Temporal consistency in real time database solved exercise

Temporal consistency, real-time database, solved exercise, find whether the given relative consistency set are temporally consistent or not? absolute consistency, relative consistency



Exercise:

To check whether the given temporal data are consistent or not.

Let us consider a boiler which is equipped with sensors to monitor its pressure and temperature at any point in time. Assume that the temperature reading at time 2000 msec is 100o C and this reading is valid for only 30 msec. Also assume that the pressure reading at time 2010 msec is 50 bar and this reading is valid for only 20 msec. If these data are relatively valid for 20 msec and the current time is 2020 msec, temperature and pressure are temporally consistent?

Solution:

For a data item to be temporally consistent, it has to be absolutely consistent and also relatively consistent with the other related data items.

Given,

  • Relative consistency set R = {Temperature, Pressure}
  • Temperature reading validity duration, Temperatureavi = 30 msec
  • Temperature = (value, avi, timestamp) = (100oC, 30 msec, 2000 msec)
  • Pressure reading validity duration, Pressureavi = 20 msec
  • Pressure = (value, avi, timestamp) = (50 bar, 20 msec, 2010 msec)
  • Relative validity interval Rrvi = 20 msec
  • Current time = 2020 msec

A data item is absolutely consistent if |current_time – dtimestamp| <= avi
A set of data items d and d’ are relatively consistent if |dtimestamp – d’timestamp| <=Rrvi

|current_time – Temperaturetimestamp| = |2020 – 2000| = 20 msec which is less than or equal to Temperatureavi 30 msec. Hence, Temperature is absolutely consistent.

|current_time – Pressuretimestamp| = |2020 – 2010| = 10 msec which is less than or equal to Pressureavi 20 msec. Hence, Pressure is absolutely consistent.

| Pressuretimestamp – Temperaturetimestamp| = |2010 – 2000| = 10 msec which is less than or equal to Rrvi 20 msec. Hence, Temperature and Pressure are relatively consistent.

Hence, the relative consistency set R = {Temperature, Pressure} is temporally consistent.


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