Number of expanded EIsTime (s)×10^5
7
6
5
4
123 45678910(a) Estimated Bollinger Bands of execution timeCosts ($)Number of expanded EIs1234567891024
22
20
18(b) Estimated Bollinger Bands of costsProduct(costs×time)×10 7
1.6
1.4
1.2
1.0
0.8Number of expanded EIs12345678910Lower BB
Middle BBUpper BB
EIC
(c) Estimated Bollinger Bands of productFigure 13: Estimated execution time, cost, and Bollinger Bands of
expanded EI zones computed with the past price history.
User bid ($)0.310 0.315 0.320 0.325 0.330 0.335Time (s)×10^5
2.5
2.0
1.5
1.0
0.5
0.0HBC
REC
EICFigure 14: Comparison of rollback time according to user bid.varies from minimum time to maximum time at the gran-
ularity of the time interval.
Figure 19shows the rollback time of EIC, HBC, and REC
according to the task time. The increase rate of rollback time
inEICissmallcomparedtoHBCandREC.Therollback
times are increased by 5.25 times, 15.84 times, and 12.41 times
forEIC,HBC,andREC,respectively,whenthetasktimesare
increased from the minimum to the maximum times. EIC
User bid ($)0.310 0.315 0.320 0.325 0.330 0.335 0.340Event count number500
400
300
200
100
0Failure count (HBC)
Failure count (REC)
Failure count (EIC)Ckp count (HBC)
Ckp count (REC)
Ckp count (EIC)
(a) Number of failures and checkpointsUser bid ($)0.310 0.315 0.320 0.325 0.330 0.335 0.340Total time (HBC)
Total time (REC)
Total time (EIC)Total failure time (HBC)
Total failure time (REC)
Total failure time (EIC)×10^6
3.2
2.8
2.4
2.0
1.6
1.2
0.8
0.4
0.0Time (s)(b) Total task execution time and total failure timeFigure 15: Performance comparison of checkpointing schemes
according to user bid.User bid ($)0.310 0.315 0.320 0.325 0.330 0.335 0.340Costs ($)Total price (HBC)
Total price (REC)
Total price (EIC)50
40
30
20
10
0Figure 16: Comparison of total costs.User bid ($)Product0.310 0.315 0.320 0.325 0.330 0.335 0.340(costs×time)×10^8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0HBC
REC
EICFigure 17: Comparison of combined metrics (total task execution
time and costs).