decdes the mode (ether push or pull) for the dssemnaton of each data tem. The proposed method s compared to pure push, pure pull, and a hybrd method wth a statc rato of push-pull bandwdth allocaton. Smulaton results regardng the frst three methods are smlar to those of Acharya et al. (1997) that were mentoned above. The proposed dynamc hybrd method, however, shows an optmal performance n all cases, as t s able to flexbly assgn bandwdth to ether push or pull mode accordng to system workload. In Stathatos et al. (1997), a hybrd method that dynamcally estmates the demand probablty of nformaton tems s used. Items are sorted based on ther demand and a lne s drawn that separates the pushed popular tems from the pulled nonpopular ones. The server artfcally changes the demand probablty estmate of tems so that even a very popular tem s excluded for short tme perods from the push mode. Ths excluson s useful snce t wll cause a number of explct requests for that tem whch wll be used by the server to obtan an estmate on the overall tem demand probablty. Repetton of ths functon obvously enables the server to keep up wth changng demand and thus adapt to t. Smulaton results by Stathatos et al. show that the method enjoys scalablty and adaptvty to changng demands, wth the rate of adaptvty beng possble to tune. Another nterestng hybrd system s proposed by Hu and Chen (2002). In ths paper, the authors propose a model that uses clent mpatence to devse an algorthm that can work onlne and establsh knowledge of tem-demands patterns n a granularty of a broadcast cycle. A clent usually has lmted patence for a push request t makes. Thus, after a certan perod of tme has elapsed and the clent has yet to receve the desred tem from the broadcast, t wll send a pull request to explctly demand the tem. However, such requests also have the beneft of helpng the server estmate the demand probablty for the pushed tems. To ths end, the server s programmed to delberately generate a pushbroadcast mss, whch wll obvously force clents to explctly demand that tem. Thus, by countng the pull requests, the server can calculate the access frequency proporton

22 22 Ncopoltds, Papadmtrou, & Pomportss of push tems on the broadcast channel. Smulaton results by Hu and Chen show that the mean dfference between the estmated access frequency dstrbuton and the real one s very small, provng the estmaton mechansm to be very useful. Hybrd systems are also covered n Datta, VanderMeer, Celk, and Kumar (1999). Ths paper addressed the problem of data broadcastng by nvestgatng both (a) good strateges that the server can use to decde on broadcast content, gven that users are hghly moble, and (b) the dentfcaton of effcent retreval algorthms for the clents so that ther energy consumpton s mnmzed. Datta et al. consder broadcast strateges beng ether of constant schedule sze (constant broadcast sze [CBS] strateges, or perodc strateges) or of varable schedule sze (varable broadcast sze [VBS] strateges, or aperodc strateges). The man characterstcs of these strateges are summarzed: In the constant schedule sze strategy, tems are ncluded or excluded from the broadcast based on ther popularty. Furthermore, n order to prevent clent starvaton, the system wll support montorng of requests for nonpopular tems. Thus, after a certan perod elapses after such a request, the tem wll be ncluded n the schedule despte ts low overall demand among the clent populaton. In the varable schedule sze strategy, schedule sze changes accordng to the number of tems that have been requested durng the precedng broadcast perod. As ths strategy can possbly nclude all tems n the database, tems are dropped from the broadcast based on the expected tme that a clent requestng an tem wll stay n the cell. Results n Datta et al. (1999) show that: The aperodc approach performs better than the perodc one at low system loads. For moderate loads, the aperodc approach provdes lower tunng tmes, whereas the perodc one provdes lower access tmes. For hgh loads, the perodc approach outperforms the aperodc one and provdes lower tunng and access tmes. When clents are nterested n only a small porton of the database, the relatve performance of the perodc and aperodc approaches from the energy-effcency pont of vew resembles that from the access-tme pont of vew. Mnor starvaton of clents requestng tems of low popularty starts to occur only n relatvely hgh loads. Schedulng Constructon wth Multple Channels The above dscusson so far assumed a sngle broadcast channel to whch all clents are tuned. However, an extenson of the basc Vadya and Hameed method for operaton n envronments wth more than one broadcast channel s also proposed. Assume that

23 Push and Pull Systems 23 H = {1, 2,..., c} s the set of avalable broadcast channels and each clent lstens to a nonempty set S H wth probablty S. The cost functon G n Equaton 4 changes to the followng one, whch s used to determne whch tem wll be broadcast on channel h, 1 h c: d 2 S G ( ) ( ( )) h = Π s T R. l (9) S H, h S The broadcast schedulng algorthm changes accordngly and agan targets mnmzaton of the overall mean access tme averages over all clents: Let T be the current tme and R h () the tme when tem was last transmtted on channel h, 1 h c. For tems that have not been prevously broadcast, R h () s set to -1. The broadcast scheduler takes the followng steps n order to determne the tem to transmt on channel h: Calculates Rs() = max hîs Rh(), " S, ", SÍ H, 1 M. Selects tem wth the largest value of G h (). If the maxmum value of G h () s shared by two or more tems, then the algorthm selects one of them arbtrarly. Fgure 8 plots the performance of the method for two avalable broadcast channels. 1, 2, and 1,2 are the probabltes of a clent lstenng ether to channel 1, channel 2, or both Fgure 8. Overall mean access tme n unt tems for varous values of Π 1

24 24 Ncopoltds, Papadmtrou, & Pomportss of these channels, respectvely. Obvously, ,2 = 1. In ths experment we assumed that 1 = 2 = 1-1,2 (Vadya & Hameed, 1999b). As n the case of the sngle channel, t can be seen that the method s able to take advantage of ncreased commonalty n tem demands for large values of θ, and exhbt a low overall mean access tme. Schedulng wth Recepton Errors The methods presented so far do not consder the effects of recepton errors, whch frequently occur n wreless lnks, on optmum schedule constructon. Such a method s dscussed by Vadya and Hameed (1999b). Specfcally, Relaton 1 s enhanced by modfyng t n order to take nto account the effect of unrecoverable recepton errors (errors that cannot be corrected usng error control codes). Assumng that E(l) s the probablty that an tem of length l contans an unrecoverable error, Relaton 2 changes to Relaton 10 n order to take errors nto account: s µ l(1 - E( l)) d (1 + E( l )) (10) Obvously, n cases of no unrecoverable recepton errors or tems of the same length, 1 E( l ) Relaton 10 reduces to Relaton 2 snce 1+ E( l ) reduces to unty or a constant, respectvely. Based on Relaton 10, the broadcast scheduler modfes the cost functon G so as to take errors nto account, as follows: 2 d 1+ E( l ) G( ) = ( T R( ) ), [1.. M ]. (11) l 1 E( l ) Takng Varance of Access Tme nto Account The methods presented so far prmarly focus on mnmzaton of mean access tme over the entre clent populaton. However, n several applcatons, t could be benefcal to reduce performance degradaton of clents wth demands largely devatng from the overall demand of the clent populaton, as t s the mean access tmes of these clents that wll largely vary from the overall mean access tme. To ths end, the work n Vadya and Hameed (1996, 1999b) was augmented n Vadya and Hameed (1998), whch proposes