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Bulk dispatch lapse (BDL) or Bulk dispatch value lapse, depicts the depreciation of a distributed object to multiple consumers.

Semantics

The BDL expects a decrease of a dispatched object's value for individuals, when delivered asynchronously. The initiation of the depreciation varies by context and may be subject of a variety of different depreciation functions. The term lapse is ambiguous. Lapse describes the delay of the object being dispatched. Also, and even more important, it depicts the depreciation of the value in the perception of an object consumer. The depreciation does not apply in the following cases. First, if the dispatch time to consumers are equal. I.e. delay c_first = delay c_last. On the other hand, if the delay of the object has neither a value depreciation nor a value appreciation. Another condition is the presence of multiple consumers. Multiple issuers of an object type is not a condition.

An extra factor that needs to be considered is the processing of the object after receiving it. If the processing time is known in advance, the depreciation can be calculated on reception of the object. If not, the perception of the depreciation has to be suspended till the processing task is completed. Subsequently, if processing times among consumers are volatile and not deterministic, a consumer may discard to invoke the processing due to the risk of partial or full depreciation. Dealing with uncertainty and availability is a related topic. Morgan , Savage and others provided approaches of probability to cope with the risk of the processing task in vain.

Expected value of including uncertainty (EVIU) is a similar concept focusing on information and decision making. EVIU can be incorporated into BDL or even represent the basis. The complementary contribution of BDL is defined by the multiplicity of the consumer of the object. The multiplicity results in a bulk dispatch.

Consumers, objects and depreciation

BDL describes the bulk dispatching of objects. Consequently it depicts how multiple recipients are supplied with an object by one or more issuers. In this context, recipients are termed consumers, because they do not simply receive an object, they also need to consume and process it to estimate its value. For the term BDL an object is a placeholder for one variable of a function. This variable is capable of holding a non-nominal value perceived by a group of equal consumers. Again, the object is exposed to depreciation by consumers. In real world scenarios objects are typically raw and industry goods but also services or pure information.

Types of depreciation

If conditions for a depreciation apply, various type of functions may determine the speed, interval and the direction.

Linear depreciation

A linear depreciation function accommodates the steady loss of the information value. This type of function might apply, for example, if a depreciation is coupled to a risk factor, which denotes the sheer chance that other consumers take note of the new dispatched object. The depreciation step equals the number of interested consumers. If the processing time of consumers are equal or similar, a linear depreciation is meaningful, too.

Threshold breaching function with knees

In other scenarios a dispatched object immediately loses its full or partial value, if certain number of consumers C_a have already received the object. In a function the ordinate value takes on zero, if value x representing c_n, has received the value. It draws a dramatic knee on the function's graph. This scenario is prevalent. e.g. On a social platform a supplier of sport gears promises the first 20 callers a free bicycle helmet. The lapse of this information is significant. And after the 20th reader having called, the information value drops down to zero. Dialling the phone number is considered the processing. Thus, the perception of the value of this information is postponed, after the processing of the information (object) is completed.

These knees in functions are defined by piecewise functions. Below is an exemplary piecewise linear function defining that as soon as x equals or is greater than x₁, the value of y is set to zero, respectively is not defined.

$f(x)={\begin{cases}mx+y_{1}-mx_{1}&{\text{if }}0\leq x<x_{1}\\0&{\text{if }}x\geq x_{1}\end{cases}}$

Polynomial, regressive, degressive and progressive functions

Polynomial functions appear rarely. Because it entails that depreciation is being reduced, respectively appreciation of the objects value occurs. This scenario might also be accompanied by multiple pivot points. More likely is the presence of stagnation. That is, the function draws a (non-strictly) monotonous decreasing slope.

Term evolution

The term BDL arose from an academic deliverable of a student, Brayan Zimmerli, at the University of Zurich in 2013. The deliverable's core research question was to mitigate the unfairness of data delivery to multiple subscribers of a topic. In context of enterprise application integration (EAI), unfairness related to the fact that technical difficulties of dispatching information inevitable leads to unfairness among the consumers of data. In other words, while consumer c_first has received an information, the value of the information to consumer c_last starts to decrease although c_last has not yet received the information. The field of research was limited to transaction of participants of financial exchanges.

Discussion on negative depreciation

It is not rule out that a depreciation may result negative. Thus, an appreciation may occur the later c_last consumes the object after c_first.

See also

• Expected value of perfect information (EVPI)
• Expected value of sample information

References

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