DYNAMIC BROADCAST SCHEDULING IN ASYMMETRIC COMMUNICATION SYSTEMS: PUSH AND PULL DATA BASED ON SCHEDULING INDEX AND OPTIMAL CUT-OFF POINT YUFEI GUO

DYNAMIC BROADCAST SCHEDULING IN ASYMMETRIC COMMUNICATION SYSTEMS: PUSH AND PULL DATA BASED ON SCHEDULING INDEX AND OPTIMAL CUT-OFF POINT by YUFEI GUO Preseted to the Faculty of the Graduate School of The Uversty of Texas at Arlgto Partal Fulfllmet of the Requremets for the Degree of MASTER OF SCIENCE IN COMPUTER SCIENCE THE UNIVERSITY OF TEXAS AT ARLINGTON December 2000

DYNAMIC BROADCAST SCHEDULING IN ASYMMETRIC COMMUNICATION SYSTEMS: PUSH AND PULL DATA BASED ON SCHEDULING INDEX AND OPTIMAL CUT-OFF POINT The members of the Commttee approve the masters thess of Yufe Guo Sajal K. Das Supervsg Professor Vasat K. Prabhu Behrooz A. Shraz Bob P. Weems

ACKNOWLEDGMENTS I am grateful to Dr. Sajal K. Das for supervsg my thess, costat ecouragemet, help, ad gudace through out ths work. He troduced me to the topc of data broadcast schedulg ad motvated me to acheve my goals. May thaks are due to Dr. Shraz, Dr. Weems, ad Dr. Prabhu for beg the defese commttee, revewg the thess, ad provdg feedback. I would also lke to thak Dr. Crsta Pott from the Uversty of Treto Italy for her commets. November 20, 2000

ABSTRACT DYNAMIC BROADCAST SCHEDULING IN ASYMMETRIC COMMUNICATION SYSTEMS: PUSH AND PULL DATA BASED ON SCHEDULING INDEX AND OPTIMAL CUT-OFF POINT Publcato No. Yufe Guo, M.S. The Uversty of Texas at Arlgto, 2000 Supervsg Professor: Sajal K. Das A Clet-Server system, where the server has much commucato capacty tha clets, s called a Asymmetrc Commucato System. It s beleved that broadcast s a effcet way to trasmt data such a system. Broadcast ca be ether pull-based, where clets ask for data from the server, or push-based, where the server pushes data to clets. How to schedule data to broadcast s mportat to the overall system performace. I ths thess, both push-based ad pull-based schedulg algorthms are studed. A ew schedulg performace metrc, called expected prortzed access tme, s troduced, ad a modfed push-based packet far schedulg based o Schedulg Idex s preseted. To make the schedule more effcet, a dyamc schedulg algorthm s proposed for systems whch the umber of data tems to broadcast s very large. The ew algorthm uses push-based schedulg to broadcast some tems ad uses pull-based v

schedulg to sed the remag tems by requests. The approach s based o choosg the optmal cut-off pot. It s show that the server s broadcast speed s very mportat selectg the cut-off pot ad hece the schedulg algorthm. v

TABLE OF CONTENTS ACKNOWLEDGMENTS... ABSTRACT... v LIST OF FIGURES... v LIST OF TABLES... x Chapter. INTRODUCTION.... Broadcast Schedulg... 3.2 Exstg Work o Broadcast Schedulg... 5.3 Cotrbutos of Ths Thess... 7 2. DEFINITIONS AND PERFORMANCE METRICS... 9 2. Deftos ad Symbols... 9 2.2 Schedulg Performace Metrcs... 2.3 Computato of Access Tme... 2 2.4 Summary... 3 3. SELECTIVE BROADCAST SCHEDULING ALGORITHMS... 4 3. Algorthms for Push-based System... 4 3.2 Algorthms for Pull-based System... 8 3.3 Summary... 9 4. A SCHEDULING ALGORITHM BASED ON SCHEDULING INDEX... 20 4. Expected Prortzed Access Tme... 20 4.2 Optmal Expected Prortzed Access Tme... 22 v

4.3 Schedulg Idex... 24 4.4 Evaluato of Usg Schedulg Idex... 25 4.5 Summary... 30 5. A NOVEL DYNAMIC SCHEDULING ALGORITHM FOR BROADCASTING... 3 5. Crtera to Set Cut-off Pot... 32 5.2 Decrease of Expected Access Tme... 37 5.3 Proposed Dyamc Schedulg Algorthm... 39 5.4 Performace Evaluato... 40 5.5 Summary... 42 6. CONCLUSIONS AND FUTURE RESEARCH... 48 APPENDIX: IMPLEMENTATION AND SIMULATION PROGRAMS... 50 REFERENCES... 58 BIOGRAPHICAL INFORMATION... 60 v

LIST OF FIGURES Fgure Page. Push-based System... 2.2 Pull-based System... 3 2. Computato of Access Tme... 3 3. Arragemet of Data Items... 5 4. Test Schedulg Smulator... 27 4.2 Schedule Performace ( = 0)... 28 4.3 Schedule Performace ( = 0.3)... 28 5. Sedg Slots ad Broadcast Slots... 36 5.2 Schedulg Cut-off Pot... 38 5.3 Cuttg for = 000, θ = 0.6 ( detal)... 43 5.4 Cuttg for = 000, θ = 0.6 (whole rage)... 43 5.5 Cuttg for = 000, θ = 0.8 ( detal)... 44 5.6 Cuttg for = 000, θ = 0.8 (whole rage)... 44 5.7 Cuttg for = 000, θ =.0 ( detal)... 45 5.8 Cuttg for = 000, θ =.0 (whole rage)... 45 5.9 Cuttg for = 000, θ =.2 ( detal)... 46 5.0 Cuttg for = 000, θ =.2 (whole rage)... 46 5. Cuttg for = 2000, θ =.0 ( detal)... 47 5.2 Cuttg for = 2000, θ =.0 (whole rage)... 47 A. Packet Far Schedulg Program... 54 A.2 Dyamc Schedulg Program... 57 v

LIST OF TABLES Table Page 3. Expected Access Tme of Dfferet Schedules... 5 4. Expected Prortzed Access Tme... 22 4.2 Expected Prortzed Access Tme (θ p = )... 29 4.3 Expected Prortzed Access Tme (θ p = 0.25)... 29 x

CHAPTER INTRODUCTION May computer systems use a Clet-Server archtecture to trasmt data tems betwee server ad clets. I such a system, data trasfer from server to clets s called dowstream commucato, ad the trasfer from clets to server s called upstream commucato. The dowstream commucato capacty s ot always equal to the upstream commucato capacty. If the former s much larger tha the latter, the such a clet-server system s called a Asymmetrc Commucato System. Some examples of such system are: Wreless etworks: where moble phoes commucate wth base stato. The base stato has a larger commucato capacty, whle a moble phoe s lmted o both battery power ad badwdth. Iformato dspersal systems: whch provde servces lke stock prce, weather formato, traffc gude, ad so forth. I such systems, the powerful broadcast capablty s utlzed to delvery data to a large populato of clets effcetly. For example, the traffc gude system has bee used may ctes to provde traffc formato to moble users o the road. New cable ad satellte televso systems: whch provde vdeo-o-demad servces. Such a system s expected to provde multmeda capablty wth lve audo/vdeo o demad. I most asymmetrc commucato systems, data tems trasmtted are eeded by may clets. Broadcast techology s a attractve ad effcet way to satsfy

2 clets requremets such systems, because t has early fte dssemato scalablty ad also a broadcast respose ca satsfy may clets smultaeously. There are two ways to broadcast data tems. I a pull-based system, clets tate the data trasfers by sedg requests to a server. After recevg the requests, the server makes a schedule ad satsfes the clets requests o the scheduled tme. I a push-based system, o the other had, clets get requred data tems by lsteg to the broadcast chael ad capturg the data wheever t goes by. The server broadcasts data tems o scheduled tme o matter whether the partcular tem s requred or ot at that tme. The data tem to be broadcast ext tme s chose by a schedulg polcy wthout ay clet terveto. Because the upstream commucato capacty s much less compared to the dowstream commucato capacty, t s wdely accepted that the push-based broadcastg s a more effcet way to trasmt data a asymmetrc commucato system. The push-based system s modeled fgure., where the server s located the ceter. It broadcasts data tems, for example, data a, b, ad so forth, oe or more chaels. May clets lste to the chaels aroud the server. server b a clet Fgure.. Push-based System.

3 The pull-based system s modeled fgure.2. Clets stll grab data tems from ar, whch are broadcast from the server. However, the server broadcasts oly the tems requested by some clets a scheduled order. Clets wll be led up order that requests are made. server b a clet a b c a b c Fgure.2. Pull-based System. I both push-based ad pull-based systems, the area at whch server ad all clets locate s small eough, so the dstace from clets to the server ca be cosdered to be the same. Hece the broadcast delay due to the dstace ca be eglgble.. Broadcast Schedulg No matter whch scheme s used to broadcast data tems, we eed to desg a trasmsso schedule. To determe whe a data tem should be trasmtted by a server s called Broadcast Schedulg. There are several reasos why we eed such schedule, for example, to save chael badwdth, to reduce watg tme for most clets, to satsfy hgher prorty requests the earlest tme, ad so o. Schedulg Theory has bee studed sce 960s. Most of the early research was focused o pot-to-pot systems, where a dvdual clet makes a request ad the

4 server respods to the request dvdually. If aother clet makes a smlar request, the server wll respod aga. The request could be for a data tem, or some computer resources, or executo of a program. Ths area of research s pretty matured [4]. The from 980s, as wreless techology ad formato dspersal systems developed rapdly, the broadcast system techology receved more ad more atteto. Some characterstcs of broadcast systems are qute dfferet from those of pot-to-pot systems. It s these dffereces that determe dfferet schedulg algorthms. Followg s the summary of these characterstcs [4]: Broadcast Delvery: Wheever the server broadcasts a data tem, all pedg requests for that data tem are satsfed, whch s dfferet from pot-to-pot systems. I pot-to-pot systems, the server must satsfy a clet s request dvdually. Heterogeety: There are may dfferet applcatos ad data tems the broadcast systems. It s uecessary to requre that all data tems have the same sze. Clarvoyace: The server has the complete kowledge of the data tems that t wll broadcast. Gve the badwdth of the chael, the servce tme for a clet s request s kow. Ths s very rarely the case most other systems, such as CPU schedulg operatg system. Because of broadcast delvery, the schedulg algorthm must try to satsfy those requests frst that are eeded by most clets. Because of the clarvoyace, t s possble to fd a optmal schedule, whch s ot the case for other systems.

5.2 Exstg Work o Broadcast Schedulg As metoed earler, research o broadcast schedulg s dvded to two subareas, push-based schedulg ad pull-based schedulg. Wag ad Ammar [3] studed the broadcast delvery teletext systems. Three alteratve archtectures were cosdered such as oe-way broadcast (push-based), twoway teracto (pull-based), ad hybrd oe-way broadcast / two-way teracto. I ther research, both push-based ad pull-based schedulg algorthms are studed. They dscussed broadcast cycle desg problem uder the codto that there s suffcet memory to store all data pages. For two-way teracto, they observed a tradeoff betwee the volume of traffc o the request chael ad the amout of formato avalable to the servce computer. The effect of local storage of related data was also dscussed. Acharya, Aloso, Frakl, ad Zdok ([], [2]) troduced the cocept of Broadcast Dsks, whch s used for schedulg asymmetrc commucato evromets. It s a push-based algorthm whch mproves performace for ouformly accessed data. I effect, the broadcast chael becomes a dsk from whch clets ca retreve data as t goes by. Data tems are assged to dfferet dsks of dfferet szes ad speeds. The these dsks are multplexed o a sgle broadcast chael. The mpact of clet cachg polcy o the performace of the schedulg was also dscussed. It was demostrated that desgg the broadcast dsks, the broadcast program ad the cachg polcy must be cosdered together. Acharya ad Muthukrsha [4] proposed a ew pull-based algorthm to mmze the performace measure called stretch, whch s the respose tme dvded by the sze of requested data tem.

6 For push-based system, the broadcast schedule wth mmum expected access tme results whe the staces of each tem are equally spaced []. Vadya ad Hameed [9] ad [4] derved the optmal expected access tme for push-based systems. They also proposed that the broadcast schedulg problem was related to packet far queueg. Packet far queueg s used o packet swtch the etwork, determg whch packet from may put queues should be trasmtted ext o the output chael [7]. The use of packet far queueg o the broadcast schedulg has show a very good result compared to other schedulg algorthms. Schedulg for multple broadcast chaels ad the mpact of trasmsso errors o schedulg were also studed [9] ad [4]. May researchers realzed that cachg ad prefetchg are very mportat o the performace of broadcast schedulg, because they ca save access tme. For example, Barbara ad Imelsk [6] studed cachg strateges moble evromets, Acharya, Frakl, ad Zdok [3] studed prefetchg from broadcast dsks. The wreless broadcastg has a uque problem. Moble devce s powered by battery, ad power cosumpto must be lmted to mprove battery lfe. Idex based orgazato of data for broadcastg ca result sgfcat mprovemet battery utlzato, as suggested [0]. The schedulg algorthms troduced so far all assumed that the kowledge of access probablty was avalable a pror ad accurate. However, fact, ths s ot the case. Stathatos, Roussopoulos, ad Baras [2] proposed to use broadcast msses to uderstad the access patters. Yu, Sakata, ad Ta [6] proposed a statstcal estmato model that s based o maxmum lkelhood estmato to estmate access probablty.

7 From the above dscusso, we observe that most of the prevous research was focused o push-based algorthms, ad they were treated separately from pull-based algorthms..3 Cotrbutos of Ths Thess Ths thess focuses o the broadcast schedulg for asymmetrc commucato systems. A ew metrc, called Expected Prortzed Access Tme, s troduced ad a dyamc schedulg algorthm based o the combato of push-based ad pull-based schemes s preseted. Most of the exstg algorthms make schedule based o access probablty, whch cosders oly popularty of the data tems. Other factors lke prorty have bee gored. Although ths was poted out [3], the authors dd ot vestgate t further. Expected prortzed access tme s developed ths thess ad by extedg access probablty to a more geeral cocept called Schedulg Idex, exstg push-based ad pull-based algorthms ca be used to make schedule based o may factors. It has bee also show the thess that ether push-based schedulg or pullbased schedulg aloe ca obta the optmal performace. I fact, the optmal performace s acheved whe the two schedulg are used together a effectve maer. Data tems are dvded to two sets, popular set ad less-popular set. Pushbased algorthm s used to schedule tems the popular set ad pull-based algorthm s used to schedule tems the less-popular set. By properly selectg the cut-off pot to dstgush these sets, ths ew dyamc algorthm ca make schedule wth less expected access tme tha the exstg algorthms. The method to compute optmal cut-off pot s also gve.

8 The above two proposals are evaluated by smulato programs, ad the evaluato results are preseted after the proposals are troduced. To evaluate the frst proposal, a schedulg program s executed to actually make broadcast schedules based o Schedulg Idex. The the expected prortzed access tme s computed from the schedule ad s compared wth the optmal expected prortzed access tme. To evaluate the secod proposal, the smulator sets the cut-off pot from the frst data tem to the last oe, ad compute expected access tme for each cut-off pot by actually readg the staces of accesses ad requests at specfed speed. Also, the smulato results are compared wth those from the proposal to evaluate the proposal. The rest of the thess s orgazed as follows. Chapter 2 troduces the schedulg performace measures, ad chapter 3 a selectve umber of exstg pushbased ad pull-based schedulg algorthms. I chapter 4, a ew schedulg performace measure ad a modfed schedulg algorthm are preseted. A dyamc schedulg to combe push-based ad pull-based algorthms s proposed chapter 5. Chapter 6 offers coclusos ad drectos for future research work. Appedx dscusses the smulato programs.

9 CHAPTER 2 DEFINITIONS AND PERFORMANCE METRICS I ths chapter, some otatos ad symbols wll be preseted whch are used through out the thess. Some schedulg performace metrcs are also troduced, whch measure how well a schedule performs. A schedulg algorthm attempts to optmze oe of these metrcs. 2. Deftos ad Symbols A server has a total of may data tems. We assume all of them are memory. So they ca be reached mmedately by the server. Each tem s dexed by, where. The legth of tem s dcated by l. Dfferet tems may have dfferet legths. I some systems, each tem s broke to several peces. Each pece s called a page of ut legth. If a tem or the last pece of a tem s shorter tha the ut legth, that tem or pece s padded wth blak to make a page. We say a server BROADCASTS tems, f the tems are scheduled by some algorthm. However, we say the server SENDS tems, f they are ot scheduled ad are put o ar oly f clets eed them. O the clet sde, we say clets ACCESS ad REQUEST data tems correspodg to broadcast ad sed o the server sde. Dfferet tems may be accessed or requested by dfferet umber of clets. We call t the degree of popularty, whch ca be represeted by Access Probablty, deoted by p. Here, the word access s used to represet both access ad request. The access probablty for tem s deoted as p. Durg a tme perod T, let there be a total M

accesses ad requests for the system. Amog them, let I accesses ad requests be for tem. Thus ad I p = (2.) M = p = (2.2) I ths thess, we assume that p s avalable to the server for, ad the value does ot chage durg the whole process. Each tem may have other assocated values besdes access probablty. Oe of them that we wll use the thess s Access Prorty, deoted as q. For tem, t s represeted by q, whch dcates the degree of mportace ad/or prorty wth whch the tem s eeded by clets. Aga, the word access meas both access ad request. We defe the lowest prorty s, ad the hghest prorty s MAX_PR, a costat. For some schedulg algorthms, the schedule repeats after broadcastg all tems. The each repeat s called a broadcast cycle. Durg a broadcast cycle, some tems wll be broadcast several tmes. A appearace of a tem the broadcast s referred to as a stace of the tem. The space betwee two cosecutve staces of a tem s the tme from the begg of the frst stace to the begg of the secod stace. Ths space s represeted by s. If all staces of tem are equally spaced, the the space for tem wll be s. We defe the server speed, τ, as the tme for t to ether broadcast or sed a tem of ut legth. Ths amout of tme s called Ut Tme. The average total umber of accesses ad requests ut tme s defed as N. For a page or a tem of ut legth, the tme perod durg whch t s broadcast or set by the server s called a tme slot. 0

From the server s pot of vew, makg broadcast schedule s the same as puttg pages or ut legth tems to tme slots. 2.2 Schedulg Performace Metrcs There are several crtera that determe whether a schedulg algorthm s properly selected. Broadly speakg, a schedulg algorthm must balace both the dvdual clet expectato ad the overall system expectato. The dvdual measures of schedulg performace clude [4]: Access Tme (T acc ): the amout of tme that a clet wats for a data tem to arrve after t begs to lste. Ths s the measuremet for push-based systems. Let T lste be the tme whe the clet begs to lste to the chael for the requred tem, ad T arr be the tme whe the tem s receved by the clet. The T acc = T arr T lste (2.) A dvdual clet expects T acc to be as small as possble. Respose Tme (T res ): the amout of tme from the completo of a request T cor, to the arrval of the data T arr. Thus T res = T arr T cor (2.2) Ths s the measuremet for pull-based systems, ad T res s also expected to be as small as possble. Stretch (S): the rato of respose tme (T res ) to the data tem s servce tme (T ser ), where the servce tme s the amout of tme to complete the request f the job to sed that partcular data tem s the oly oe the system. S = T res / T ser (2.3) Stretch s the respose tme wth the cosderato of the request servce tme. The dea s that a log job should wat for a log tme. To mmze the absolute

respose tme for a log job s ufar for short jobs. However, the relatve respose tme,.e., stretch, s expected to be as small as possble. Correspodg to each dvdual measure, there s a overall measure of the schedulg performace. Bascally, the overall measure s ether the average or the maxmum of all the dvdual measures a system. May schedulg algorthms use average measure as the crtera to compare wth other algorthms. Ad the average measure s ot smply the arthmetc average. It s the expected measure, whch takes to accout popularty or access probablty of each data tem. 2 2.3 Computato of Access Tme I a push-based system, the access tme ca be used as the measuremet of schedulg performace. Oe of the overall measures s called Expected Access Tme, T exp-acc, defed as T exp-acc = p Tacc, (2.4) = Where T acc, s the average access tme for tem. Assume the requests for a tem are govered by Posso process. If staces are equally spaced, the T acc, = s / 2. If staces are ot equally spaced, the average access tme ca be computed as the followg example (Fgure 2.) shows.

3 Fgure 2.. Computato of Access Tme. If there are 3 tems (A, B, ad C) to broadcast, the broadcast tme s ut for each tem, ad the schedule s A-A-B-C repeatedly, the the probablty that a request for tem A falls to the area s ¼, ad the probablty area 2 s ¾. So T acc, A = ¼ ( ½ x ) + ¾ ( ½ x 3) = 5/4 =.25 Applyg the same method, we get T acc, B = T acc, C = 2. Therefore, T exp-acc = p Tacc, =.25p A + 2p B + 2p C. = May schedulg algorthms are desged to mmze T exp-acc. Oe of them, called Packet Far Schedulg, wll be troduced chapter 3. The same approach ca be also used to get the overall measure, expected respose tme (T exp-res ), for pull-based system. 2.4 Summary I ths chapter, we troduced several deftos ad symbols, to be used the thess. We also troduced some performace metrcs. Broadcast schedulg attempts to maxmze or mmze oe of the metrcs.

4 CHAPTER 3 SELECTIVE BROADCAST SCHEDULING ALGORITHMS As troduced chapter, broadcast schedulg algorthms are dvded to two groups, push-based algorthms ad pull-based algorthms. Amog push-based algorthms, Broadcast Dsks ad Packet Far Schedulg perform very well ad are more ofte cted the lterature. Therefore, we summarze them ths chapter. Because the expected access tme from Packet Far Schedulg s very close to the optmal value, t wll be used as the base algorthm for comparso wth our proposed algorthms ths thess. Pull-based algorthms, o the other had, are dvded to o-preemptve ad preemptve schedulg. We wll troduce mportat algorthms from these two groups. 3. Algorthms for Push-based System Ths secto revews the two wdely used approaches, amely broadcast dsks ad packet far schedulg. 3.. Broadcast Dsks [] I a push-based broadcast system, the server repeatedly broadcasts data tems, whch s smlar to the dsks the hard drver. The broadcast chael s thought as a dsk from whch clets ca capture data wheever t goes by. I the system, there are may such dsks havg dfferet szes ad rotatg at dfferet speeds. Data tems are assged to dfferet dsks, ad the multple dsks are multplexed o the broadcast chael. Broadcast Dsk Schedulg ams to mmze the expected access tme. Items stored o faster dsks are broadcast more ofte tha tems o slower dsks. Ths algorthm makes schedule based o the popularty of data tems. By assgg more

popular tems to faster dsks, we may reduce the access tme for these tems so as to reduce the overall expected access tme for the system. The way to arrage data tems o the dsks ca be llustrated by the followg example. Suppose the server has three data tems to broadcast. Let us cosder three dfferet schedules as show o fgure 3.. Case (a) s called Flat schedule, case (b) s Skewed schedule, ad case (c) s Mult-dsk schedule. Wth the flat schedule, the access tme for ay tem o the broadcast s same regardless of ther popularty to the clets. For the skewed schedule, subsequet broadcast staces of a tem are clustered together. Whle the mult-dsk schedule has the broadcast staces equally spaced. 5 Fgure 3.. Arragemet of Data Items (a) Flat (b) Skewed (c) Multdsk. Table 3.. Expected Access Tme of Dfferet Schedules Access Probablty Expected Access Tme (each tem ut tme) A B C Flat (a) Skewed (b) Mult-dsk (c) 0.333 0.333 0.333.50.75.67 0.50 0.25 0.25.50.63.50 0.75 0.25 0.25.50.44.25 0.90 0.05 0.05.50.33.0.0 0.0 0.0.50.25.00

Items A, B, ad C may have dfferet access probablty ad we ca compute the Expected Access Tme for each case. Table 3. lsts some results for fve access probablty arragemets []. From ths example, the followg coclusos ca be draw o how to make schedules for push-based systems: The umber of broadcast staces of a tem amog the total umber of staces should be proportoal to the tem s access probablty. The popular data tems eed to be trasmtted more tha the less popular tems. Istaces of a tem a broadcast perod should be equally dstrbuted. Assume all tems have bee broke to pages. Broadcast Dsk Schedulg frst orders the pages from the most popular to less popular. The they are parttoed to multple groups. Each group s referred to as a dsk. Relatve frequecy of broadcast of each dsk s computed. Each dsk wll be further splt to chuks. All of these chuks are multplexed o a broadcast chael based o the relatve frequecy of the broadcast dsk to whch the chuks belog. 6 3..2 Packet Far Schedulg ([9], [4]) A Packet Far Schedulg algorthm s used for push-based systems to reduce the expected access tme. Ths algorthm has better performace tha others. We wll use t as the base push-based algorthm the evaluato of our proposals. For ths reaso, t s troduced detal. Data tems may have varous legths. The umber of tems s ever chaged. After makg a schedule, data tems are trasmtted scheduled order. The algorthm makes a schedule based o the popularty of each data tem. Popular tems are trasmtted more ofte tha the less popular oes.

Packet far queueg algorthms determe whch packet from the may put queues should be trasmtted ext o the output chael, typcally attemptg to satsfy two codtos: For a specfed value φ Q, put queue Q should get at least a fracto φ Q of the Q output badwdth such that φ Q =. Badwdth allocated to a partcular put queue should be evely dstrbuted, rather tha bursty. For each tem, the algorthm matas a varable B, whch s the earlest tme whe ext stace of tem should be trasmtted. Through mathematcal aalyss, the mmum expected access tme s obtaed whe the space betwee two cotuous staces of a data tem s gve by: 7 s = j= pjlj l p (3.) From ths equato, we get l s = j= p l p l j j (3.2) Let φ be the rght-had sde of equato (3.2). The l s = φ, ad φ = =. Thus, the two codtos for obtag a optmal broadcast schedule are: l s = φ for each tem, whch s the fracto of the broadcast chael badwdth allocated to tem. All staces of each tem should be spaced equally apart wth space s.

Let S dcate the set of tems that are ready for ext trasmsso. The schedulg algorthm s executed followg steps [9]: Step 0: Set tme T=0. Set B =0 for each tem. Compute s for each tem. Step : Let S={ B T, }. Step 2: Select tem j that B j +s j s the mmum amog all tems S. Step 3: Broadcast tem j at tme T ad set B j =B j +s j. Step 4: Set T=T+l j ad go to step. 8 3.2 Algorthms for Pull-based System There are bascally two groups of algorthms for pull-based systems, opreemptve ad preemptve. For o-preemptve algorthms, a request must be fshed before broadcastg data for aother request. For preemptve algorthms, the data for a request s broke to may pages. After a page s set, the algorthm s appled to check f to select aother request. Some proposed o-preemptve algorthms are [4]: Frst-Come Frst-Serve (FCFS): Data tems are broadcast the order of ther requests. Logest Wat Frst (LWF): the wat tme s ot just for oe request. It s the sum of watg tme of all requests that wat for the data tem. The tem that has the largest total wat tme s pcked up for broadcast. Shortest Servce Tme Frst (SSTF): amog all the pedg requests, the data tem that has the shortest servce tme s broadcast ext. Logest Total Stretch Frst (LTSF): smlar to LWF, the total stretch s the sum of stretch of all requests that wat for the tem. The tem of the logest stretch s selected for broadcastg.

9 Some proposed preemptve algorthms clude [4]: Preemptve Logest Wat Frst (PLWF): ths s LWF algorthm but appled after trasmttg a page. Shortest Remag Servce Tme (SRST): ths s the preemptve verso of the SSTF algorthm. SSTF s appled to select ext request after broadcastg a page. Amog all of these algorthms, FCFS s the smplest. Ths algorthm s desged for pot-to-pot system to mmze the maxmum respose tme. For broadcast systems, t has extremely poor performace. However, because t s very smple to mplemet ad, due to some restrctos, the watg queue for FCFS ca be set o loger tha oe o average our case ad all other algorthms have the same performace uder ths codto, we stll use ths algorthm for clets to pull data. LWF, PLWF, SSTF, ad SRST have better performace tha FCFS for broadcast systems. I [4], t has bee show that LWF ad PLWF have average respose tme hgher tha SSFT ad SRST have. However, LWF, PLWF, ad SSTF have almost the same average stretch. For ether case, SRST performs best geeral. 3.3 Summary I ths chapter, some exstg algorthms are troduced for both push-based ad pull-based schedulg. They have bee cted wdely ad have very good performace. Amog these algorthms, Packet Far Schedulg for push-based systems ad FCFS for pull-based systems are preseted detal. These two algorthms wll be used as the base algorthms the evaluato of our proposals.

20 CHAPTER 4 A SCHEDULING ALGORITHM BASED ON SCHEDULING INDEX I geeral, the algorthms troduced chapter 3 were used to mmze ether access tme for push-based systems or respose tme for pull-based systems. To obta the mmum access tme for push-based systems, the schedule s made based o access probablty such that the popular data tems are broadcast more tha the less popular tems. However, practce, the mmum access tme may ot be the oly goal that a schedulg pursues. Some accesses may have hgher prortes, but lower popularty. So f the schedulg algorthm cosders oly popularty, may mportat or urget accesses ca ot be fully satsfed. For ths reaso, the schedulg performace metrc eeds to be revsed. If both access probablty ad access prorty are cosdered, the metrc ca be the expected prortzed access tme as troduced below. I our opo, a good schedulg algorthm should balace may cosderatos. Based o ths dea, we propose to use Schedulg Idex stead of just access probablty to make a schedule. Schedulg dex s a value whch s computed from access probablty, access prorty, ad other mportat parameters. 4. Expected Prortzed Access Tme Each data tem or request s assocated wth a prorty. The lowest prorty s defed to be. The ext prorty s 2, ad so o. For a lmted prorty system, the system may defe the hghest prorty to be some teger, whch s dcated by MAX_PR. We troduce the cocept of Prortzed Access Tme, P T acc. For a request of prorty, t s stll the actual access tme T acc. However, f a access wth prorty q >

has the same access tme T acc, t wll be cosdered that ts access tme s loger tha the same value of T acc for lower prorty access. For ths reaso, the prortzed access tme ca be defed to be: 2 T P acc = T q (4.) acc I other words the accesses wth hgher prortes expect less prortzed access tme. At the system level, the overall measure s Expected Prortzed Access Tme, P T exp acc, whch s the prortzed access tme wth the cosderato of popularty. Hece T P P exp acc = p Tacc, ) = ( (4.2) where p s the access probablty of tem, ad T, s the average prortzed access P acc tme for tem. The same method ca be used to get Prortzed Respose Tme, T P res P T res, as = T q (4.3) res Ths s the respose tme wth the cosderato of the request prorty. The hgher prorty request expects less prortzed respose tme. For the same example that we used chapter 3, the computato of expected prortzed access tme s llustrated here. Suppose A has the hghest prorty, say 3; ad B ad C have prorty 2 ad, respectvely. For skewed case, access probablty s 0.5, 0.25, ad 0.25 for A, B, ad C. Therefore, P T exp acc =.25x0.5x3 + 2x0.25x2 + 2x0.25x = 3.375 Applyg the same procedure, the results for dfferet cases are show table 4.. From ths table, the schedulg prcples chapter 3 ca stll be draw here. Table 4.. Expected Prortzed Access Tme

Access Probablty Expected Prortzed Access Tme (each tem ut tme) A q A =3 B q B =2 C q C = Flat (a) Skewed (b) Mult-dsk (c) 0.333 0.333 0.333 3 3.25 3 0.50 0.25 0.25 3.38 3.375 3 0.75 0.25 0.25 3.938 3.56 3 0.90 0.05 0.05 4.275 3.675 3.0 0.0 0.0 4.50 3.75 3 22 4.2 Optmal Expected Prortzed Access Tme To derve the optmal expected prortzed access tme, assume that the clet accesses are govered by Posso process. We kow that to obta the optmal expected access tme, all staces must be equally spaced. So the average access tme for tem s: By defto, the prortzed average access tme for tem s: P acc ad the prortzed expected access tme s: P T exp acc = = T acc, = s / 2 (4.4) T, = T acc, q = (s q ) / 2 (4.5) P ( p Tacc, ) = ( p s q) (4.6) 2 = Let r = l, whch s the fracto of badwdth allocated to tem f staces are s equally spaced. Whe we add up the fractos of all tems, we get = r =. Replacg s wth s = l, we have: r

23 P T acc exp = ) ( 2 = q p r l (4.7) The legth l, access probablty p, ad request prorty q of a tem are all uchaged for a gve system. We ca oly adjust the fracto r to get optmal P T acc exp. For optmal value of r, we must have P acc r T exp = 0 for all. For tem, we have 0 = exp r T P acc = ) ( 2 = q p r l r = ) l ( 2 2 = = = + + r q p r p q l r q p l r = + = 2 2 l 2 r q p r q p l. So 2 r q p l = 2 l = r q p. Smlarly, 2 2 2 2 2 r q p l = 2 l = r q p. We the have 2 r q p l = 2 2 2 2 2 r q p l, whch yelds 2 r r = 2 2 2 q p l q p l. I geeral, j r r = j j j q p l q p l. So the optmal r must be learly proportoal to q p l. Because

24 = r =, we set r = j = l pq l jpjqj. Replacg r equato 4.7, the optmal prortzed expected access tme s gve by T (4.8) P 2 exp acc, opt = ( l p q) 2 = Ths equato shows that the optmal prortzed expected access tme ca oly be obtaed whe the schedulg s based o both access probablty ad access prorty. Exstg algorthms must be modfed to cosder both of them, stead of just access probablty. If there are other factors to cosder whle makg schedule, algorthms must be modfed to corporate the effect of those factors. Ths led us to the dea of makg schedule based o a geerc dex, whch tegrates all the factors that we are terested for schedulg purpose. 4.3 Schedulg Idex As dscussed secto 4.2, hghly popular tems are broadcast ofte ad tems wth hgher prorty are broadcast more ofte. We wll try to make a schedule so that the prortzed expected access tme s mmal. However, popularty p ad prorty q may be oly two of may factors that ca decde a tem s broadcast frequecy. We ca geeralze may such factors by usg a dex, called Schedulg Idex, ad represeted by D. If we oly cosder popularty to make a schedule, the D = p Broadcast schedule ca be made based o D. Istaces of a tem accout oly a fracto of broadcast cycle cosstg of staces of all broadcast tems. The tems wth hgher values of schedulg dex D have more staces a cycle. So D s

proportoed to the broadcast fracto of a tem the whole cycle, ad collectvely all D must be. The broadcast crtera by usg schedulg dex wll be:. Schedulg dex D dcates the fracto of staces of a tem the whole broadcast cycle. 2. = D =. A exstg algorthm based o access probablty ca be upgraded to use schedulg dex to make schedule wthout ay other chages. We ow cosder how to compute the schedulg dex. If the algorthm cosders prorty as well as access probablty whe makg a schedule, we may buld the schedulg dex as: 25 D = j = p q ( pj qj) (4.9) For ths case, the schedulg dex ca be called prortzed access probablty. 4.4 Evaluato of Usg Schedulg Idex We use a program to smulate the broadcast schedule process. Assume that the access probablty ad access prorty of each tem follow Zpf s dstrbuto. Zpf s dstrbuto has bee show to closely approxmate the access or request frequeces asymmetrc systems [8]. May other researchers have used Zpf s dstrbuto ther asymmetrc system research ([], [2], [9], [4], ad [5]). We also use Zpf s dstrbuto to evaluate coclusos ths thess, too. However, all coclusos draw the thess are ot based o the codto of Zpf s dstrbuto. (If aother dstrbuto s appled, smlar evaluato results are expected.) Let us defe θ p to be the skew coeffcet for

access probablty ad θ q to be the skew coeffcet for access prorty. For example, the access probablty ca be computed as: 26 p = ( / ) ( / j) j= θp θp (4.0) Dfferet values of access skew coeffcet yeld dfferet Zpf s dstrbutos. Whe θ = 0, the Zpf s dstrbuto reduces to uform dstrbuto. The request prorty ca be computed smlarly. Access probablty ad access prorty may have the same patter of dstrbuto, that s, the tem has the hghest probablty ad prorty, whle the last tem has the lowest probablty ad prorty. Ther dstrbuto patter may also have tems dfferece. For example, the tem may stll have the hghest access probablty, but the hghest prorty s o the tem (+ ). The smulato program uses the prevously troduced Packet Far Schedulg as the basc algorthm. The program makes schedule based o prortzed probablty ad computes prortzed expected access tme. We may compare the smulated results wth the optmal prortzed expected access tme to fd out how well the prortzed probablty (Schedulg Idex) s used makg schedule. Frst of all, we test the smulato program to make sure t follows the orgal algorthm. I ths case we do ot cosder prorty. So prorty ca be set to for all tems. The umber of scheduled tems s 500. The program makes schedule for the frst 50,000 staces. The program computes expected access tme for dfferet dstrbutos of access probablty. Fgure 4. shows some results. The correspodg θ p are 0.25, 0.5, 0.75, ad.

27 Program Test 250 230 20 Acc. Tme 90 70 50 30 0.25 0.5 0.75 Theta of Access Probablty Exp. Acc. Opt. Acc Fgure 4.. Test Schedulg Smulator. From ths chart, we see that the results from the smulato match theoretcal optmal access tme very well. The percetage dfferece s about 0.6% betwee the expected access tme ad the optmal access tme. So the smulato ca be used to evaluate our algorthm. Now we compute the algorthm performace whe prortzed access probablty (Schedulg Idex) s used for makg schedule. Fgures 4.2 ad 4.3 are the charts to show the results for two test cases. The complete results ca be foud tables 4.2 ad 4.3. I our computato, prorty has 5 levels. Prorty s the lowest, ad prorty 5 s the hghest. Prorty dstrbuto ad probablty dstrbuto vary as the charts dcate.

28 330 Schedule Perfomace Delta of dstrbuto = 0 30 290 Prortzed Acc. Tme 270 250 230 20 90 70 50 0.25 0.5 0.75 Theta of Prorty (Theta of Probablty = ) Exp. Acc. Opt. Acc Fgure 4.2. Schedule Performace ( = 0). 300 Schedule Performace Delta of dstrbuto = 0.3 280 260 Prortzed Acc. Tme 240 220 200 80 60 40 0.25 0.5 0.75 Theta of Prorty (Theta of Probablty = ) Exp. Acc. Opt. Acc Fgure 4.3. Schedule Performace ( = 0.3).

We frst compute the schedule performace whe access probablty ad request prorty have the same dstrbuto. The delta of dstrbuto = 0. We test the cases whe the access skew coeffcet θ p s ad 0.25. For each of the two cases, the prorty skew coeffcet θ q vares from 0.25 to at step of 0.25. We the test the schedule performace for cases that = 0.3 ad = 0.5. By testg all of these cases, we try to compute the performace for all dfferet combato of access probablty dstrbuto ad request prorty dstrbuto. From the results, we see that the schedulg based o the Schedulg Idex performs very well compared wth the optmal results. The dfferece betwee the expected prortzed access tme ad the optmal prortzed access tme s less tha 0.6%. 29 Table 4.2. Prortzed Expected Access Tme (θ p = ) Prortzed Expected Access Tme (θ p = ) θ q = θ q =0.75 θ q =0.5 θ q =0.25 Test Optmal Test Optmal Test Optmal Test Optmal =0 5.36 52.27 57.00 57.96 73.6 74.66 320.85 322.80 =0.3 40.62 4.48 42.69 43.57 5.60 52.5 296.93 298.72 =0.5 39.82 40.67 4.43 42.28 48.27 49.3 29.69 293.39 Table 4.3. Prortzed Expected Access Tme (θ p = 0.25) Prortzed Expected Access Tme (θ p = 0.25) θ q = θ q =0.75 θ q =0.5 θ q =0.25 Test Optmal Test Optmal Test Optmal Test Optmal =0 248.82 250.30 25.8 253.3 263.28 264.84 57.34 520.09 =0.3 250.85 252.26 254.90 256.28 272.8 273.45 53.94 534.6 =0.5 250.40 25.83 254.9 255.59 270.29 27.66 529.0 53.8

30 4.5 Summary Based o the above aalyss ad smulato results, we ca say that Schedulg Idex ca be used to make broadcast schedule. If a smple algorthm works well whe access probablty s the oly cosderato to make schedule, the the algorthm wll be a caddate to make schedule whe may tems are used to decde the schedule. The oly dfferece s that, stead of usg access probablty, we use the Schedulg Idex.

3 CHAPTER 5 A NOVEL DYNAMIC SCHEDULING ALGORITHM FOR BROADCASTING Exstg broadcast schedulg algorthms are ether push-based or pull-based. They ca ot be used to obta the optmal performace due to the followg reasos. I purely push-based systems, the server decdes whch data tems to be trasmtted ad also trasmts by some schedule. To be able to satsfy all clet accesses, the server must sed all data tems ts storage. Ths wll cause a problem. If the umber of data the server s very large, each broadcast cycle wll take a log tme. Ad t wll take a log tme for clets to wat for less popular tems. The system expected access tme wll be large. So, t s ot a good dea to broadcast all of the data tems. Also, the push-based broadcast s effcet whe the data to be broadcast has may accesses. If the server has huge umber of data tems, may tems wll have very small access probabltes. It may be effcet to broadcast these tems. Pull-based schedulg ca resolve ths problem by sedg just what clets request. However, a pure pull-based schedulg s effcet ad ca ot be used asymmetrc systems. If some of the less popular tems are set by requests mmedately after broadcastg the curret scheduled tem, the access tme for these tems wll be very small. So the overall expected access tme for the system wll drop. As more ad more less popular tems are set by requests, the overall expected access tme wll become smaller ad smaller. However, whe too may such tems are set, the system teds to be

pull-based ad the expected access tme wll become large aga. There must be a pot where the expected access tme s the mmum. Based o ths aalyss, t s better to combe pull-based schedulg wth pushbased schedulg. We may use push-based schedulg to broadcast hghly popular tems. At the same tme, pull-based schedulg s used to sed less popular tems whe clets have such requests. Ad they are set mmedately after the server fshes broadcastg the curret scheduled tem. The cut-off pot to separate the tems eeds to be chose properly. We defe the set T to clude all tems, T = { }. We also defe the set A = { K, T}, ad R = { > K, T}. So A R = T. The tems A are broadcast, ad the tems R are set by requests. The K s called Cut-Off pot, whch separates A ad R. To make t smple, we assume that all tems have ut legth. 32 5. Crtera to Set the Cut-Off Pot We kow the broadcast schedule s based o access probablty p. Because of K cut-off pot, = p. For schedulg purpose, the access probablty of tem A eeds some modfcato. The modfed access probablty ^ p = K p j= p j (5.) The value of K wll have sgfcat effect o the total expected access tme. The probablty that tems R are requested s K p. If we defe x as the umber of = ew requests for R ut tme, the

K x = N p (5.2) = If K s too small, the tems R are requested wth very hgh probablty. So t s possble that x >. That meas whle the server s sedg a requested tem, there are more tha oe ew requests geerated. After sedg curret tem, the server eeds to sed aother tem R mmedately. So there wll be o tme to broadcast scheduled tems A. The watg tme for A s very hgh, ad the total expected access tme wll be hgh. Whe K becomes smaller ad smaller, there wll be more ad more ew requests geerated ut tme. If there are more tha oe requested tem pedg, these tems ca be set FCFS order. A FCFS queue s eeded to store all u-servced requests. Because the umber of ew requests for R ut tme s more tha, the FCFS queue wll buld up loger ad loger. The value of K that satsfes K N p = (5.3) = s called the BUILD-UP pot. Because f K N p >, = the FCFS queue begs to buld up. From equato (5.3), we may compute the buld-up pot by computg K that satsfes 33 K = p = N (5.4)

34 If p follows Zpf s dstrbuto, p = (/ ) j= θ (/ j) θ θ (/ ) =, where SUM SUM = j= (/ j) θ, the K (/ ) θ = SUM = N (5.5) Whe K = p < N, due to the buldg-up of the FCFS queue, the total access tme wll suddely crease. To make t practcal, the relato K = p > N (5.6) must be satsfed. So there wll be o buld-up o FCFS queue. Whe K moves away from the buld-up pot ad becomes larger ad larger, the probablty that tems R are requested becomes smaller ad smaller. As the expected access tme for A drops, the total expected access tme also drops. However, as K creases, the set A becomes larger ad larger. Access probabltes for tems set A wll have a large rage. For those tems that are close to K, because they have lower access probabltes compared wth other tems A, they are ot broadcast frequetly. If a clet just msses a broadcast for such a tem, t eeds to wat a very log tme for ts ext broadcast stace. The result s that the total access tme becomes larger. Thus, there exsts a optmal cut-off pot. If we separate A ad R at that pot, we wll get the mmum expected access tme.

35 To be able to compute the optmal cut-off pot, we eed to kow, o a average, after how may uts of tme to sed the requested tems, there wll be a empty slot to broadcast a scheduled tem. Let us defe the space betwee two cosecutve broadcast slots to be y. If x =, there s always a requested tem to sed. Scheduled tems ever have a chace to be broadcast ad y =. If x = 0, whch s the case that all tems are broadcast, the y = 0. If 0 < x <, the, o the average, the space wll be y = (5.7) x Let us defe U = K p = (5.8) V = K = p (5.9) ad replace x equato (5.7) wth equato (5.2). Now we get the space betwee two cosecutve broadcast slots as N( U ) y = (5.0) N( U ) whch meas that betwee two broadcast slots, there wll be y slots to be used to sed tems R as fgure 5. shows,

36 Fgure 5.. Sedg Slots ad Broadcast Slots. The optmal stace space for tem A s gve by ^ ^ K j j p p s = = (5.) From equatos (5.), (5.8), ad (5.9), we have U V U p K j j K j j p = = = = ^ (5.2) So p V p U U V U V s p = = = ^ (5.3) However, because broadcast s terrupted by sedg ew requested tems, broadcast s ot cotuous. Betwee s broadcast slots, there are ) ( ) ( U N U N s (5.4) sedg slots. So the accrual stace space for tem A s gve by p U N V U N s U N U N s s s ) ( ) ( ) ( ) ( ^ = = + = (5.5) The average access tme for tem A ca ow be computed as

^ s T acc, B = (5.6) 2 Because the ew requested tems are set mmedately, the average access tme for tem R s oly ½. T acc, R = (5.7) 2 The total expected access tme s the 37 T exp acc ^ K s = p + p = 2 = K + 2 K V = 2 N( U ) = V 2 N( U ) = p = K + + ( = = 2 V = + U. 2 N( U ) K p p + K p p ) (5.8) Ths formula s oly good for computg expected access tme after the Buld-Up pot. Before ths pot, because of the buldg up of the FCFS queue, there wll be o tme to broadcast tem A. So the access tme for these tems s ad for the same reaso T exp =. acc Ayway, we ca the compute T exp acc by cuttg at the Buld-Up pot, whch ca be computed by equato (5.4) or (5.5), to the last tem. The cuttg pot at whch we get the mmum T exp acc wll be called the Optmal Cut-Off Pot. 5.2 Decrease of Expected Access Tme From equato (5.6), we kow that the expected access tme depeds o the umber (N) of accesses ad requests ut tme ad the cut-off pot, K. Whe N s

smaller, the optmal expected access tme wll become smaller. Whe K s too small or too large, the expected access tme wll become larger. Oly whe K s properly chose, ca we get the optmal expected access tme. N depeds o two factors: server broadcast speed, τ secod/tem, ad access desty d, whch ca be defed as the umber of total accesses ad requests oe secod. Hece N = dτ So f the broadcast speed creases (τ drops), we may get less expected access tme. Or, f access desty decreases (d drops), we wll get less expected access tme, too. Comparg wth the stuato whe all tems are broadcast, the expected access tme at optmal cut-off pot wll decrease by the amout of: 38 2 = p 2 2 V N ( U ) + U. 0.0004 Access Probablty (000 tems, Theta =.2) 0.00035 Access Probablty 0.0003 0.00025 0.0002 0.0005 0.000 If ut tme tau = 0., ad total accesses N = 5 tau, the the schedule cut-off wll be at tem 200. 0.00005 0 200 5 29 43 57 7 85 99 3 27 4 55 69 83 97 2 225 239 253 267 28 295 Item (oly the frst 300 tems are dsplayed) Fgure 5.2. Schedulg Cut-off Pot.

For example, suppose the server has =,000 tems, access probablty follows Zpf s dstrbuto wth θ =.2, ad N = 5 (f τ = 0. secod/tem, the the access desty wll be d = 50 tems per secod). The optmal cut-off pot wll be at K = 200 ad the optmal expected access tme by cuttg off wll be 9.24. If we broadcast all 000 tems, the optmal expected access tme becomes 63.7. Ths saves 72.47 tme ut, whch s 44.3% reducto expected access tme. 39 5.3 Proposed Dyamc Schedulg Algorthm The server seds data ad the correspodg dex o dfferet chaels. Wheever a clet eeds some data tem from server, t frst lstes to the dex chael to check whether the tem s curretly broadcast by the server. If the data tem that the clet eeds s the dex, the the clet just wats utl the data s broadcast. If the tem s ot the dex, the the clet asks the server to sed the tem for t. The clet provdes a prorty level for the request at the same tme. I ths way, the dex ca be used for two purposes. To save eergy for clet devce [9]. To decde f the clet eeds to make a ew request to the server. O the server sde, we suppose that the server kows access probablty (for Zpf s dstrbuto, θ s kow) ad access desty (whch ca be estmated by the umber of requests ut tme). The server eeds to compute the buld-up pot from equato (5.4), ad compute the optmal cut-off pot K from equato (5.8). The t wll broadcast dex to K o the dex chael perodcally. At the same tme, the schedulg algorthm s executed to make the broadcast schedule ad the server broadcasts tems to K based o the schedule. Ay push-based schedulg algorthm,

such as Packet Far Schedulg, ca be used for ths purpose. Wheever the server receves a request from a clet, t wll stop broadcastg the ext scheduled tem, to sed the requested tem. Upo completo of the sed, t wll resume broadcastg. 40 Dyamc Schedulg Algorthm. Compute Buld-Up Pot from equato (5.4) 2. For (K=Buld-Up Pot; K total umber of tems; K K+) Compute expected access tme from equato (5.8) If expected access tme creases, the stop 3. K wll be the optmal cut-off pot 4. Broadcast dex to K o dex chael perodcally 5. If there s o clet request Compute ext broadcasted tem by Push-Based Schedulg Broadcast ext tem Else Sed requested tem 6. Retur to step 5 5.4 Performace Evaluato I ths secto, the evaluato results of the schedulg performace o dfferet cut-off pots are gve. To be able to perform evaluato, a smulato program s used to smulate the actual accesses ad requests. I the smulato, a total of 00,000 staces of accesses ad requests are geerated. The staces of each tem are equally dstrbuted. Ad staces of dfferet tems follow Zpf s dstrbuto. These staces are actually the results of the schedulg algorthm. We kow that the schedulg algorthm outputs a lst of tem staces that the broadcast schedule should follow, ad staces ths lst have the same dstrbuto as the put access probablty. So by cotrollg the put access probablty to the schedulg algorthm, dfferet dstrbutos for staces of access ad request ca be obtaed.