EP2044541A2

EP2044541A2 - Method for testing the real-time capability of a system

Info

Publication number: EP2044541A2
Application number: EP07785867A
Authority: EP
Inventors: Karsten Albers; Frank Bodmann; Frank Slomka
Original assignee: Inchron GmbH
Current assignee: Inchron GmbH
Priority date: 2006-07-03
Filing date: 2007-06-28
Publication date: 2009-04-08
Also published as: WO2008003427A3; EP2306349A1; IL196155A0; JP2009541876A; US8306784B2; CA2656673C; CA2656673A1; KR20090040312A; US20100017168A1; WO2008003427A2

Abstract

The invention relates to a method for analyzing, especially in real time, a system, particularly a computer system, which comprises a set of different tasks (τ). At least some of the tasks (τn) are requested and processed in a repetitive manner by the system or repeatedly generate requests to partial system components (events). The occurrence pattern of the events that request the tasks or are generated by the task are represented at least in part by a description during the analysis, said description being composed of a set of elements, each of which describes the occurrence pattern of events. The inventive method is characterized that a set of not necessarily uniform elements is used once again with at least two elements for describing the occurrence pattern represented by said at least two elements, while said sets of elements, and thus the occurrence pattern described thereby, are different from each other.

Description

Method for checking the real-time capability of a system

The invention relates to a method for testing the real-time capability of a system, in particular of a computer system.

The analysis of the temporal behavior of embedded real-time systems is needed to automate the development of such systems. For the correct functioning of real-time systems, not only the correct, but also the timely determination of calculation results is necessary. Examples of such systems are the airbag control or a motor control.

A model of inter-communicating tasks according to FIG. 1 is considered. A "task" is a sequence of processing steps which processes a set of input values and thereby generates calculation results or changes of the system. A task may be represented by an algorithmic description or a description of a hardware performing the functionality. Tasks can activate other tasks, which, for example, further process the calculation results of the activating task. Tasks can also access resources. The activations or resource accesses can take place at any point in the process of the task. The activations of a task or the resource access will be referred to as "event" in the following.

In order to be able to carry out rapid analyzes for such a model, a description of the "occurrence behavior of events" is needed. "Occurrence of events" is the temporal behavior, ie the temporal distances of several events from each other.

TÄTIGUNGSKOPIE stand. A "performance pattern" is a description of the performance behavior to understand. The "performance pattern" consists of a plurality of descriptors. The descriptors may be the same or different; they each represent a part of the "performance behavior of events". A possible description of a "performance pattern" is the so-called "event density". In addition, it is also possible to describe a "performance pattern", for example by a period and a jitter.

In the description of the "event density", the maximum / minimum number of events is specified in time intervals of given length. The event density can be subject to fluctuations.

In addition, the description should also support a quick analysis of the temporal behavior, in particular the guaranteed compliance with given time limits. In particular, it is important to quickly determine from a description of the "occurrence behavior of events" for given intervals the number of events occurring in them and, for given event numbers, an interval in which this number can occur. Usually, only the interval lengths are important and maximum or minimum interval lengths are required for certain number of events or maximum or minimum number of events for particular interval lengths. Descriptions that make this determination possible with a linear effort with regard to the number of elements of the description are particularly advantageous.

Many works in the field use a purely periodic appearance pattern.

From K. Gresser. Real-time evidence of event-driven real-time systems. Dissertation, VDI Verlag, Dusseldorf, 10 (286), In 1993, a description is known for occurrence patterns of events called the event stream model. An "event stream" is described here by a set of tuples, each consisting of a cycle z and a distance a. The tuples can be referred to as "event stream elements". The distance is assumed to be the same as specified for event stream elements. Each event stream element generates its own occurrence pattern, wherein the first event of the event stream element can occur with a distance a from the common origin and then follow the following events offset by the cycle z. The second event may therefore follow with a distance of a + z to the origin, the third event with a + 2z and so on. The entire event stream results from a superposition of the occurrence patterns of all event stream elements. Furthermore, in the work only those event streams are considered valid, which generate an occurrence pattern in which the largest densities of events each start from the origin. Therefore, at least one event stream element must be assigned the initial distance zero. It is assumed here that the event stream describes an upper limit for a "maximum occurrence pattern ¹¹ of events." A "maximum occurrence pattern" is understood as an occurrence pattern which has a maximum possible event density Allow events in a system to be considered as allowed by the event stream Permitted means that time limits that can be guaranteed to be met for the event stream will be met even if the event density is reduced.

In recent work (K. Albers, F. Slomka, An Event Stream Driven Approximation for the Analysis of Real Time Systems, IEEE Proceedings of the 16th Euromicro Conference on Real- Time Systems, 2004, pp. 187-195; K. Albers, F. Slomka. Efficient Feasibility Analysis for Real Time Systems with EDF Scheduling. Proceedings of the Design Automation and Test Conference in Europe (DATE '05) pp. 492-497) describe a very efficient real-time analysis. The problem with this description is that event bursts can not be efficiently represented and thus can not be analyzed efficiently. An "event thrust" is understood to mean a time-limited increase in density of events within a "performance pattern". The event stream model requires that each event within an event batch must be represented by its own event stream element. Only when event bumps occur repetitively within a performance pattern, it is sufficient to assign an event stream element to the events of the first event push. Since bursts of events can include thousands of elements, the event stream model is unsuitable as a form of description for such systems.

In S. Chakraborty, L. Thiele, A New Task Model for Streaming Applications and Its Schedulability Analysis, IEEE Proceedings of the Design Automation and Test in Europe Conference (DATE ^λ 05), pp. 486-491, 2005 a description possibility for performance patterns is presented, which specializes in an efficient representation of event surges.

Again, the appearance patterns are described by a lot of tuples. These consist of an event number and an interval in this model, and indicate the maximum number of events that can occur in an interval of this length. The individual tuples are limited to each other, so that only performance patterns are allowed that meet all tuples. This model can be used to efficiently describe certain event bumps. However, the problem with the description format is that the proposed analysis Mood requires many linear combinations of all tuples and therefore is not feasible efficiently. Furthermore, many types of event bouts can not be efficiently represented by the model. An occurrence pattern in which, for example, the first two events occur with a distance t and all other events with a distance l> t to their respective predecessor event can not be efficiently represented by this model. Each event except the first would have to be described by its own tuple. Furthermore, such performance patterns are not describable, occur in which event bouts with different internal performance patterns.

In K. Richter, Compositional Scheduling Analysis Using Standards Event Models, Dissertation, TU Braunschweig, 2005 a description is presented in which events are described by a period, an event time and a minimum distance between events. The "event member" describes a time interval in which the principally periodic appearances can fluctuate. If the event member comprises several periods, all those events that occur within the time interval can occur almost simultaneously. They are only separated by the minimum distance.

This model can be used to describe a simple initial occurring burst of events with a simple minimum distance between events within the event. More complex event boosts, which z. For example, events with a more complex occurrence pattern of events within the event batch can not be represented by this description. The object of the present invention is to eliminate the aforementioned disadvantages of the prior art.

This object is solved by the features of claims 1, 13 and 20. Advantageous embodiment will become apparent from the features of claims 2 to 12 and 14 to 19.

A method is proposed for analysis, in particular real-time analysis, of a system, in particular of a computer system, in which a set of different tasks (τ) is provided,

wherein the tasks (τ _n ) are at least partially requested by the system and processed

or

repeatedly generate events by requests to subcomponents of the system,

wherein an occurrence pattern of the events requesting the tasks or generated by the task during the analysis is at least partially represented by a description of event densities,

which consists of a set of elements, each describing a part of the occurrence pattern of the events,

wherein at least two elements for describing the occurrence pattern represented by them comprise a further set of further elements,

and the other amounts and the pattern of occurrence they describe differ from each other. Furthermore, a method for analysis, in particular for real-time analysis, of a system, in particular of a computer system, is proposed, in which a set of different tasks (τ) is provided,

or

repeatedly generate events by requests to subcomponents of the system,

where at least one task generates multiple events when activated,

wherein an internal behavior of the task is described by a control flow, which is represented by a control flow graph,

wherein a step is provided in which a further occurrence pattern for the control flow graph is determined from occurrence patterns of the events determined for a plurality of contiguous subgraphs and / or nodes of the control flowchart

and

at least one additional one for this determination

Occurrence pattern of events of the subgraphs is used,

and this additional occurrence pattern represents a possible occurrence pattern of events in time dependence on certain pass points of the subgraphs.

These methods are explained in more detail below. In this case, resources are understood as means of work in a system which are available only to a limited extent or are allocated in quantity or time, such as, for example, Memory, capacity on communication media such as buses, processing time on processors and application specific switching logic.

For the purposes of the present invention, the term "occurrence pattern" is understood to mean a temporal occurrence pattern that describes the occurrence of events on a timeline.

A "further control flow graph" in the sense of the present invention can be a subset of the "control flow graph".

In the following, "costs" are understood to mean the types of costs required for the analysis, such as computing time or energy expenditure. These are available in limited time intervals only limited. An analysis that determines a minimum cost of certain outcomes, such as the maximum number of occurrences, thus also determines the minimum time required for that outcome.

In the following, a first embodiment for the solution according to the invention according to claim 1 and the embodiments according to claims 2 to 12 are presented:

The hierarchical event streams (HES). An "event sequence" describes the "occurrence pattern" of events by their "event density", an "event sequence element" is a subelement of this description. An occurrence pattern of events is described by a "hierarchical event sequence Θ". This consists of a set of hierarchical event sequence elements. A "hierarchical event sequence element ω" is characterized by a period (or cycle) p, an initial initial distance a, a boundary n and a recursively embedded hierarchical event sequence Θ ¹ (ω = (p, a, n, Θ ')). The limit n limits the maximum number of events that can be generated in a period of the embedded hierarchical event sequence Θ ¹ . In order to allow a recursive beginning, a hierarchical event sequence element ω may include an embedded hierarchical event sequence or even a simple event. In this case, only one limit with the value one makes sense. The period can also be occupied by the value ∞, which represents a one-time generation of the occurrence pattern.

A concrete hierarchical event sequence whose event occurrence patterns have the largest densities of events always at the beginning is called a "hierarchical event stream". It enables efficient methods for real-time analysis. To this extent, for example, in Karsten Albers, Frank Slomka, An Event Stream Driven Approximation for the Analysis of the Real-Time System, IEEE Proceedings of the 16th Euromicro Conference on Real-Time Systems 2004 (ECRTS '04), Catania, Italy, p 187-195 real-time analysis methods are applied mutatis mutandis.

In the first embodiment, a value of the limit is represented by a number of events. However, it is also conceivable to use a maximum interval length as the limit specify. In the first embodiment, at most as many events in a period are generated by the hierarchical event sequence element as can be generated by the recursively embedded event sequence at most in one interval with the length of the boundary.

The occurrence pattern of the events of a hierarchical event sequence is formed by a superimposition of the occurrence patterns of the individual hierarchical event sequence elements. The first event in the occurrence pattern of a hierarchical event sequence element can take place after the initial distance a. The occurrence pattern of this and the following events is described by the occurrence pattern of the embedded hierarchical event sequence Θ ', which, however, is shifted from the origin of the occurrence patterns by the initial distance a. It includes only the first n events of the embedded hierarchical event sequence Θ ¹ . These are referred to below as "event group". This embedded hierarchical event sequence Θ ¹ is now repeated with the period p, thus starting at a + p, a + 2p, a + 3p, etc.

A hierarchical event sequence Θ can in turn be recursively embedded in a hierarchical event sequence. In this case, the above procedure is repeated.

In order to enable an efficient realization of the analysis, it is advantageous to use exclusively hierarchical event streams Θ in which the event groups generated by the individual event stream elements are separated from one another, ie must not overlap (separation condition). For example, the following HES satisfies the separation condition: Θ _A = {(100, 0, 7, Θ _B ), (100, 30, 5, Θ _c )}. The hierarchical event streams Θ _B and QC recursively embedded in Θ _{A are} needed: Θ _B = {(3, 0, l, e) and Θ _c = {(7,0, l, e), (7,3, l , e)}. In the first element of this HES Θ _A , seven events can be generated per period, and five events in the second element of HES Θ _A. The distances between these events and thus the intervals at which the seven or five events can be generated are determined by the respective recursively embedded event streams Θ _B and Θ _c . Thus, for the first element of the HES, a further event can occur in each case in an interval that is greater by three cost units. A maximum of two events can occur in an interval of length three because the first event can occur at time zero and the events have a period of three. In an interval of length six, a maximum of three events, in an interval of length nine, a maximum of four events, the length 12, a maximum of five events occur. For the total of seven events per period, there is thus a minimum total interval of 18 cost units in which these events can occur. - For the second element, the occurrence is determined by the recursively embedded event stream Θ _c . Two events can occur for the first time in a cost interval of length three, three events in a cost interval of length seven, four events in a cost interval of length 10, and five events in a cost interval of length 17. The total amount of events that can be generated in a period of the second element of Θ _A is limited to five, which can thus be generated in a cost interval of length 17. Since the second element of Θ _{A is assigned} an initial distance of 30, the events of the first period of this element are generated in an interval between the cost points 30 and 47. The events of the first period of the first element of Θ _A are generated in the case of the maximum occurrence pattern in an interval of 18 cost units starting at the cost point zero. The intervals at which the events of the second period are generated are [100,118] and [130,147], respectively. The intervals do not overlap, so Θ _A satisfies the separation condition. For a simple validation of the separation condition, it is advantageous if identical periods (homogeneous HES) are assigned to the individual elements of a hierarchical event stream. However, this is not absolutely necessary, in particular if the elements are at least partially limited to the total number of events that can be generated by them.

The introduction of the separation condition enables a simple and efficient determination of the number of occurrences occurring in an interval I starting at the origin of the occurrence pattern as a function of the length of the interval. It can be determined, for example, by the following formula:

1 if Θ = e + ™ n (n _ω , ESF (((I - a _ω ) modp _ω ), Θ _ω ) otherwise The formula evaluates the individual event sequence elements separately, whereby due to the separation condition only the last period of each element has to be analyzed more precisely and therefore recursively evaluated. For the preceding periods, the limit may be used as the generated number of events. In the formula, mod represents the modulo operation that determines the remainder of the division. It is also conceivable to use descriptions in which the separation condition is not always met. This leads to a higher analysis effort, because of the elements whose occurrence patterns can overlap, several periods are to be analyzed separately.

The form of description can also be used, with minor adjustments, to represent minimally occurring number of events in intervals.

In the following the methods according to claims 13 to 19 are explained in more detail.

It enables an exact determination of the set of events originating from a task separately for each permissible interval length. The method enables a determination of the temporal density of the events originating from the task from the activations entering the task and the description of the control flow of the task. "Outbound events" may be activations of other tasks, access to resources such as memory and buses, or other actions on the system, parts of it, or the environment. Activations and events may preferably be described using the hierarchical event sequence model. A method is proposed for determining from the internal control flow of a task and the hierarchical event sequence entering this task the hierarchical event sequences emanating from this task. The hierarchical event sequence describes the possible temporal densities of the events. In the method according to the invention, the information about the temporal relationships is abstracted from the internal control flow of the task. This makes it possible to determine the cases of maximum occurrence patterns across all execution paths within the task. In the following a possible embodiment of the methodology, the event dependency analysis, will be described in detail.

A task is modeled by a control flow graph, which can contain both branches and loops. The individual nodes of the control flow graph can represent basic blocks. A "basic block" is a sequence of consecutive instructions and is characterized in that branching and the generation of events can only take place at the end of the basic block. Events are generated on certain excellent base blocks. Essential for the advantage of the analysis according to the invention is the existence of tasks which generate several events in one run. It is particularly advantageous if these events lead to activations of the same task or are otherwise in competition with each other for the same resource. The goal is to efficiently determine the possible temporal behavior of these events relative to one another from the control flow graph of the task.

The analysis consists of the following steps:

There is a step by step through the control flow graph of the task. At each step, an update is made of the event sequence (or sequences) emanating from the partial graph of the task that has already passed through and of additional event sequences described in more detail below. For this purpose, operations are described with which an outgoing event sequence of a control flow graph can be obtained from the outgoing event sequences of subgraphs, from which the control flow graph is composed. Also indicated are the event sequences for simple subgraphs consisting of a single node. It is with this information and the operations then it is possible to determine the outgoing event sequences for any control flow graphs.

If the control flow includes branches, they will be traversed separately. Within a branch, the outgoing event sequences and event sequences for each branch are described separately. The individual descriptions are combined when the different branches come together. The details of this method will be described in more detail below.

First, the analysis is described for tasks whose control flow contains no loops.

FIG. 2 illustrates a step by step execution of a task graph. The control flow graph represents the control data flow of a task. It consists of the basic blocks of the task and their activation or communication relationships. A basic block contains an execution section and is characterized in that it can only be activated as a whole and branches and activations other basic blocks or tasks only at the end of the basic block. The concrete execution of a task thus results from wandering through the control flow graph along the activation relationships of the individual basic blocks. Of the

Pass starts at a startup node of the task. This is activated by the events arriving in the task. At each step of the run, a follower node from an already analyzed node is considered. For branches, the different branches are processed separately.

Nodes that have several predecessor nodes are not processed until all predecessor nodes have been processed. The control flow graph is thus reconstructed step by step during the run. At each step of the iteration, another node is added to the already analyzed subgraph. added. This reconstruction need not be done in the procedure, it only determines the execution order of the nodes. In each step of the processing, the event stream resulting from the previous subgraph is determined. For this purpose, the information for the node itself, such as execution costs, for example in the form of calculation time, whether an event is generated, and the event streams determined for the predecessor nodes are used. Information from the other nodes or structure information about the partial graphs that have passed so far is no longer relevant. As basic operations for this step-by-step processing methods are needed to

1. to attach a node to an existing subgraph (concatenation operation) or

2. to reunite two (or more) sub-branches of the subgraph (union operation).

For these cases, calculation methods are now required to generate the corresponding information for the subgraph to be formed from the information available for the precursor subgraphs. "Information" is understood to mean the maximum and minimum event streams resulting from the subgraph and the event sequences required for their determination.

The event sequences are in particular the start event sequence, the end event sequence, the inside event sequence and the total event sequence. Not all event sequences are always needed. They are defined by the outcome of their event sequence analysis. The "start event sequence" describes, for each possible number of events, the cost involved in activating the first node of the event Subgraphs are needed to generate the number of events in question from the subgraph.

Conversely, looking back on the completion of the sub-node's end node, the "end event sequence" describes how much cost was last needed to generate a certain number of events.

The "inside event sequence" determines, for each possible number of events, the minimum cost needed in any run of the subgraph to generate that number of events. It corresponds to the resulting event stream of the subgraph.

The "total event sequence" describes, for each possible number of events, the minimum cost needed to pass through the subgraph from the start node activation to the final node completion. As the number of events increases, only monotonically increasing costs have to be considered. Are the costs to

For example, generating four events lower than generating three events also assumes the cost of four events for generation for the three events.

The sequences can be described, for example, efficiently in the form of an event sequence, advantageously a hierarchical event sequence (HES). In the case of the total event sequence (TS), the costs of a potential path s should preferably be determined by the subgraph, in which none

Events are generated, in addition to the event sequence are noted (TS = (a, Θ)). The total event sequence plays an important role in the consideration of loop constructs. Not only a maximum possible number of loop passes is taken into consideration, but also every possible number between the maximum and the minimum number of loop passes.

The smallest possible unit to be considered as it passes through the control flow graph is a single node. Each node of the control flow graph can itself be interpreted as a graph again. The node may be characterized by an initial start, end, in and total event sequence. There are two different possible initial sets of event sequences, depending on whether a node generates an event or not. The following are the initial event sequences for a node that generates an event: StS = {(∞, k, 1, e)}, ES = {(oo, 0,1, e)}, IS = {(oo , 0,1, e)} and TS = (k, (∞, k, l, e)).

StS represents the start event sequence, ES the end event sequence, IS the inner event sequence and TS the total event sequence, the value of k is the cost of the node. To determine the maximum event densities, the minimum execution cost of the node is required here. TS is described as a tuple from the minimum throughput costs even without event generation and the event sequence.

For a node that does not generate an event, the following initial event sequences result: StS = {}, ES = {}, IS = {} and TS = (k, {}). It should be noted that without violation of the general applicability, the generation of events occurs only at the end of a node. In order to build the event sequences for complex graphs stepwise from these sequences of events, methods are needed for the union of subgraphs (union operator) and for the concatenation of a node to a subgraph (concatenation operator).

In the following it will be shown how exclusively with the event sequences listed above and the two methods the event stream emanating from a control flow graph can be determined.

First, consider the case where the task is activated by only one event. Since each node can be considered as a subgraph, each step is the union of two subgraphs into a new one, which includes both subgraphs. The problem is thus reduced to the problem of how the event sequences of the subgraph can be used to determine the event sequences of the resulting subgraph.

The individual subgraphs may include different paths through the control flow graph in which the same number of events occur. The union of the subgraphs can lead to further additional paths. These additional paths can lead to different costs. The event sequences of the merged subgraph must cover the minimum and maximum costs, respectively, of the subgraphs and the additional paths resulting from the union.

In the concatenation of two sub-graphs A and B, the event sequences of the resulting sub-graph C are determined as follows. The start event sequence of C results from a combination of the start event sequence of A with a concatenation of the total event sequence of A with the start event sequence of B. The final event sequence of C is determined by merging the final event sequence of B with the concatenation of the final event sequence of A and the total event sequence of B.

The inner event sequence results from the stepwise union of three event sequences. These are, on the one hand, the inner event sequences of the subgraphs A and B and, on the other hand, an event sequence which results from the concatenation of the end event sequence of A with the start event sequence of B.

The total event sequence of C is just a concatenation of the total event sequences of A and B.

When subgraphs are combined, only the individual event sequences of one sub-graph are combined with the respectively corresponding event sequence of the other subgraph. So all start, end, total and internal event sequences are combined with each other. The resulting inner event sequence of the overall graph corresponds to the resulting event sequence of the overall graph.

For efficient implementation of the operations, it is advantageous if the hierarchical event sequences at least largely satisfy the separation condition.

In the following, a possible, concrete and efficient variant for the combining operation of two or more (hierarchical) event sequences will now be explained in more detail. It is explained using the hierarchical event streams, but it can also be applied in a simplified form to the simple event streams. Continue to be only the event sequences are considered at maximum event density and it is assumed in the explanations that all events also occur according to this maximum occurrence pattern. But this is no limitation. In the real system, events can also occur with a lesser temporal density, as long as the maximum or minimum densities of events specified by the event sequence are not exceeded or undershot. The resulting combined event sequence contains the maximum number of events that can be generated in each of the cost intervals

Unification operation incoming event sequences. The execution of the operation for the best possible event sequences follows analogously. In case the incoming event sequences satisfy the event stream property, the event sequence resulting from this embodiment of the merge operation also satisfies the event stream property. The merge operation thus receives this property.

The combination of two event sequences is carried out in the proposed embodiment by a stepwise

Determination of the event sequence, which dominates in each case. An event sequence dominates another event sequence if it can generate more events in the same interval. If it can generate the same number of events, then one of the two event sequences can be regarded as the dominant one. The full range of possible numbers of events that can be generated is split into individual subregions, each of which completely dominates a single incoming event sequence. These individual subsections are referred to below as "Dominierungsabschnitte". For each dominating section, the corresponding element can now be converted into the resulting event sequence from the respectively dominating incoming event sequence. The parameters, in particular the initial distance and the maximum number of events that can be generated, are It may be advantageous to adapt such that the events generated by these elements can occur only within the dominating section.

FIG. 3 illustrates the process for efficiently determining the doping sequence. First, for ease of illustration, only single simple event sequence elements are considered. These are each marked by a period and an initial distance. The function which specifies for an element the minimum (maximum) interval in which a certain number of events occur (= event function) can be described by a straight-line equation. The initial value of the straight line is the initial distance and the slope is given by the period. A comparison of two different event sequence elements of different event sequences is thereby reduced to stepwise minimum formation of two lines. There are two possible cases. Either there is an intersection between the lines or not. If no intersection exists, a straight line over the entire possible number of events forms the minimum and, consequently, the event sequence element that determines this straight line dominates the other element in all possible number of events. In this case, the resulting event sequence is formed only from this dominating element.

If there is an intersection between the lines, the domination changes. The resulting event sequence is then formed from at least two elements. These result from the elements dominating in the subsections, which are adapted to the individual dominating sections by adapting the initial distance and the maximum number of events that can be generated in a period. The first element is provided with a limit on the maximum number of events it can generate, so that only events up to the point of intersection are generated. The second element is provided with an initial distance that allows only event generation at or beyond the intersection. The limit of the second element is adjusted so that the total number of events that can be generated is not exceeded. As a result, the separation condition is retained in the resulting event sequence as well. An intersection occurs when one element has a smaller initial distance but a larger period than the other element. If event sequences consist of more than one element, corresponding straight lines result separately for the separation areas resulting from the individual elements. This can cause the domination to change several times. In the proposed embodiment of the operation, a separate event sequence element is inserted into the resulting event sequence for each dominating section. However, these can then be combined in part with exact or approximate compression methods. For example, if neighboring elements have the same period, they can be grouped into one element with that period. All such event sequence elements in the individual sections, which can lead to the same number of events, are always compared with one another. If event sequence elements are repeated periodically, this can lead to a repetitive change of domination. By way of example, the following simple event sequences are given: Θi = {(oo, 0, 200, e)}, Θ ₂ = {(∞, 0, 100, e)},

Θ ₃ = {(25, 0,1, e), (25, 1,1, e)} and Θ ₄ = {(12, 0, 1, e)}.

The domination changes in this example from the third event to the Dominierungsgrenze constantly between a

Element of Θ ₃ and an element of Θ ₄ . In order to be able to find clear dominions, such elements now become interconnected which result in the same number of events. For this, the number of affected elements of the involved event sequences are adapted to each other. This can be done, for example, by bringing the number of elements in all event sequences to the least common multiple of the element numbers of the individual event sequences. The number of elements of an event sequence is increased by increasing the period (for example, doubling) and, for compensation, the missing events are generated by additional elements. For example, at Θ ₄ , the

Number of elements increased to two by doubling the period to 24 and inserting an additional element with (24,12, l, e). The events for this event sequence are then no longer generated by an element, but alternately by the two elements. If the numbers of the affected elements of the different event sequences are brought to a common denominator, then the respective corresponding elements, which lead to the same number of events, can be directly compared with each other. The periods of the individual event sequence elements are irrelevant. For example, in the above example, the first elements each determine the odd number of event slots 1,3,5,7, ..., and the second elements the intervals of the even number of events 2,4,6, .... This is true at least after the adaptation of the element number and possible sorting of the elements according to increasing initial distance. For these elements, the domination intervals can now be determined separately and the corresponding event sequence elements inserted into the resulting event sequence. In the case of complex event sequences with, for example, several recursion levels, it is proposed to extend these to an identical structure in each case and then to combine them step by step via the dominance rules. The event sequences Θ ₃ and Θ ₄ listed above have an example following expansion:

Θ ₃ = {(25,0, l, e), (25, 1,1, e)} and Θ ₄ = {(24, 0, 1, e), (24, 12, 1, e)}. Figure 5 shows the domination graphs for these two event sequences. The resulting event sequence can be noted as follows:

Θ _r = {(∞, 0.50, {(24, 0.1, e)}), (co, 0, 11, {(25, 0, 1, e)}), (oo, 264, 39 , {(24,12, l, e)}), (∞, 1188, 50, Θ ₃ )}.

After simplification, the resulting event stream has the following description: Θ _r = {(∞, 0, 22, {(24, 0, 1, e), (25, 1, 1, e}), (oo, 264.78 , {(12, 0.1, e)}), (∞, 1188, 100, Θ ₃ )}

It may be that a line segment breaks off due to the limitation of the total number of events. In this case, one of the remaining straight lines dominates. In the example, this is the case for all event numbers from 100 events. In the section of the first 100 events, the first element of Θ ₃ dominates in the odd number of events and the second element of Θ ₄ in the case of the even number of events. There, after 11 events, the domination of the second element of Θ _{3 changes} . After 100 events, only the elements of Θ _{3 dominate} .

In the following, an exemplary embodiment for the concatenation operation is presented. It is mainly needed to determine the inside event sequence. In the variant embodiment for the merge operation, the elements of the involved event sequences were compared with each other separately. In concatenation, the elements of an event sequence are complemented by elements of the other event sequence. This leads to more combination possibilities for the individual event numbers. Many event numbers can be involved by each element of the th event sequences are generated at a corresponding supplement with a corresponding element of the other event sequence.

With the concatenation operator, the resulting event sequence contains only intervals that by definition always contain the interface between the event sequences in possible result intervals. The different combinations of elements lead to different minimum event numbers. For each combination, there is an initial distance that results from the sum of the initial distances of the two elements involved. The combinations can be continued at maximum in two directions periodically. Corresponding to the merging operation, only the combinations which lead to the same number of occurrences even if they are continued are compared with one another. This again results in possible domination sections. The combinations are compared in two dimensions, namely their initial distance and their period. If a combination can be continued periodically in both directions, it will be included twice in this comparison. If several combinations are identical in both values, any one can be selected. For the resulting event sequence, those combinations are not relevant that are at most equal to or worse than other combinations in both criteria. A combination with a shorter initial interval is better than one with a longer, one combination with a shorter period better than one with a longer one. Each combination is continued with the event sequence element that has the lower period since the initial distances within a combination are always the same. For the remaining combinations, as in the merge operation, the domino sections and intersections are again determined via the straight line equations, and from this the resulting event sequence elements are determined determines their initial distances and their limits. A special feature of the concatenation operation is that when a limitation of the number of events for an event sequence element has been reached, the combination can be continued by the corresponding event sequence element until its limitation has also been reached. Intermediate combinations, in which only part of their maximum possible events are included in both event sequence elements, are not relevant. If an event sequence can, for example, generate a maximum of five events and the event sequence combined with it, a maximum of eight events, then only combinations of the two event sequences are considered for the event numbers 2, 3, 4, 5, 6, in which case one of the two sequences is only an event generated. All other combinations, for example, a combination in which one

Event sequence two and an event sequence generates three events (intermediate combination) at equal or greater intervals and are therefore not relevant to the formation of the case of the maximum performance pattern.

The continuation only in the direction of the smallest period leads to smaller intervals for the same number of events, since the same initial distance is received. The operation will be explained below with reference to an example which is also shown in FIG. 4:

Θi = {(oo, 0.200, {(25.0, l, e), (25, l, l, e}) and Θ ₂ = {(∞, 0.100, {(24, 7.1, e), (24, 19, 1, e)).

Θi represents an end event sequence and Θ ₂ a start event sequence. Let ωi, i be the first event sequence element of Θi, COi ₁₂ the second event sequence element of Θi, ω _{2 /} i the first event sequence element of Θ ₂ and ω ₂ , ₂ the second event sequence element of Θ ₂ . At the concatenation of the two Event sequences results in an initial distance for two events, which is determined by the sum of the initial distances of both event sequences. For each of the event sequences involved, this is the smallest initial distance of all their event sequence elements. In the present example, this sieving amounts to and results from the event sequence elements ωi, i with initial distance zero and co _{2 /} i with initial distance sieve. If the event sequence elements are sorted, the respective first elements always result in this interval of two events.

This result leads to the event sequence elements (∞, 0, l, e) and (oo, 7, l, e) as an aperiodic beginning part of the resulting concatenated event sequence. The number of 3,5,7,9 ... events can be generated either by a combination of the event _{sequence elements} (o ₁ ₂ and ω ₂ , i or by a combination of the elements CO ₁₄ and ω ₂ , _2. Since both combinations of Each of the two involved event sequence elements can be continued periodically, resulting in a total of four possibilities 3,5,7,9, ... to generate events These possibilities are compared with each other via the parameters of initial distance and period and thus the dominating combinations are determined . In the present case this is the combination of the Ereignissequenzelemen- th C0i _{/ 2} and ω _2, i, which is periodically continued by the element ω _{2 /} i. Only if the limit is reached, the combination is continued by the other element, The number of events 4, 6, 8, 10, ... are assigned either by a combination of the event sequence elements ω _{i / 2} and ω _2/2 or by a co A combination of the elements ω _x , i and ω _{2 / i} achieved. In the second combination, to get to the corresponding number of events, one period is set to the initial distance of the Combination included. By including a period, the corresponding limit must be reduced by one in the further analysis. The following possible combination elements thus result (without limitation): (25,20, l, e), (24, 20,1, e), (25,25, l, e) and (24,24, l, e ). It dominates first the second combination. This results in the same period 24 for the elements which initially dominate, which allows a combination of these elements into a hierarchical event sequence element. In principle, such a summary is also possible with different periods up to the points at which one element "overhauls" the other, ie changes the order in which the elements generate events. Thus, without taking into account the limitation for the resulting event sequence, the event sequence elements (24, 8, 1, e) and (24, 20, 1, e) result. These can be summarized to the equivalent element (12,8, l, e). Taking into account the limitation and the resulting possibility of the periodic continuation of the combinations by the respective other subelement and taking into account their limitation, the event sequence {(∞, 0, 1, e), (oo, 7, 1, e ), (∞, 8, 98, qA), (oo, 1220, 200, Θ _B )} with the recursively embedded event sequences Θ _A = {(12, 0, 1, e)} and Θ _B = {(25, 0, 1, e), (25, 1, l, e)} as a result. As can be seen in the example, the embodiment of the concatenation operation enables the efficient determination of an output event sequence whose resulting descriptive complexity is limited and thus can be further processed efficiently.

One way of handling loops is to roll them out and then analyze the resulting graph with the presented methodology. It is possible to analyze the loop body in advance as a subgraph and to reduce it to its event sequences. These will be at the Analysis should then continue to concatenate with each other, and also a possible cancellation of the loop below the maximum number of iterations should be considered. However, due to the regular structure, the loop analysis can also be carried out with less effort by using the methods presented by exploiting the regularity of the structure and the occurrence patterns of events.

The procedure was described for the determination of maximum event sequences. However, it can also be used correspondingly for the determination of minimal or average event sequences. If a task is activated by several events, this can for example be modeled by a continued concatenation of the control flow graph of the task itself. Minimum separation distances and time limits can be included or an event sequence calling the task can be translated into a loop construction.

These methods can be realized with a computer program product and a computer.

LIST OF REFERENCE NUMBERS

τ _n task system τ task HES hierarchical event sequence

Θ hierarchical event sequence

Θ ¹ further hierarchical event sequence τ ¹ further task

I time interval ω hierarchical event sequence element p period a initial distance n limit

Θ ¹ recursively embedded hierarchical event sequence ω = (p, a, n, Θ ')

Claims

claims

1. Method for analyzing, in particular real-time analysis, a system, in particular a computer system, in which a set of different tasks (τ) is provided,

or

repeatedly generate events by requests to subcomponents of the systems,

and the other quantities and thus the other performance patterns described by them differ from each other.

2. The method of claim 1, wherein the elements are at least partially characterized by at least one distance a and a boundary n.

3. The method of claim 2, wherein the elements are partially characterized by a period.

4. The method of claim 3, wherein the limit specifies the number of occurrences of the occurrence pattern in a period of the element.

5. The method according to any one of the preceding claims, wherein the limitation is described by a number of events.

6. The method according to any one of claims 1 to 4, wherein the limitation is described by an interval length.

7. The method according to any one of the preceding claims, wherein at least one element is described by an initial distance, a limitation and a period.

The method of any one of the preceding claims, wherein some elements represent a single event.

9. Method according to one of the preceding claims, wherein the same elements are used on a plurality of hierarchy levels to describe the occurrence pattern represented by an element ω.

10. The method according to any one of the preceding claims, wherein the parts produced by the individual elements of the overall pattern emergence do not overlap for the greater part.

11. The method according to any one of the preceding claims, wherein the parts of the appearance pattern generated by the individual elements do not overlap.

12. The method according to claim 12, wherein the following formula is used to determine the number of events described by an amount θ of elements, occurring in an interval I:

ESF (I, Θ) _otherwise

13. Method for analyzing, in particular for real-time analysis, a system, in particular a computer system, in which a set of different tasks (τ) is provided,

or

repeatedly generate events by requests to subcomponents of the system,

where at least one task generates multiple events when activated,

wherein a step is provided in which from the occurrence patterns of the events determined for a plurality of contiguous subgraphs or nodes of the control flow graph, a further occurrence pattern for a further control flow graph comprising these subgraphs and nodes is determined and

for this determination at least one additional occurrence pattern of events of the subgraphs is used,

and

this additional occurrence pattern represents a possible occurrence pattern of events in time dependence on certain pass points of the subgraphs.

The method of claim 13, wherein one of the additional occurrence patterns of events to be considered is determined by passing an end node of the subgraph back in time.

15. A method according to claim 13 or 14, wherein one of the additional occurrence patterns of events to be considered is determined by traversing an initial node of the subgraph.

16. The method of claim 13, wherein one of the occurrence patterns to be considered represents, for each possible interval length, the maximum number of events generated within the subgraph in an interval of that length.

17. The method of claim 13, wherein one of the occurrence patterns to be considered for each possible interval length represents the maximum number of events generated within the subgraph in an interval of that length, and both the passing point of a start node and an end node within of the interval.

18. The method of claim 17, wherein at least in one step for a subgraph all occurrence patterns are determined according to claims 14 to 17.

19. The method according to any one of claims 13 to 18, wherein the occurrence patterns are described at least partially by one of the proposed in the claims 1 to 12 description options.

20. A computer programmer for analyzing the time response of complex systems with program code means for carrying out the method according to one of the preceding claims.