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Algorithms for System Expansion
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15.3 Row-Permutated Data Reorganization
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We present in this section the Row-Permutated Data Reorganization algorithm to redistribute media data after a new node is added to the system. We use two performance metrics, namely, data reorganization overhead and streaming load balance to compare its performance with the round-robin data reorganization algorithm [2] and the SCADDAR algorithm [3].
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15.3.1 Placement Policy
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In striped storage a media object is rst divided into xed-size blocks, denoted by vi, j , where i 0, 1, . . . is the group number and j 0, 1, . . . , (N 1) is the media block number within the same group. To maintain streaming load balance it is necessary to ensure that every block in the same group resides in a different node of the system. As Ghandeharizadeh and Kim s study [2] showed, the data reorganization overhead incurred in maintaining the round-robin data placement order is very high. This is illustrated in Figure 15.1 which shows the data placement before and after adding a node to a 4-node system. The shaded data blocks all have to be moved from one node to another to restore the round-robin placement in the new 5-node con guration. This obviously incurs signi cant overhead. In streaming applications, the client will process and play back media data sequentially (ignoring interactive playback control). This implies that if the client always receives one group of media data before playback, then the exact order in which the data blocks arrival at the client will become irrelevant. Therefore, instead of enforcing the round-robin placement order we can relax the constraint to reduce the number of block movements row-permutated placement policy.
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v0,0 v0,4 v1,3 v2,2 v3,1 . . . n0
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v0,1 v1,0 v1,4 v2,3 v3,2 . . . n1
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v0,2 v1,1 v2,0 v2,4 v3,3 . . . n2
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v0,3 v1,2 v2,1 v3,0 v3,4 . . . n3 n4
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v0,0 v1,0 v2,0 v3,0 . . .
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v0,1 v1,1 v2,1 v3,1 . . .
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v0,2 v1,2 v2,2 v3,2 . . .
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v0,3 v1,3 v2,3 v3,3 . . .
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v0,4 v1,4 v2,4 v3,4 . . .
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Before reorganization
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After reorganization
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Figure 15.1 Reorganization under round-robin placement (from 4 to 5 nodes). The shaded blocks all need to be relocated to form the new con guration
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Scalable Continuous Media Streaming Systems
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Divides media data stream into fixed-size blocks v0,0 v0,1 v0,2 v0,3 v1,0 v1,1 v1,2 v1,3 . . .
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Round-robin Placement
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Row-Permutated Placement
v0,0 v1,0 v2,0 v3,0 v4,0 . . . n0
v0,1 v1,1 v2,1 v3,1 v4,1 . . . n1
v0,2 v1,2 v2,2 v3,2 v4,2 . . . n2
v0,3 v1,3 v2,3 v3,3 v4,3 . . . n3
v0,0 v1,3 v2,0 v3,1 v4,0 . . . n0
v0,1 v1,0 v2,2 v3,0 v4,1 . . . n1
v0,3 v1,1 v2,1 v3,2 v4,3 . . . n2
v0,2 v1,2 v2,3 v3,3 v4,2 . . . n3
Figure 15.2 The row-permutated placement policy
Speci cally, in a N -node system the rst N media data blocks {v0, j | j = 0, 1, . . . , N 1} will be distributed to all N nodes in pseudo-random order, with each node storing exactly one of the N data blocks as shown in Figure 15.2. This process repeats for the next N data blocks {v1, j | j = 0, 1, . . . , N 1}, and so on until all data blocks are distributed. As long as the client receives a whole parity group before decoding it for playback, this row-permutated placement policy can achieve perfect streaming load balance, same as the original round-robin placement policy.
15.3.2 Data Reorganization
To determine which data blocks will need to be moved after adding a new node, we rst re-index all the media data blocks according to the new con guration. Figure 15.3 shows an example of reorganizing from a 4-node system to a 5-node system. For example, media blocks v1,0 and v1,1 will be re-indexed to v0,4 and v1,0 respectively in the 5-node con guration. If we consider the rst group of media blocks in the new con guration, we can see that node n 1 now needs to send two media blocks v0,1 and v0,4 while the new node is not used. This is the reason why load imbalance will occur if the data blocks are not reorganized.
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n1 overflows while n4 underflows.
v0,0 v1,3 v2,0 v3,1 v4,0 . . . n0
v0,1 v1,0 v2,2 v3,0 v4,1 . . . n1
v0,3 v1,1 v2,1 v3,2 v4,3 . . . n2
v0,2 v1,2 v2,3 v3,3 v4,2 . . . n3 Re-indexing
v0,0 v1,2 v1,3 v2,3 v3,1 . . . n0
v0,1 v0,4 v2,0 v2,2 v3,2 . . . n1
v0,3 v1,0 v1,4 v2,4 v3,4 . . . n2
v0,2 v1,1 v2,1 v3,0 v3,3 . . . n3 n4
Original block indices (4 nodes)
New block indices (5 nodes)
Figure 15.3 Re-indexing the rst group of media data blocks
n1 overflows while n4 underflows.
Block v0,4 is moved from n1 to n4.
v0,0 v1,2 v1,3 v2,3 v3,1 . . . n0
v0,1 v0,4 v2,0 v2,2 v3,2 . . . n1
v0,3 v1,0 v1,4 v2,4 v3,4 . . . n2
v0,2 v1,1 v2,1 v3,0 v3,3 . . . n3 n4 Re-organize
v0,0 v1,2 v1,3 v2,3 v3,1 . . . n0
v0,1
v0,3 v1,0
v0,2 v1,1 v2,1 v3,0 v3,3 . . . n3
v0,4
v2,0 v2,2 v3,2 . . . n1
v1,4 v2,4 v3,4 . . . n2
Group 0 before reorganization
Group 0 after reorganization
Figure 15.4 Reorganizing the rst group of media data blocks
Since we do not need to maintain the strict round-robin placement order under RPDR, we can simply move the excess block from the over ow node to the under ow node. For example, we move data block v0,4 from node n 1 to node n 4 as shown in Figure 15.4 to restore the streaming load balance of the new 5-node con guration. As a further illustration, we consider the second group of data blocks in Figure 15.5. Now there are two over ow nodes n 0 and n 2 , as well as two under ow nodes n 1 and n 4 . To restore