“A cost-based admission control algorithm for digital library multimedia systems storing heterogeneous objects” – I.R. Chen & N. Verma – The Computer Journal – Vol. 46, No. 6, Oct. 2003, pp Andy Connors

Abstract Multimedia Systems Mixed workloads – Video, Images & Text Cost-based admission control algorithm Based on rewards & penalties Resource reservation instead of serving requests until all resources exhausted Reservation based on maximizing total reward Exploit left over resources Simulate algorithm and compare to other schemes

Multimedia System

Challenge Service mixed workloads Real-time video/audio request – resource demanding and varying data rates Discrete media – images and text Need algorithm to “squeeze” in image & text requests without affecting QoS of video requests However, 70% of data types on Web are image & text

Previous algorithms Video taking higher priority over image/text data not justified as 70% of requests are image/text not video Shenoy & Vin – two-level disk scheduling framework Level 1: class-independent scheduler – assign bandwidth to application classes – used to dynamically allocate bandwidth to adapt to workload changes – no details on adaption scheme Level 2: class-specific scheduler – order requests into a common queue for access – minimizes seek time and rotational latency overhead – satisfies QoS requirements of each class – discussed in detail To & Hamidzadeh – Continious Media-to-Discrete Media redirection ratio Redirect bandwidth from CM to DM Allocate more buffer space to CM – reduces admissible CM requests Optimize disk reads Use leftover bandwidth for DM requests How much bandwidth to move from CM to DM requests?

Basic Idea Dynamically partition resources based on run- time workload changes Maximize value metric Ensuring that response time requirements met Image/text have “own” resources rather than use “leftovers” Assign value/penalty pair to each request Value: reward if serviced successfully Penalty: loss if service rejected due to lack of resources High value → video higher priority over image/text

Multimedia Server Model Cycle based disk scheduling: All requests serviced in T SR – service round duration Image/text either serviced after video/audio or interleaved – use interleaving to minimize disk seek time and latency Video/audio requests As many data blocks as covered by T SR Double buffered – disk buffer & network buffer Image/text requests As many blocks to cover requests object SCAN algorithm: Requests ordered and heads traverse in one direction only Minimizes seek time

Refresher - Scan Algorithm

Resource Partitioning Text/images serviced in batch Depart at end of service cycle Two FIFO queues, one for text, other for images Statistics of each multimedia object Distribution of all images and text objects Histogram of distribution of size needed to satisfy playback Partition T SR into three parts – video, image and text Based on cost & workload Estimate maximum amount of resources allocated to each type Use left-over time to service more image/text requests

Performance Metric Maximize reward without compromising QoS (bandwidth & response time) Reward rate v V N V + v I N I + v T N T - q V M V + q I M I + q T M T N {V,I,T} = requests completed per unit time M {V,I,T} = requests rejects per unit time v {V,I,T} = average reward values q {V,I,T} = average penalty values

Algorithm Use models derived from queing theory Build lookup table for run-time bandwidth allocation Estimation of reward rate under given workload condition Best bandwidth allocation to maximize reward rate f {V,I,T} = ratio of disk bandwidth for video, image & text requests f V + f I + f T = 1 (when normalized) Service times: f {V,I,T} T SR = disk service time Use statistical admission control to compute number of requests of each type so that probability of disk overload is below a threshold (10 -4 ) (f V, f I, f T ) → (n V, n I, n T ) System behaves like three separate partitions – three queues For image/text requests n {I,T} image/text requests per T SR Total of K {I,T} * n {I,T} image/text requests – K {I,T} = maximum queue size for image/text requests – can use requests in queue to use left-over bandwidth – K {I,T} depends on QoS

Video Request Model M/M/ n V /n V queue each video stream acts as if served by separate server until departs V,  V = arrival/departure rate of video requests

Video Request Model P v (j) = probability that j video out of n V slots occupied 0 ≤ j ≤ n V V,  V = arrival/departure rate of video requests

Video Request Reward With probability P v (j), reward rate = j* v V *  V So total reward gained =  j v V  V P v (j) Rejection rate = V P v (n V ) Lost reward = q V V P v (n V ) Reward rate from video = R V R V = (  j v V  V P v (j) ) - q V V P v (n V )

Image & Text Model For K {I,T} ≥1 - M/M/ 1 [n {I,T} ] / K {I,T}* n {I,T} queue Let K {I,T} = 2

Image & Text Model P I (j) = probability that j video out of n V slots occupied 0 ≤ j ≤ n I I,  I = arrival/departure rate of video requests Let K I = 1

Image & Text Model P I (j) = probability that j video out of n V slots occupied 0 ≤ j ≤ n I I,  I = arrival/departure rate of video requests Let K I = 2

Image/Text Request Reward With probability P I (j) reward rate = j*v I *  I if j < n I n I *v I *  I if j ≥ n I Rejection rate = I P I (K I n I ) Lost reward = q I I P I (K I n I ) Reward rate from video = R I R I = (  jv I  I P I (j) ) + (  n I v I  I P I (j) ) - q I I P I ( K I n I ) j = 1 … n I -1 j = n I … K I n I

Maximizing Reward Given V,  V, I,  I, T,  T,v V,q V,v I,q I,v T,q T Maximize R by searching for optimal (n V, n I, n T ) → (n* V, n* I, n* T ) Subject to condition (normalized to text requests) Here N V, N I, N T are maximum number of requests that can be served of each type (if all bandwidth allocated to each type) To use total disk bandwidth

Search Exhaustive Search all possible solutions Complexity O(N T 2 ) Once found all solutions build lookup table Nearest Neighbor When N T is too large and exhaustive is computationally too expensive Complexity O(N T ) Fix one n V, n I, n T then next etc. Heuristic – largest product of arrival rate and reward selected first

Admission Control Algorithm Use lookup table to dynamically change to a set of (n* V, n* I, n* T ) depending on workload By monitoring input rates Use for admission control Worst case response time for image and text is K {I,T} T SR Use common schedule queue for disk requests If total schedule time < T SR use image/text at head of respective queues to use up remaining time by moving to common queue Probablity that image will be placed on queue f * I / (f * I + f * T ) And for text f * T / (f * I + f * T )

Analysis Numerical analysis of reservation system Parameters: Disk Array 4 disks Average seek time = 11ms Rotational latency of 5.5ms Read/write rate  = 33.3MBps T SR = 1 Block size = 4 sectors (512bytes) = 2Kbytes Images Evenly distributed across [10kB, 500kB] Text Evenly istributed across [1kB, 50kB] Video Star Wars – 7200 groups of pictures = 0.5s playback time 12 frames per group Calculate N V = 53, N I = 37, N T = 57 Simulate V in range [10,100] arrivals/min, V in range [100,2000], I in range [100,2000]

Other schemes Compare with other algorithms: Video First Highest priority to video requests Left-overs used for image/text (n V, n I, n T ) = (N V, 0, 0) Use queue sizes of K {I,T} n* {I,T} Greedy Allocates disk in proportion to product of reward and arrival rate (n V, n I, n T ) = (,, )

Analysis Results

Effect of Arrival Rates Effect of varying image/text arrival rates as video arrival rate increases For lower image/text rates reward rate increases as video rates increase until hit a maximum where we see a decrease For higher image/text rates Steadingly decreases due to rejects

Effect Of Video Departure Rate Using varying video departure rates shows effect on increasing video arrival rate At higher departure rates See an increase in reward rate as arrival rate increases until a threshold where server is heavily loaded and rejects requests At lower Video requests stay in system for longer time and so system admits fewer requests

Effect Of Video Reward Value Using varying video reward values shows effect on increasing video arrival rate At higher reward rates Systems admits more requests – threshold shifts higher

Results – Reward Rate Under light loads Close to predicted lower- bound reward rates At higher loads Higher than calculated – due to effect of using left-over bandwidth which is more pronounced at higher loads In limit Returns back to theoretical as text/image queues are full and consume all server resources Same as video-first at lower loads as system can accommodate most users at these loads At higher loads Out performs both video-first and greedy algorithms

Results – Response Time Under light loads Close to other algorithms At higher loads As explicitly allocate time for image/text request see better response times than video-first – difference between 1s and 5s Greedy favors video/text and so has better response times – but compares favorably

Results – Utilization Does not show greedy algorithm as shows same trends as reservation algorithm For video-first Higher utilization for video requests – lower for image/text For reservation Better utilization for image/text Lower for video

Results – Rejection Rates At higher loads Rejects fewer image/text requests than video-first or greedy Achieved by rejecting more video requests Video-first rejects 0 video requests but a high number of image/text

Conclusions Significant improvement in reward rate compared to video-first and greedy algorithms Without sacrificing performance metrics such as response time & system utilization