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“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

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

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

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

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

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 -1j = 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(NT2)
- 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) = ( , , )

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

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