The serial execution of a transaction is defined as Schedule. It is made up of a number of transactions each comprising of a number of instructions.
- Serial Schedules
- Non-Serial Schedules
Calculation of Number of Schedules :
Consider there to be N number of transactions t1, t2, t3, …., tN with k1, k2, k3, ….., kN number of operations respectively.
- Total Number of Schedules –
(N1 + N2 + N3 + ..... + Nn)! / (N1! * N2! * N3! * ... * Nn!)
- Number of Serial Schedules –
It is all possible permutations of n transactions = N!
- Number of Non-Serial Schedules –
Total Schedules = Serial Schedules + Non-Serial Schedules
Number of Non-Serial Schedules = Total Number of Schedules – Number of Serial Schedules
((N1 + N2 + N3 + ..... + Nn)! / (N1! * N2! * N3! * ... * Nn!)) - (N!)
Consider there to be three transactions with 1, 2, and 3 operations respectively.
We have to find –
- Total number of schedules possible.
- Total number of serial schedules and non-serial schedules possible.
Total Number of Schedules,
= (1 + 2 + 3)! / (1! + 2! + 3!) = 6! / 9 = 120 Number of Serial Schedules, = 3! = 6 Number of Non-Serial Schedules, = Total Number of Schedules - Number of Serial Schedules = 120 - 6 = 114
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