1. Absolute and relative validity interval
Database items can be divided into:
- Continuous items, i.e., they reflect values from an entity, such as a sensor, that changes continuously in the external environment.
- Discrete items, i.e., they are updated at discrete intervals, for example stock prices are updated when the trading with them increases or decreases.
- Derived, i.e., the database item is calculated from other database items stored in the database.
A continuous data item does not truly reflect the entity’s correct state, since it takes some time to acquire the value from the entity and store it in the database. Hence, a data item is said to correctly reflect the true value for a specific and finite amount of time. A data item is said to be absolute consistent with its entity when the following condition holds:
,
where 
is the time when data
item 
was created. 
is the so called
absolute validity interval associated with data item 
.
For derived data, the base data items used in the derivation
constitute the derived items read set denoted 
. The read set is relative consistent if:
- the
difference between the timestamps of any pair of data items in
is less than the
relative validity interval of 
denoted 
. That is: 
, where 
is the relative
validity interval on 
. This is used mainly for continuous data items. - the
data items in the read set
are all absolute
consistent at the same time. That is: 
. This is mainly used for discrete data items.
Figure 1 shows both the absolute validity interval and the two
ways of using the notion of relative consistency. The interval that is colored
green is the length of the relative validity interval, 
. From the figure we can see that according to the first
definition above the three data items: sensor1, sensor2, and sensor3 are
relatively consistent. The second definition says that the data items sensor1,
sensor2, and sensor3 are relatively consistent in the yellow interval, i.e.,
when they are all absolutely consistent with their respective entity.
Figure 1 Validity intervals on data items.
A derived item is valid from its creation time and until, as
in Figure 1,
any of the items in 
is not absolute
consistent with its entity anymore. This is further discussed in section 3.
2. Dynamic validity interval
A data item reflects the status of an entity for a specified, bounded amount of time. When this time has expired the data items is considered to not be valid anymore. The absolute validity interval of a data item is not necessarily fixed during the execution of the system. Figure 2 shows two sensors where one is initially changing very much and to correctly reflect this the absolute validity interval of the sampled and installed value in the database has to be small, whereas the other sensor changes less and therefore the absolute validity interval can be larger. After some time the rapidly changing sensor value starts to change less and now it is not necessary to sample the sensor as often, i.e., the absolute validity interval can be increased. The other sensor starts to change more often after some time (note that this amount of time is not necessarily related to the amount of time for the other sensor) and thus need to be sampled more often. The validity interval of the sensor value starts to be smaller.
Figure 2 The change in behavior of two sensors as time passes by.
In an engine control system one sensor is used for measuring the temperature of the engine. The temperature changes more rapidly in the beginning compared to when the engine has reached its working temperature. This means that the engine temperature value and data items that are derived from the engine temperature are absolutely consistent during a shorter period of time during the heating up of the engine compared to when it reaches the working temperature.
To have a fixed absolute validity interval on data items require that you design for the worst-case of all modes, and basically oversample data. Considering the needs of the application in various modes, to accurately model the data items the database system must be able to change the validity interval. We define a dynamic validity interval as:
A data item has, in addition to its absolute validity
interval, a dynamic validity interval 
, where 
is an upper limit of
the possible increase of the value’s life time, that extends the time a data
item is considered valid. The absolute consistency is now changed into:
.
3. Absolute validity on derived items
It is not obvious how the absolute validity interval of a
derived item shall relate to the items in its read set. In Figure 1 the derived item is valid only as long as all the
data items in 
are absolute
consistent with their respective entity. This works adequately when the sensor
values are updated periodically (as soon as the sensor value is not absolute
consistent anymore it is updated), since when a data item in the read set is
installed the derived item can be considered to not be consistent anymore. One
other possible way to get the absolute validity interval of a derived data item
is to consider the change of the read set members in the external environment,
see Figure 3. The database system is updating the sensor values when
they are not valid anymore and if the value has changed more than a threshold
from the value the sensor had when deriving a data item the derived data item
is not valid anymore. If it is cheap to update a sensor value in the database
it can be updated more often than what its absolute validity says.
Figure 3 A threshold value is associated witb a sensor value. When the real-world value has changed more than the threshold stipulates it is considered not to be absolute consistent anymore.
4. Approaches
Develop algorithms for concurrency control and scheduling for managing dynamic validity intervals.
· Use dynamic validity intervals in the system, since then it is possible to model the behavior of the system more accurately. The main advantage is that the CPU can be better utilized, since it is not necessary to be pessimistic about how often a sensor value[1] needs to be updated when the system is constructed. Also cascading effects can occur, that is when one data item is valid for a longer time gives that derived items based on it are also valid for a longer time, i.e., these data items do not have to be updated as often as before.
·
Add information in the reoccurring transactions to tell
the scheduler when a transaction will appear in the system again, which data
items it needs, what the timing constraints are (relative validity interval).
This information can be used both for scheduling updates in a manner so they do
not occur all at the same time, and to tell the database system which data
items that is needed in the future if versions of data items will be stored in
the database system.
The knowledge of future requests of data items can also be used for handling
overload situation of the CPU. The system now has the possibility to focus on
the most important data items.