Tuesday, March 22, 2016

Real time database - formal definition of temporal consistency

Formal definition of temporal consistency in real-time database, Explain temporal consistency with examples, when would we say that data items are relatively consistent?

Formal definition of temporal consistency

Temporal consistency has two components, namely, Absolute consistency, and Relative consistency.

Let us denote the data item in real-time database by,

d: (value, avi, timestamp)


dvalue - the current state (current value) of d at the time dtimestamp
-         This shows the value of the data item as observed by the controlling system.
dtimestamp – the time at which the dvalue observed
-         This shows the time at which the value is read by the controlling system.
davi – absolute validity interval of dvalue.
-         This shows the length of the time interval the dvalue is considered to have absolute validity. That is, dvalue is absolutely valid between dtimestamp and dtimestamp + davi.

The set of data items that are relatively consistent with each other, form a relative consistency set R. Each such set R is associated with a relative validity interval denoted by Rrvi.

Assume that d Є R, then we can define the conditions for absolute and relative consistency as follows;

Absolute consistency: a data item d is absolutely valid if and only if,
|Current time – dtimestamp| ≤ davi.

Relative consistency: a set R of data items is relatively consistent if and only if,  
d, d’ Є R, |dtimestamp – d’timestamp| ≤ Rrvi.


Assume that the current altitude of a taking-off aircraft is 100 metres. If you have observed this value at time 2000 msec, and if that aircraft can maintain this altitude for at most 20 msec more, then this data item is temporally specified as,
daltitude: (100 metres, 20 msec, 2000 msec)
altitude = (100, 20, 2000)
The given value (100 metres) can be absolutely valid for 20 msec since the time it was observed. That means, at the time 2021 msec (at time > 2000 + 20) the validity will be lost.

Let us assume the relative consistency set R as {altitude, cabin-pressure}. And the relative validity interval Rrvi = 5, then set R is relatively consistent if the difference between the observation times of altitude and cabin-pressure is less than or equal to Rrvi, ie. 5.

Altitude = (100, 20, 2000) and Cabin-pressure = (50, 25, 2002) are temporally consistent (both absolutely and relatively consistent) at time 2020.

Altitude = (100, 20, 2000) and Cabin-pressure = (50, 25, 2006) are absolutely consistent but not relatively consistent at time 2020. Because, |Altitudetimestamp – Cabin_pressuretimestamp| = 6, which is greater than the given Rrvi 5.


Go to Temporal Consistency page to view explanation.


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