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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

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andy connors

“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
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
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
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
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
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
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
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
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
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 model1
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
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)

image text model
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 model1
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 model2
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
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

maximizing reward
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
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
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
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
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 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
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
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
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
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
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
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
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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