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Formula: $e = \frac{\frac{1}{S} - \frac{1}{p}}{1 - \frac{1}{p}}$ Significance: Quantifies the empirical parallel efficiency and identifies the portion of a parallel program that does not scale well.

Formula: $Scale{-}Up = \frac{T_{new}(p)}{T_{old}(p)}$ Significance: Measures the system's ability to handle larger problems as the number of processors increases.

Formula: $S' = p - (p-1) (1-P)$ Significance: Provides an alternative to Amdahl's Law, emphasizing scalability with problem size.

Formula: $\frac{T_{compute}}{T_{communication}}$ Significance: Indicator of the balance between computation and communication in parallel processing.

Formula: $S = \frac{T_{serial}}{T_{parallel}}$ Significance: Measures the performance improvement gained by parallel processing.

Formula: $Throughput = \frac{Number\ of\ tasks}{Total\ time}$ Significance: Indicates the rate at which tasks are being completed by the system.

Formula: $T_{overhead} = T_{parallel} - \frac{T_{serial}}{p}$ Significance: Accounts for the additional work and time associated with managing parallel tasks.

Formula: $Resource\ Utilization = \frac{\sum active\ processor\ time}{Total\ processor\ time}$ Significance: Reflects the extent to which the available processing power is being used effectively.

Formula: $S = \frac{1}{(1-P) + \frac{P}{p}}$ Significance: Predicts the maximum possible speedup of a computation, considering its serial and parallel components.

Formula: $E = \frac{S}{p}$ Significance: Reflects the portion of the time for which a processor is usefully utilized.

Formula: $Load{-}Imbalance = 1 - \frac{T_{ideal}}{T_{actual}}$ Significance: Represents inefficiency due to uneven distribution of work among processors.