“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. 645-659

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

Text

VideoAudio + Images

StreamsImages

`

Disk ArrayData Blocks

Disk Buffer Network Buffer

Streaming Video(Real-time)

Mixed-Workload Multimedia Server

Data Blocks

Different Bandwidth

Requirements

High Low

Data BlockFrom

Stripe Across Disk Array

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 TSR – 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 TSR 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 Algorithm14 30 60 62 83 95 123 145 160

Time

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 TSR 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

vVNV + vINI + vTNT - qVMV + qIMI + qTMT

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 fV + fI + fT = 1 (when normalized) Service times: f{V,I,T}TSR = 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)

(fV, fI, fT) → (nV, nI, nT) System behaves like three separate partitions – three

queues For image/text requests

n{I,T} image/text requests per TSR 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/nV/nV queue each video stream acts as if served by

separate server until departs V, V = arrival/departure rate of video requests

0 1 2 V-1 V

λ

µ

λ λ λ

2µ 3µ Vµ(V-1)µ

λ

Video Request Model

Pv(j) = probability that j video out of nV slots occupied 0 ≤ j ≤ nV

V, V = arrival/departure rate of video requests

PVj 1

jVVj

1 k1

nV 1

kVVk

Video Request Reward

With probability Pv(j), reward rate = j*vV*V

So total reward gained = jvVV Pv(j)

Rejection rate = V Pv(nV)

Lost reward = qV V Pv(nV)

Reward rate from video = RV

RV = ( jvVV Pv(j) ) - qV V Pv(nV)

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

0

λ

1 2 3 I-1 I I+1 2I-1 2I

λ λ λ λ λ λ λ λ λ

µµ

µ

µ

µ

µ

µ µ

Image & Text Model PI(j) = probability that j video out of nV slots occupied 0 ≤ j ≤ nI

I, I = arrival/departure rate of video requests

Let KI = 1

Image & Text Model PI(j) = probability that j video out of nV slots occupied 0 ≤ j ≤ nI

I, I = arrival/departure rate of video requests

Let KI = 2

Image/Text Request Reward

With probability PI(j) reward rate = j*vI*I if j < nI

nI*vI*I if j ≥ nI

Rejection rate = I PI(KInI)

Lost reward = qI IPI(KInI)

Reward rate from video = RI

RI = ( jvII PI(j) ) + ( nIvII PI(j) ) - qI I PI(KInI)

j = 1 … nI -1 j = nI … KInI

Maximizing Reward

Given V,V,I, I,T,T,vV,qV,vI,qI,vT,qT

Maximize R by searching for optimal(nV, nI, nT) → (n*V, n*I, n*T)

Subject to condition (normalized to text requests)

Here NV, NI, NT 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(NT

2) Once found all solutions build lookup table

Nearest Neighbor When NT is too large and exhaustive is

computationally too expensive Complexity O(NT) Fix one nV, nI, nT 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}

TSR

Use common schedule queue for disk requests If total schedule time < TSR 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 TSR = 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 NV = 53, NI = 37, NT = 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 (nV, nI, nT) = (NV, 0, 0) Use queue sizes of K{I,T} n*{I,T}

Greedy Allocates disk in proportion to product of

reward and arrival rate (nV, nI, nT) = ( , , )

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