Today we continue our discussion of the paper titled "Pelican: a building block for exascale cold data storage". Pelican treats a group of disks as a single schedulable unit. Resource restrictions such as power consumption, vibrations and failure domains are expressed as constraints over these units.
With the help of resource constraints and scheduling units, Pelican aims to be better than its over provisioned counterpart racks using computations in software stacks.
We were discussing the evaluation of Pelican and listing out the metrics chosen. To compare the evaluations, a simulator was used in addition to the Pelican hardware rack and the simulator and the rack were cross validated. It was configured in such a way that the prototype Pelican rack hardware matched the simulator. We were discussing the metrics and the Pelican performance against metrics. These included completion time, time to first byte, service time, average request rate and throughput.
The actual throughput of disks in a quiescent system is measured and the simulator is configured with an average throughput of 105 MB/s Seeks are simulated using a constant latency of 4.2ms for all disk accesses. This has negligible effect on performance. Reads are for large blobs with a stripe forming a single contiguous file on disk
Pelican was compared with an ideal system - one where there is full provisioning of power and cooling, which we denote as FP. In the FP, configuration disks are never spun down, but the same physical internal topology is used as in Pelican. In FP, however, all 48 groups can be accessed concurrently. The maximum queue depth per scheduler for both is set to 1000 requests and the maximum reordering allowance is set to 500 GB. For the cross validation configuration, all four schedulers are run by a single server with one 10 Gbps NIC. In the rest of the evaluation, the rack has two servers such that the servers such hat each server runs two schedulers.
The first set of experiments measured the base performance of both the systems. The scheduler does poorly with a straw man algorithm but does very well with the Pelican scheduling.
#puzzle
Joey has to arrange 2N sandwiches which are wrapped by different color wrapper in N pairs such that he can feed his N girlfriends (A hypothetical situation it is where we have to ignore the fact “JOEY DOESN’T SHARE FOOD ”). He has to serve them for 2N-1 Days. Girls don’t like repeated pair of color wrapper of their sandwiches.
Design an algorithm for joey so that for 2N-1 days no pair would be same.
Design an algorithm for joey so that for 2N-1 days no pair would be same.
Solution: This problem is solved by keeping a 2N table with numbers ranging from 1 to 2N-1. The pairs are given by the column of the table. Each day all the entries except one are rotated in a clockwise manner ensuring different color wrapper for the girls sandwiches.
2) There was a prison consisting of 1000 cells numbered from 1 to 1000.
Each cell can be marked with ‘+’ or ‘-‘sign. Initially, all cells were marked with ‘-‘ sign.
From days 1 to 1000,the jailor toggles marks on the cell from + to – or vice versa.
On the i-th day ,the signs on cells that are multiples of i get toggled.
Now in the process of verification on 1001-th day, all cells marked with + signs are opened.
Can you identify the cell numbers with ‘+’ sign?
Solution: When we toggle 1000 times we are toggling even number of times. All multiples are formed from odd and even or odd and odd or even and even. And since they are two times odd and even, most multiples will reset back to original state. This is true for almost all multiples except perfect squares. Therefore perfect squares form the answer.
#another puzzle
Two friends A and B play a game with 9 cards lying face up and labeled 1 to 9. They take turns to draw a card and the first person to collect three cards that totals fifteen wins. A is given the first chance to play. Does he have a winning strategy ?
Solution : There are eight subsets that sum up to 15. These are :
{1,5,9}, {2,8,5}, {3,5,7}, {4,5,6}, {1,6,8}, {2,4,9}, {2,7,6} and {3,8,4}
These can be arranged in a magic square as
8 1 6
3 5 7
4 9 2
where the horizontal, vertical and diagonal form the required sum. Since this is a game of Tic Tac Toe, there is no winning strategy.
Each cell can be marked with ‘+’ or ‘-‘sign. Initially, all cells were marked with ‘-‘ sign.
From days 1 to 1000,the jailor toggles marks on the cell from + to – or vice versa.
On the i-th day ,the signs on cells that are multiples of i get toggled.
Now in the process of verification on 1001-th day, all cells marked with + signs are opened.
Can you identify the cell numbers with ‘+’ sign?
Solution: When we toggle 1000 times we are toggling even number of times. All multiples are formed from odd and even or odd and odd or even and even. And since they are two times odd and even, most multiples will reset back to original state. This is true for almost all multiples except perfect squares. Therefore perfect squares form the answer.
#another puzzle
Two friends A and B play a game with 9 cards lying face up and labeled 1 to 9. They take turns to draw a card and the first person to collect three cards that totals fifteen wins. A is given the first chance to play. Does he have a winning strategy ?
Solution : There are eight subsets that sum up to 15. These are :
{1,5,9}, {2,8,5}, {3,5,7}, {4,5,6}, {1,6,8}, {2,4,9}, {2,7,6} and {3,8,4}
These can be arranged in a magic square as
8 1 6
3 5 7
4 9 2
where the horizontal, vertical and diagonal form the required sum. Since this is a game of Tic Tac Toe, there is no winning strategy.
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