Andy Connors

1. “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

2. 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

3. Multimedia System

4. 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

5. 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?

6. 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

7. 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

8. Refresher - Scan Algorithm

9. 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

10. 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

11. 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

12. 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

13. 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

14. Video Request Reward • With probability Pv(j), reward rate = j*vV*V • So total reward gained = jvVV Pv(j) • Rejection rate = V Pv(nV) • Lost reward = qV V Pv(nV) • Reward rate from video = RV RV = (jvVV Pv(j) ) - qV V Pv(nV)

15. 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

16. 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

17. 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

18. 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 = ( jvII PI(j) ) + (nIvII PI(j) ) - qI I PI(KInI) j = 1 … nI -1j = nI … KInI

19. 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

20. 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

21. 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)

22. 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]

23. 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) = ( , , )

24. Analysis Results

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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

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