2-68. An article in the Journal of Database Management [\"Experimental Study of

Question

2-68. An article in the Journal of Database Management ["Experimental Study of a Self-Tuning Algorithm for DBMS Buffer Pools" (2005, Vol. 16, pp. 1-20)] provided the workload used in the TPC-C OLTP (Transaction Processing Performance Council's Version C On-Line Transaction Processing) bench- mark, which simulates a typical order entry application. See Table 2E-1. The frequency of each type of transaction (in the second column) can be used as the percentage of each type of trans- action. The average number of selects operations required for each type of transaction is shown. Let A denote the event of transactions with an average number of selects operations of 12 or fewer. Let B denote the event of transactions with an aver- age number of updates operations of 12 or fewer. Calculate the following probabilities. (a) P(A) (d) P(A'nB) (e) P(AUB) (b) P(B) (c) P(AnB)

Explanation / Answer

Event A: Transactions with 12 or lesser selects operations
Event B: Transactions with 12 or lesser updates operations
(a)
As can be seen from chart "Payment" , "Order Status" and "stock level" transactions have average number of select operations < = 12.
P(A) = 0.44 + 0.04 + 0.04 = 0.52

(b)
As can be seen from chart "New Order" , "Payment" , "Order Status" and "stock level" transactions have average number of update operations < = 12.
P(B) = 0.43 + 0.44 + 0.04 + 0.04 = 0.95

(c)
P(A B)
As can be seen from chart "Payment" , "Order Status" and "stock level" transactions have average number of both select and update operations < = 12.
P( A B) = 0.44 + 0.04 + 0.04 = 0.52
d)
Only "Delivery" transaction has average number of both select and update operations > 12.
P(Ac Bc) = 0.05
e)
P(A U B) = P(A) + P(B) - P(A B) = 0.52 + 0.95 - 0.52 = 0.95

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