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Service Models

Service Models. Example Server has 50 movies, 100 min. each Request rate: 1 movie/min Max. capacity: 20 streams Random Access Model Case 1: after 20 movies, no more memory left. 21 st movie waits for 80 minutes, 22 nd movie waits for 81 minutes …

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Service Models

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  1. Service Models • Example • Server has • 50 movies, 100 min. each • Request rate: 1 movie/min • Max. capacity: 20 streams • Random Access Model • Case 1: after 20 movies, no more memory left. 21st movie waits for 80 minutes, 22nd movie waits for 81 minutes … • Case 2: after 20 movies, more memory can be allocated. 21st movie has to wait (initial latency) till one round of the previous 20 movies each has been served. • EPPV Model: • At any time 20 movies are served, movies are initiated every 5 minutes • Streams are distributed uniformly during these 20 minutes

  2. A Disk Striping Model • Assume compressed videos stored on m disks with stripe units of size d – each round gets 1 stripe unit • Period P for a video: # rounds to get successive streams • q = max. number of videos serviced in a round / disk • If total memory=R • Optimal d given by: • If R=2GB, m=50, display rate=1.5Mbps • d=0.9Mb, q=20, round=600ms • Period for a video of 100 min = 1 min. round duration buffer/video is 2d tseek= avg. time to reach a track

  3. Vertical Striping • A situation • 4 supervideos V1 .. V4 • V1, V2: 3 stripe units per disk • V3, V4: 2 stripe units per disk • 2 stripe units/round/disk • Round 1..3: get data for V1 and V2 from disk 0 • Round 4, 5: get data for V3 and V4 from disk 0 • get data for V1 and V2 from disk 1 • Round 6: get data for V1 and V2 from disk 1 • get data for V3 and V4 from disk 1 • 4 streams from a disk!!! • A solution • Partition videos into sets that reduce the difference between the lengths of videos of any two sets as much as possible

  4. Scheduling for Vertical Striping • The Problem: • Get w stripe units for every super video Vi at intervals of Pi from disk 0, when a maximum of q streams can be retrieved from a disk in one round • Schedule non-preemptible tasks T1…Tr with periods P1…Pr and computation time w on q processors • How complex is the problem? • What can be done? • Result 1: if n.w  gcd(P1…Pn) then the tasks are schedulable on a single processor, where n=r/q • If tasks T1..T4 have periods 4,4,6,6 and w=1, they can be scheduled at 0,2,1,3 respectively – a stronger result is needed

  5. Example • Tasks T1..T4 have periods 4,4,6,6 and w=1 • g=2 • n=4, so n > g • Make tasks T1…T4 with periods 2, 2, 3, 3 • Initial subsets S1=T1, T2 S2=T3, T4 • Next iteration: • From S1: {(T1, 0) (T2, 1)} From S2: {(T3, 0) (T4, 1)} • Step 5: {(T1, 0) (T2, 2) (T3, 1) (T4, 3)}

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