' $ Throughput-Comp etitiv e Admission Con trol for Con tin - PowerPoint PPT Presentation

' $ Throughput-Comp etitiv e Admission Con trol for Con tin uous Media Databases Minos N. Garofalakis (Univ. of Wisc onsin { Madison) Y annis E. Ioannidis (Univ. of Wisc onsin { Madison) � Ban u Ozden (Bel l L ab or atories) Avi Silb ersc hatz (Bel l L ab or atories) & % Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 1

' $ Outline � In tro duction and Motiv ation � Problem F orm ulation � Con tributions 1. Algorithms and Theoretical Results 2. Exp erimen tal V alidation � Conclusions & % Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 2

' $ In tro duction and Motiv ation � : Real-time resource requiremen ts for deliv ery Continuous Me dia MPEG-1 clip C i 1.5 Mbps stream( C ) i duration � E�ectiv e resource managemen t for on-demand supp ort & % Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 3

' $ In tro duction and Motiv ation (con t.) � : pro vide service guaran tees for accepted streams A dmission Contr ol B A N accept D Admission W Control I D reject T H T I M E � decision making { non-preemptiv e! On-line & % � Crucial for high serv er utilization Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 4

' $ Problem F orm ulation � Study the implications of the on-line nature of admission con trol � Admission Con trol Ob jectiv e: Maximize total serv er throughput o v er a sequence of requests � Metric: , i.e., b ound on w orst-case b eha vior o v er an y Comp etitive r atio p ossible sequence { v ery robust! & % Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 5

' $ Problem F orm ulation (con t.) accept r i Admission B Control reject l i time t i l � = max f l g , = min f l g , � = l l max max i i min i i l min r � = max f r g , = r � max max i i B P � r l i i � Comp etitiv e ratio of algorithm A = sup O P T seq uences P � r l i i A & % � W an t small (i.e., close to 1) ratios Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 6

' $ Our Con tributions � � � � Comp etitiv e ratio of con v en tional, \greedy" adm. con trol is � 1 � � � � log � � Lo w er b ounds of � on the comp etitiv e ratio of an y deterministic 1 � � randomized strategy or � No v el strategies, based on with ratios of Bandwidth Pr ep artitioning (log �) (i.e., near-optimal) for large O B � Strategies can easily b e adapted to accommo date clip p opularities to impro v e a v erage case � Exp erimen tal v alidation & % Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 7

' $ Con v en tional Wisdom: \Greedy" Admission Con trol � Work-Conserving str ate gy ( W C ): admit incoming request if 9 su�cien t bandwidth, reject otherwise B time t 1 t 2 1+� & % Theorem: W C is -comp etitiv e 1 � � Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 8

' $ Lo w er Bounds on Comp etitiv eness Theorem: An y deterministic randomized on-line admission con trol or � � log � strategy has a comp etitiv e ratio of � 1 � � � Exp onen tial gap w.r.t. W C | lots of space for impro v emen t! & % Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 9

' $ The Basic Idea: Simple Prepartitioning � Idea: isolate requests with large length di�erences so that short requests cannot monop olize the serv er Simple Bandwidth Prepartitioning ( S B P ): B 1. Divide bandwidth in to d log � e partitions, of size eac h B d log � e i � 1 i th 2. Sc hedule requests with lengths in [2 � 2 � ) in the l ; l i min min partition using W C ( Note that � � 2 within e ach p artition ) & % Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 10

' $ Example S B P B log ∆ B log ∆ t 1 B log ∆ B log ∆ t 2 & % Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 11

' $ Reducing F ragmen tation: Do wn-shift Prepartitioning � Idea: again, prohibit short requests from monop olizing the serv er but also allo w long requests to \steal" from lo w er partitions Do wn-shift Bandwidth Prepartitioning ( D B P ): B 1. Divide bandwidth in to d log � e partitions j B j = B i d log � e i � 1 i 2. Sc hedule requests with lengths in [2 � 2 � ) in [ [ l ; l B : : : B 1 min min i using W C � Ma jor b ene�t: reduce e�ects of bandwidth fragmen tation due to prepartitioning & % Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 12

' $ Example D B P B log ∆ B log ∆ t 1 t 2 B log ∆ B log ∆ t 2 & % Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 13

' $ Comp etitiv eness of Bandwidth Prepartitioning Theorem: � � log � 1 r (a) Assuming = , S B P and D B P are - � < O max B d log � e 1 � � � log � comp etitiv e 1 (b) If , then S B P and D B P are (log �) - comp etitiv e � < O 2 �d log � e � Realistic assumptions. E.g., if = 8 Mbps, = 120 � , then r l l max max min r � d log � e = 56 Mbps ( << B ) max � F or reasonably large , S B P and D B P are B ne ar-optimal & % Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 14

' $ Better Av erage Case: P opularit y-based Prepartitioning � Idea: emplo y clip to de�ne partition sizes (simple S B P or p opularities D B P ma y underutilize the serv er) � = cum ulativ e p opularit y of clips with length p l j j i � 1 i � = f ( p ) j 2 [2 � 2 � ) g P L ; l l l ; l i j j j min min P opularit y-based Bandwidth Prepartitioning ( P B P ): th � Same as D B P , but de�ne the size of the partition as: i f ( P L ) i j B j = � B i P f ( P L ) i i for some function f & % Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 15

' $ Exp erimen tal Results � Goal: Prepartitioning w as based on comp etitiv e (w orst-case) analysis | what ab out a v erage-case? P � W C vs. P B P ( results sho wn with ( P ) = � ) f L p l i j j P L i � A rrival Pr o c ess : P oisson , Burst y , P oisson + Short Bursts { capture short-term o v erloads (e.g., 6 o'clo c k news) � : Zip�an Popularities : P ositiv e , Negativ e , Random L ength-Popularity Corr elation � : fraction of serv er capacit y utilized Metric P sc heduled � l r i i B � sim ulation time & % Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 16

' $ Exp erimen tal Results (con t.) � P oisson Arriv als � Burst y Arriv als, Random Correlation Poisson Arrivals, z=0.6, Random Correlation Bursty Arrivals, Batch Size=40, z=0.6, Random Correlation 1 1 PBP PBP WC WC Fraction of Server Capacity Used Fraction of Server Capacity Used 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0 0.5 1 1.5 2 2.5 3 300 250 200 150 100 50 & % Request Arrival Rate Burst Separation Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 17

' $ Exp erimen tal Results (con t.) � Burst y Arriv als, Negativ e Correlation � P oisson+Short Bursts Bursty Arrivals, Batch Size=40, z=0.6, Negative Correlation Poisson + Short Burst Arrivals, lambda(long)=0.7 1 1 PBP PBP WC WC Fraction of Server Capacity Used Fraction of Server Capacity Used 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 300 250 200 150 100 50 0 0.01 0.02 0.03 0.04 0.05 0.06 & % Burst Separation lambda(short) Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 18

' $ Conclusions and F uture W ork � Comp etitiv e analysis for admission con trol in Con tin uous Media DBs: l 1. Con v en tional W C has comp etitiv e ratio linear in � = max l min 2. Lo w er b ounds of �(log �) for an y deterministic or randomized strategy 3. Prepartitioning strategies { near-optimal for su�cien tly large bandwidth 4. Exploit kno wledge of p opularities for go o d a v erage-case p erformance 5. Exp erimen tal v alidation � Incorp orate other resources (e.g., memory) � On-line load balancing in distributed con tin uous media serv ers & % Throughput-Comp etitiv e Admission Con trol for Con tin uous Media DBs 19