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If i=1 Bi (τ ) > 0 for all τ satisfying t1 ≤ τ ≤ t2 , the system is called continuouslybacklogged in the interval [t1 , t2 ]. Here we give the definition of service capacity as follows. Definition 4 (Capacity Curve). We say that a DSMS has a capacity curve C(t) if within any interval [t1 , t2 ] in which the system is continuously backlogged, the amount of basic operation that the system performs is at least C × (t2 − t1 ). 20 S. Wu et al. With the definition of capacity curve, the right side of Equation 11 and Equation 12 in Feasible Allocation condition could be generalized to C × (t2 − t1 ).

Prediction Model Buffers ------- Precision Manager Approximate Answer Register queries Register queries (query + precision constraint) Continuous Queries Evaluator No Update the coordinator with new value Is prediction value close (with some precision) to the actual observed value? Precision control messages Data sources f1 Updates . Yes Drop the data tuple . . PM s-1 Remote nodes Is prediction value close to the fs-1 actual observed value? Updates Yes Drop the data tuple Significative update value PM s Is prediction value close to the actual observed value?

Wu et al. (3) QoS-Guaranteed Algorithm Analysis To evaluate the ability of our QoS-Guaranteed scheduling algorithm, we implement FIFO algorithm as well. 2 0 100 300 500 Input rate of Q1 (tuple/s) Fig. 5. QoS-Miss Ratio of Q1 300 500 Input rate of Q1 (tuple/s) Fig. 6. 3 guaranteed under our QoS-Guaranteed Scheduling Algorithm. 1 increases, more tuples appear on the input of Q1 with relative earlier arrival 0 100 300 500 time. Therefore, the query engine is Input rate of Q1 (tuple/s) over occupied with the processing of the tuples of Q1 .

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