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CN113726672B - Method and system for self-adjusting flow control threshold - Google Patents

Method and system for self-adjusting flow control threshold Download PDF

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Publication number
CN113726672B
CN113726672B CN202011148739.9A CN202011148739A CN113726672B CN 113726672 B CN113726672 B CN 113726672B CN 202011148739 A CN202011148739 A CN 202011148739A CN 113726672 B CN113726672 B CN 113726672B
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flow control
control threshold
value
period
now
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CN113726672A (en
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袁海
张继东
宋文慧
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Tianyi Digital Life Technology Co Ltd
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Tianyi Digital Life Technology Co Ltd
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L47/00Traffic control in data switching networks
    • H04L47/10Flow control; Congestion control

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  • Computer Networks & Wireless Communication (AREA)
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Abstract

The invention provides a method and a system for self-adjusting a flow control threshold. The method comprises the following steps: determining the deviation degree of the time consumption of the previous period of the current period compared with the standard time consumption; calculating a flow control threshold calculation value of a next cycle of the current cycle in response to the degree of deviation being greater than a predetermined time-consuming deviation threshold; and if the flow control threshold value calculated value is larger than the upper extreme value of the flow control threshold value or smaller than the lower extreme value of the flow control threshold value, setting the upper extreme value or the lower extreme value as the flow control threshold value of the next period, otherwise, setting the flow control threshold value calculated value as the flow control threshold value of the next period.

Description

Method and system for self-adjusting flow control threshold
Technical Field
The present invention relates to the field of IT and software development, and more particularly, to a method and system for flow control threshold self-adjustment.
Background
The current various bus and gateway products basically have the flow control according to the modes of message quantity, connection number, flow quantity, current concurrent message quantity and the like, and the flow control threshold values are all preset fixed values, so that the flow control cannot be automatically adjusted according to the busyness degree of the providing service end.
In the chinese patent application "method and system for dynamically adjusting flow control threshold" (CN 104408656 a), it is proposed to adjust flow control of API according to failure rate (failure amount/request amount=failure rate) so as to achieve failure rate reduction. The failure rate is a flow control adjustment based on the service result, namely the data after the failure occurs, and belongs to post feedback. The method described in the patent application automatically adjusts the flow control threshold, but the method automatically adjusts after the occurrence of the fault, and cannot sense the running state of the service, guarantee the service and avoid the service backlog fault in advance.
In the chinese patent application "a flow control method and apparatus" (CN 107454004 a), dynamic flow control is proposed according to average response time, and flow control is achieved according to a preset degradation rate, that is, response time is too long, and the reduction of the modulation amount is achieved directly according to the modulation amount multiplied by the ratio. The patent sets a new call volume threshold = 60% + reference value + flow control threshold of 20% + (t+2) cycles for lengthy call volume according to a time-consuming growth ratio, where the ratio is set as needed. Therefore, in this patent application, the degradation rate is preset, dynamic change cannot be performed based on the analysis result of the historical operation data and the like, and only the decrease of the call volume can be realized, but the increase of the call volume cannot be realized according to the actual situation.
Therefore, although the current flow control method can automatically adjust the flow control according to the busyness of the service end by dynamically adjusting the flow control threshold, the historical factors, the current factors, the expected factors, the limiting factors and the like of the flow control are not considered, the flow control is not accurate enough or the algorithm is too complex to influence the execution efficiency, in order to realize the enrichment of the flow control means and the accuracy of the flow control effect, the flow control method is more suitable for the actual situation of service provision, the service provision is ensured to be more stable, and the improved flow control threshold self-adjusting method is hoped to be provided.
Disclosure of Invention
This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter.
The invention forms the data with the dimensions of time consumption, call quantity, failure quantity, time period and the like through the service call record in the database, calculates according to the data, and the ideal time consumption and the ideal service quantity of the corresponding time period of each flow control index. And meanwhile, calculating the call quantity of each preset time consumption in the A+2 period through interval time consumption records in the cache, triggering to calculate a new flow control threshold according to the ideal call quantity and the call quantity of time consumption amplification abnormality when the call quantity exceeding the preset time consumption threshold appears and the amplification reaches 50%, and taking effect in the A+2 periods after the time consumption amplification abnormality period A. Thus, the aims of time-consuming dynamic flow control and threshold self-adjustment are achieved, and the service provision is ensured to be more stable.
According to one aspect of the present invention, there is provided a method for self-adjusting a flow control threshold, the method comprising:
determining the deviation degree of the time consumption of the previous period of the current period compared with the standard time consumption;
calculating a flow control threshold calculation value of a next cycle of the current cycle in response to the degree of deviation being greater than a predetermined time-consuming deviation threshold; and
and if the flow control threshold value calculated value is larger than the upper extreme value of the flow control threshold value or smaller than the lower extreme value of the flow control threshold value, setting the upper extreme value or the lower extreme value as the flow control threshold value of the next period, otherwise, setting the flow control threshold value calculated value as the flow control threshold value of the next period.
According to one embodiment of the present invention, the determining the deviation degree of the time consumption of the previous cycle of the current cycle from the standard time consumption further includes:
determining a standard offset rate SDr of the time elapsed for the previous cycle of the current cycle, the standard offset rate SDr being calculated by the following formula:
SDr=1-(T now -T stand )/T stand
wherein T is now Is time consuming of the last period, T stand Is a standard time consuming.
According to a further embodiment of the invention, the predetermined time consuming deviation threshold is 5%.
According to a further embodiment of the present invention, calculating a flow control threshold calculation value for a next cycle of the current cycle further comprises:
obtaining reasonable time consumption and reasonable traffic of the next period from a feature library;
time consuming T based on the last cycle now Traffic B now Flow control threshold C now And calculating a flow control threshold calculation value C of the next period by using the reasonable time consumption RT and the reasonable traffic RQ of the next period result
According to a further embodiment of the invention, the feature library is formed by:
average time-consuming data of each time period is collected, and the data is abstracted into a time period list CT: [ CT ] 1 ,CT 2 ,...CT N ]Each of which is CT i Containing time-consumingTraffic volume, traffic success rate;
processing the time period list CT and deriving respective reasonably time-consuming, traffic volume [ CT ] based on the time period list CT i ,RT i ,RQ i ]The method comprises the steps of carrying out a first treatment on the surface of the And
storing and dynamically updating the respective reasonable time consumption, traffic volume [ CT ] of the time period list CT i ,RT i ,RQ i ]。
According to a further embodiment of the invention, the processing comprises: for each CT in the time period list CT i And (3) cleaning, screening and processing the service success rate, removing records without traffic, removing data exceeding a limit value, carrying out the highest and lowest success rates in the residual data above a preset success rate threshold, and averaging the rest values.
According to a further embodiment of the invention, the time consumption T based on the last period now Traffic B now Flow control threshold C now And calculating a flow control threshold calculation value C of the next period by using the reasonable time consumption RT and the reasonable traffic RQ of the next period result Further comprises:
calculating a time-consuming expected deviation rate RDr of the next period, wherein
RDr=1-(T now -RT)/RT, and
calculating a flow control threshold calculation value C based on the following formula result
C result =(B now *a+C now *b+RQ*c)*(SDr*d+RDr*e)
Wherein rdr=1- (T) now -RT)/RT, a+b+c=1 and d+e=1.
According to a further embodiment of the invention, the upper extremum of the flow control threshold is 150% of the flow control threshold standard value and the lower extremum of the flow control threshold is 50% of the flow control threshold standard value.
According to another aspect of the present invention, there is provided a system for self-adjusting a flow control threshold, the system comprising:
a database configured to record business data; and
a flow control threshold adjustment unit configured to:
determining the deviation degree of the time consumption of the previous period of the current period compared with the standard time consumption;
calculating a flow control threshold calculation value of a next cycle of the current cycle in response to the degree of deviation being greater than a predetermined time-consuming deviation threshold; and
and if the flow control threshold value calculated value is larger than the upper extreme value of the flow control threshold value or smaller than the lower extreme value of the flow control threshold value, setting the upper extreme value or the lower extreme value as the flow control threshold value of the next period, otherwise, setting the flow control threshold value calculated value as the flow control threshold value of the next period.
According to one embodiment of the present invention, the determining the deviation degree of the time consumption of the previous cycle of the current cycle from the standard time consumption further includes:
determining a standard offset rate SDr of the time elapsed for the previous cycle of the current cycle, the standard offset rate SDr being calculated by the following formula:
SDr=1-(T now -T stand )/T stand
wherein T is now Is time consuming of the last period, T stand Is a standard time-consuming one,
the upper extreme value of the flow control threshold value is 150% of the standard value of the flow control threshold value, the lower extreme value of the flow control threshold value is 50% of the standard value of the flow control threshold value, and
calculating a flow control threshold calculation value for a next cycle of the current cycle further includes:
obtaining reasonable time consumption RT and reasonable traffic RQ of the next period from a feature library;
calculating a time-consuming expected deviation rate RDr of the next period, wherein
RDr=1-(T now -RT)/RT, and
calculating a flow control threshold calculation value C based on the following formula result
C result =(B now *a+C now *b+RQ*c)*(SDr*d+RDr*e)
Wherein a+b+c=1 and d+e=1, b now Is the traffic of the last period, C now Is the flow control threshold of the previous cycle.
Compared with the scheme in the prior art, the method and the system for self-adjusting the flow control threshold value have the following advantages:
(1) The flow control threshold self-adjusting method based on the service response average time-consuming amplification algorithm has the advantages of automatic adjustment of the threshold and dynamic flow control;
(2) The algorithm has comprehensive factors, is simple, convenient and efficient to realize, forms a periodic flow control adjustment mechanism, and is more accurate;
(3) Enriching the flow control method, providing accurate, timely and effective flow control means for the operation of the fitting service;
(4) The automatic adjustment of the flow control threshold value is realized, and the controllable, adjustable and automatic application is realized according to the set amplification algorithm.
These and other features and advantages will become apparent upon reading the following detailed description and upon reference to the associated drawings. It is to be understood that both the foregoing general description and the following detailed description are explanatory only and are not restrictive of aspects as claimed.
Drawings
So that the manner in which the above recited features of the present invention can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only certain typical aspects of this invention and are therefore not to be considered limiting of its scope, for the description may admit to other equally effective aspects.
Fig. 1 is an exemplary architecture diagram of a system for fluidic threshold self-adjustment according to one embodiment of the present invention.
Fig. 2 is a flow chart of a method for generating a feature library storing parameters for flow control threshold self-tuning according to one embodiment of the invention.
Fig. 3 is a flow chart of a method for flow control threshold self-adjustment according to one embodiment of the invention.
Fig. 4 is a schematic flow chart of a time-consuming amplitude of change algorithm for self-tuning of flow control thresholds according to one embodiment of the invention.
Detailed Description
The features of the present invention will become more apparent from the detailed description set forth below when taken in conjunction with the drawings.
Fig. 1 is an exemplary architecture diagram of a system 100 for flow control threshold self-adjustment according to one embodiment of the invention. As shown in fig. 1, the system 100 of the present invention includes: a database 101 and a flow control threshold adjustment unit 102, wherein the flow control threshold adjustment unit 102 comprises a data acquisition module 103, a data processing module 104, a data storage module 105 and a flow control threshold calculation module 106. The database 101 records service data. The data acquisition module 103 scans from the database the average time-consuming data for each time period, abstracts the data into a list, and the list references are the daily time period, the corresponding time consumption and the service success rate. The data processing module 104 calculates respective reasonable time consumption and traffic volume based on the time periods according to the abstracted time period list. The data storage module 105 stores these reasonably time consuming, traffic volumes as amplitude of change algorithm reference values, forms a feature library, and maintains dynamic updates. In the case where the deviation of the time consumption of the previous cycle (a cycle) from the standard time consumption is greater than the predetermined time consumption deviation threshold (e.g., 5%), the flow control threshold calculation module 106 calculates the flow control threshold of the next cycle using the time consumption variation amplitude algorithm according to the previous cycle (a cycle) and the related data of the standard time consumption, the standard flow control, etc., and the reasonable time consumption and the reasonable traffic of the a+2 cycle acquired from the feature library.
Those skilled in the art will appreciate that the system of the present invention and its various modules may be implemented in either hardware or software, and that the various modules may be combined or combined in any suitable manner.
Fig. 2 is a flow chart of a method 200 for generating a feature library storing parameters for flow control threshold self-tuning according to one embodiment of the invention. The method begins at step 201 with the data acquisition module 103 scanning from the database 101The average time consumption data of each time period is obtained, the data is abstracted into a list, and the list reference forms a time period list CT (Cycle time: cycle time) of daily time period, corresponding time consumption and service success rate 1 ,CT 2 ,...CT N ]Each of which is CT i Contains time consumption, traffic volume and service success rate.
In step 202, the data processing module 104 calculates, for each CT in the time period list CT i And (3) cleaning, screening and processing the service success rate, such as eliminating record without service volume, removing data exceeding a limit value (such as setting the time consumption to be 50% compared with the basic time consumption, namely exceeding the limit value and not participating in calculation), and then carrying out the highest and lowest success rate in the residual data above a preset success rate threshold (for example, 99.99%), and averaging the rest values. From this, the CT is derived i Reasonable time-consuming value RTi (real time: reasonable time-consuming, the service in the value has the characteristics of high success rate, stability, etc.), and the CT is obtained in the same way i Reasonable value RQ of traffic i (Reasonable quantity: reasonable amount, the in-value traffic has the characteristics of high success rate, stability, etc.), thereby forming respective reasonable time-consuming, traffic volume based on time period CT, i.e. [ CT ] i ,RT i ,RQ i ]。
In step 203, the data storage module 105 stores the resulting time period CT-based respective reasonable time consuming, traffic [ CT ] i ,RT i ,RQ i ]And storing the characteristic library as a variation amplitude algorithm reference value, forming a characteristic library, and storing dynamic update.
Fig. 3 is a flow chart of a method 300 for flow control threshold self-adjustment according to one embodiment of the invention. The method begins at step 301 with the flow control threshold calculation module 106 determining a degree of deviation of the elapsed time of the previous cycle from the current cycle from the standard elapsed time. For example, the degree of deviation may be based on a standard deviation rate of time elapsed for the previous cycle.
In step 302, in the case where the determined deviation degree is greater than the predetermined time-consuming deviation threshold, the flow control threshold calculation module 106 takes out related data such as the previous period and the standard time consumption, the standard flow control, and the like, and obtains reasonable time consumption and reasonable traffic of the next period from the feature library. For example, the flow control threshold calculation process is triggered if the time-consuming standard deviation rate of the last cycle is greater than 5%. Further, the flow control threshold calculation process may be triggered, for example, by determining that the time consuming values of the last two cycles have changed.
In step 303, the flow control threshold calculation module 106 calculates a flow control threshold calculation value for the next cycle based on the time elapsed, the traffic volume, the flow control threshold for the previous cycle, and the reasonable time elapsed and the reasonable traffic volume for the next cycle, an example of a time elapsed change magnitude algorithm used in this calculation process is further described in fig. 4.
In step 304, the flow control threshold calculation module 106 compares the flow control threshold calculation value with the limit value of the flow control threshold, if the flow control threshold calculation value is greater than the upper limit value of the flow control threshold or less than the lower limit value of the flow control threshold, the upper limit value or the lower limit value is set as the flow control threshold of the next cycle, otherwise, the flow control threshold calculation value is set as the flow control threshold of the next cycle. For example, the upper extremum of the flow control threshold may be preset to 150% of the flow control threshold standard value, and the lower extremum of the flow control threshold may be preset to 50% of the flow control threshold standard value.
Fig. 4 is a schematic flow chart of a time-consuming amplitude of change algorithm for self-tuning of flow control thresholds according to one embodiment of the invention.
As shown in fig. 4, the threshold standard deviation SDr of the a period can be calculated according to the following formula (1):
SDr=1-(T now -T stand )/T stand (1)
wherein T is now Is the time consumption value of A period, T stand Is a preset standard time consuming.
The threshold expected deviation rate RDr of the a+2 period can be calculated according to the following formula (2):
RDr=1-(T now -RT i )/RT i (2)
where RT is the reasonable consumption value of the a+2 cycles obtained from the feature library.
The root is then triggered in the case of a threshold standard deviation SDr > 5% for the A periodThe flow control threshold C of the A+2 period is calculated according to the following formula (3) resultt
C result =(B now *a+C now *b+RQ*c)*(SDr*d+RDr*e) (3)
Wherein B is now Is the traffic value of A period, C now Is the flow control threshold for the a period, RQ is a reasonable traffic value for the a+2 period obtained from the feature library, where a+b+c=1 and d+e=1 (e.g., a=40%, b=30%, c=30%, d=70%, e=30%), where the value of a, b, c, d, e can be preset empirically and can be adjusted as needed.
In the calculation of C result Then, it is combined with C stand Comparison is made in which C stand Is a preset standard threshold value, if C result >C stand The actual flow control threshold C applied to the a+2 cycle is calculated as follows:
if C result ≤C stand The actual flow control threshold C applied to the a+2 cycle is calculated as follows:
table 1 below shows, as an example, a table in which flow control thresholds applied to a+2 cycles are calculated from related data of a cycle (the previous cycle of the current cycle) and standard time consumption, standard flow control, etc., and reasonable time consumption and reasonable traffic of a+2 cycle (the next cycle of the current cycle) acquired from a feature library:
table 1: flow control threshold calculation example
As can be seen from Table 1, standard time T stand 300, standard flow control threshold C stand 10000, the predetermined time-consuming deviation threshold is 5%, the upper extremum of the flow control threshold is 15000, and the lower extremum of the flow control threshold is 5000. For example, when the current period is the 2 nd period (when a=1), the standard deviation rate of the time consumption of the 1 st period is found to be larger than the preset time consumption deviation threshold value, namely SDr =17% > 5%, thereby triggering calculation and obtaining the calculation result (namely C) of the 3 rd period (namely A+2 period) result ) 2733.333333, and the calculation result is lower than the lower extreme value, the lower extreme value is set as the flow control threshold value of the 3 rd period (i.e. 5000). When the current cycle is the 8 th or 12 th cycle (at this time a=7 or 11), the standard deviation rate (67% or 100%) of the time consumption of the 7 th or 11 th cycle is found to be greater than the predetermined time consumption deviation threshold value by 5%, so as to trigger the calculation and obtain the calculation result of the 9 th or 13 th cycle as 7350 or 11365.07143, and the calculation result is between the upper extreme value and the lower extreme value, and the calculation result is set as the flow control threshold value of the 9 th or 13 th cycle (namely as 7350 or 11365). When the current period is the 17 th period (at this time a=16), the standard deviation rate (133%) of the time consumption of the 16 th period is found to be greater than the predetermined time consumption deviation threshold by 5%, so that the calculation is triggered and the calculation result of the 18 th period is 16752.825, and the calculation result is higher than the upper extremum, and the upper extremum is set as the flow control threshold of the 18 th period (i.e. 15000).
Therefore, the flow control threshold based on time-consuming change can be obtained, and meanwhile, service protection is carried out on the service provider based on time-consuming reaction, namely, service calling is properly increased to improve service experience and support amount when service processing efficiency is high, and service calling can be reasonably controlled to be reduced when service processing efficiency is low, so that basic service provision and power-assisted service provision recovery are guaranteed, and service calling impact is reduced.
What has been described above includes examples of aspects of the claimed subject matter. It is, of course, not possible to describe every conceivable combination of components or methodologies for purposes of describing the claimed subject matter, but one of ordinary skill in the art may recognize that many further combinations and permutations of the claimed subject matter are possible. Accordingly, the disclosed subject matter is intended to embrace all such alterations, modifications and variations that fall within the spirit and scope of the appended claims.

Claims (10)

1. A method for self-adjusting a flow control threshold, the method comprising:
determining the time consumption T of the previous period of the current period now And standard time consumption T stand Degree of deviation of the phase ratio;
based on the time consumption T of the last cycle in response to the degree of deviation being greater than a predetermined time consumption deviation threshold now Traffic B now Flow control threshold C now And calculating a flow control threshold value C of the next period of the current period by reasonable time consumption RT and reasonable traffic RQ of the next period result The method comprises the steps of carrying out a first treatment on the surface of the And
if the flow control threshold value is calculated to be C result The upper extreme value or the lower extreme value is set as the flow control threshold value of the next period if the upper extreme value or the lower extreme value is larger than the upper extreme value or smaller than the lower extreme value of the flow control threshold value, otherwise, the flow control threshold value is calculated to be C result Set as the flow control threshold for the next cycle.
2. The method of claim 1, wherein the time-consuming T of the last cycle of the current cycle is determined now And standard time consumption T stand The degree of deviation of the phase ratio further includes:
determining the time consumption T of the previous period of the current period now The standard deviation rate SDr is calculated by the following formula:
SDr=1-(T now -T stand )/T stand
3. the method of claim 2, wherein the predetermined time-consuming deviation threshold is 5%.
4. The method of claim 2, wherein the reasonable time consumption RT and the reasonable traffic RQ for the next cycle are obtained from a feature library.
5. The method of claim 4, wherein the feature library is formed by:
average time-consuming data of each time period is collected, and the data is abstracted into a time period list CT: [ CT ] 1 ,CT 2 ,...CT N ]Each of which is CT i Contains time consumption, traffic and service success rate, wherein i is an integer between 1 and N;
processing the time period list CT and deriving for each CT of the time period list CT i Reasonable time-consuming RT of (1) i Reasonable traffic RQ i The method comprises the steps of carrying out a first treatment on the surface of the And
storing and dynamically updating each CT for the time period list CT i Reasonable time-consuming RT of (1) i Reasonable traffic RQ i
6. The method of claim 5, wherein the processing comprises: for each CT in the time period list CT i And (3) cleaning, screening and processing the service success rate, removing records without traffic, removing data exceeding a limit value, carrying out the highest and lowest success rates in the residual data above a preset success rate threshold, and averaging the rest values.
7. The method of claim 2, wherein the time elapsed T based on the last period now Traffic B now Flow control threshold C now And calculating a flow control threshold calculation value C of the next period by using the reasonable time consumption RT and the reasonable traffic RQ of the next period result Further comprises:
calculating a time-consuming expected deviation rate RDr of the next period, wherein
RDr=1-(T now -RT)/RT, and
calculating a flow control threshold calculation value C based on the following formula result
C result =(B now *a+C now *b+RQ*c)*(SDr*d+RDr*e)
Wherein a+b+c=1 and d+e=1.
8. The method of claim 1, wherein the upper extremum of the flow control threshold is 150% of a flow control threshold standard value and the lower extremum of the flow control threshold is 50% of a flow control threshold standard value.
9. A system for self-adjusting a flow control threshold, the system comprising:
a database configured to record business data; and
a flow control threshold adjustment unit configured to:
determining the time consumption T of the previous period of the current period now And standard time consumption T stand Degree of deviation of the phase ratio;
based on the time consumption T of the last cycle in response to the degree of deviation being greater than a predetermined time consumption deviation threshold now Traffic B now Flow control threshold C now And calculating a flow control threshold value C of the next period of the current period by reasonable time consumption RT and reasonable traffic RQ of the next period result The method comprises the steps of carrying out a first treatment on the surface of the And
if the flow control threshold value is calculated to be C result The upper extreme value or the lower extreme value is set as the flow control threshold value of the next period if the upper extreme value or the lower extreme value is larger than the upper extreme value or smaller than the lower extreme value of the flow control threshold value, otherwise, the flow control threshold value is calculated to be C result Set as the flow control threshold for the next cycle.
10. The system of claim 9, wherein the time-consuming T of the last cycle of the current cycle is determined now And standard time consumption T stand The degree of deviation of the phase ratio further includes:
determining the time consumption T of the previous period of the current period now The standard deviation ratio SDr of (2) is determined byThe formula:
SDr=1-(T now -T stand )/T stand
the upper extreme value of the flow control threshold value is 150% of the standard value of the flow control threshold value, the lower extreme value of the flow control threshold value is 50% of the standard value of the flow control threshold value, and
calculating a flow control threshold value C of the next period of the current period result Further comprises:
obtaining reasonable time consumption RT and reasonable traffic RQ of the next period from a feature library;
calculating a time-consuming expected deviation rate RDr of the next period, wherein
RDr=1-(T now -RT)/RT, and
calculating a flow control threshold calculation value C based on the following formula result
C result =(B now *a+C now *b+RQ*c)*(SDr*d+RDr*e)
Where a+b+c=1 and d+e=1.
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