CN102158357A - Method for analyzing performances of single closed fork-join queuing network based on horizontal decomposition - Google Patents
Method for analyzing performances of single closed fork-join queuing network based on horizontal decomposition Download PDFInfo
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- CN102158357A CN102158357A CN201110073362XA CN201110073362A CN102158357A CN 102158357 A CN102158357 A CN 102158357A CN 201110073362X A CN201110073362X A CN 201110073362XA CN 201110073362 A CN201110073362 A CN 201110073362A CN 102158357 A CN102158357 A CN 102158357A
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Abstract
The invention discloses a method for analyzing performances of a single closed fork-join queuing network based on horizontal decomposition. The method is characterized in that a horizontal decomposition method is utilized to decompose a single closed fork-join queuing network model into a plurality of product-form queuing network models, thus an average value analysis method can be used to quickly solve the model, and the horizontal decomposition is only carried out on a queuing network comprising nested fork-joint operations once without recursive decomposition like a layer decomposition method, thereby greatly reducing the computational complexity, improving the efficiency that a computer computes and analyzes the single closed fork-join queuing network model, and promoting the computational performance.
Description
Technical field
The present invention relates to queuing network performance evaluation field, mainly is the closed bifurcated of a kind of single class based on horizontal decomposition-compile queuing network method for analyzing performance.
Background technology
Queuing network (Queueing Network) model is a kind of system performance analysis method of classics, it describes a software and hardware resources with a service centre (Service Center), and whole system can be regarded the network that several service centres form according to certain composition of relations as.Service centre can be divided into two types of formation type and time lagged types: formation type service centre is made up of a formation and several servers, and server is used for executable operations, and formation then is used for buffer memory and waits for the request of serving; And time lagged type service centre is mainly used in the simulation delay operation.Network of queues's model can be divided into open model (Open Model) and closed type model (Closed Model) again according to the loadtype difference.
Queueing network has portfolio effect preferably between complexity and accuracy, be widely used in the performance evaluation of various computer software and hardware system.Yet along with the appearance of technology such as parallel computation, Distributed Calculation, simple queueing network can't be applicable to the performance evaluation of this type of scale complex system.A kind of queueing network that comprises bifurcated-compile (Fork-Join) operation is widely used in the performance evaluation of systems such as parallel computation, Distributed Calculation and workflow management.Bifurcated-integration operations can be used to describe the parallel processing scene: a request (or being called task) will be broken down into the plurality of sub task after arriving the bifurcated running node, and these subtasks can be by different service centre's parallel processings; And after the integration operations node must wait for that relevant subtask is all complete, their result is aggregated into a new request send to next service centre.Bifurcated-integration operations makes such queueing network can't use the mode of product form (Product-Form) to calculate, thereby has increased the difficulty of such model analysis, particularly for the network of closed type.
At present, about the exact algorithm of bifurcated-compile queueing network only based on the analytical method of Markov chain (Markov Chains), but such algorithm only is applicable to the model that scale is less.Therefore, adopt approximate analytical method usually for large-scale bifurcated-compile queueing network.And most methods all is to utilize a kind of level to decompose the method for (Hierarchical Decomposition).This method at first resolves into multi-level sub-network with large-scale queueing network, and each sub-network is represented bottom-up then each sub-network model of finding the solution respectively with the relevant service centre of a load in the layer network thereon.If one comprises
NThe closed bifurcated of single class of individual request-compile queueing network to be divided into by the level decomposition method
LLayer, every layer comprises 1 sub-network, then need find the solution for each sub-network
NInferior (request number from 1 to
NSituation), and whole network needs to find the solution at least
N L Individual closed queuing network model.Therefore, use the analytical method of decomposing to have higher computation complexity for large-scale bifurcated-compile queueing network based on level.
Summary of the invention
The present invention is directed to the existing in prior technology defective, proposed the closed bifurcated of a kind of single class-compile queueing network's method for analyzing performance based on horizontal decomposition.
In order to solve the problems of the technologies described above, technical scheme of the present invention may further comprise the steps:
1), sets request number N according to the load scale of system, and obtain D service time in the historical record of corresponding computational resource to a class request only being arranged and comprise in the system of bifurcated-integration operations
iDescribed system is set up single class closed queuing network model in computer, corresponding service centre of each computational resource wherein will request number N and D service time of each service centre
iTwo input parameters as this model;
2) computer decomposes the model usage level of described foundation, with the parallel processing of bifurcated-between compiling
The subtask decompose obtain 1 trunk and
The queuing network of individual branch product type;
3) count D service time of N and each service centre according to described system request
i, use the mean value analytical method to calculate the throughput of system of closed trunk, and the response time of each service centre;
4), use the mean value analytical method to calculate other with the throughput of system of described trunk request arriving rate as other branch
The response time of each service centre in the individual branch;
5) response time of each service centre that calculates according to step 3) and step 4) is according to each service centre's response time of recomputating in trunk and each branch;
6) determining step 4) the longest response time, if the trunk of selecting in step 3) has the longest response time, then the selection before the explanation is correct, flow process finishes; Otherwise the branch that the response time is the longest is chosen as trunk, and decomposes original model again, returns step 3) then and re-executes, and has the longest response time up to the trunk of selecting;
Described trunk is closed queuing network's model; The described open queuing network's model that branches into.
As possibility, described step 2) in, definite method of trunk is the average queue length for each service centre
A rational initial value is provided
Thereby, estimate response time of each subtask, and the subtask execution route that the response time is the longest is set at trunk; Described
NBe the sum of asking in closed queuing network's model,
KSum for service centre in closed queuing network's model.
As possibility, use in the described closed queuing network model
When estimating the average queue length of each service centre, the response time of each service centre
Can calculate by following formula:
Described
Be the queue length of request due in,
It is the formation average length.
As possibility, the response time of described trunk and described each branch
Can calculate by following formula:
Described
Be the B of branch
iThe service centre's number that comprises.
As possibility, other parameter of described service centre is based on that response time of described throughput of system and described each service centre calculates.
The effect that the present invention is useful is:
By the horizontal decomposition method, can be with the closed bifurcated of a single class-compile the queueing network that several product types are resolved in queueing network, thus can use the mean value analytical method to find the solution this model apace.Separate for maximum the demands of model after each decomposition
N B Inferior, and if use traditional level decomposition method, the subsystem after each decomposes all needs to find the solution
NInferior.In real system,
NValue be far longer than usually
N B Also only need carry out one time horizontal decomposition for the queuing network that comprises nested bifurcated-integration operations, and do not need as the level decomposition method, to carry out the decomposition of recurrence, greatly reduce computation complexity, improve calculating, the analysis list class closure bifurcated-compile the efficient of queueing network of computer, promoted calculated performance.
Description of drawings
Fig. 1 horizontal decomposition schematic diagram;
Fig. 2 is based on the closed bifurcated of the single class of horizontal decomposition-compile queueing network to find the solution flow process.
Embodiment
The invention will be described further below in conjunction with drawings and Examples:
The present invention at first sets up single class closed queuing network model, the wherein corresponding service centre of each computational resource to the system that a class request is only arranged and comprise bifurcated-integration operations.Analyze D service time that two required input parameters of this model are respectively request number N and each service centre
iRequest number N can set D service time of service centre according to the system load scale
iCan obtain in the historical record by corresponding computational resource.Then the computer usage level method of decomposing is with a closed bifurcated of single class-the compile queueing network that some product types are resolved in queueing network.As shown in Figure 1, one comprises 2 couples of bifurcated-integration operations (F
1-J
1And F
2-J
2) closed model 1 obtaining after decomposing of single class closed queuing network model usage level and two open models 2 and 3.Wherein, closed model 1 is by operation F
1-J
1Trunk (comprising task S2, S3, S4 and S6) and F
1-J
1Service centre in addition (comprising S1 and S9) forms; Open model 2 is by F
2-J
2Branch (S5) form; Open model 3 is by operation F
1-J
1Branch's (comprising task S7 and S8) form.Trunk is the branch that has the longest response time in the parallel processing subtask.Therefore, for bifurcated-compile queueing network, its overall performance is determined by trunk.Because operation F such as the request arriving rate of task S5
2Throughput, the operation S7 request arriving rate equal task F
1Throughput, so the throughput that can use closed model 1 is as the input of open model 2 and 3 promptly
With
Yet the response time of each service centre is unknown before model solution, can't determine that also which branch is a trunk.The present invention uses following steps to estimate the response time of each branch, thereby finds possible trunk:
1), the service centre beyond itself and the bifurcated-integration operations is formed the queueing network of a closure for each branch.If
NBe the sum of asking in the master mould,
KBe service centre's sum of this closed queuing network's model,
D i Be the service time of each service centre.
2), use for above-mentioned closed model
Estimate the average queue length of each service centre, then the response time of each service centre
Can be calculated as follows:
Wherein,
Be the queue length of request due in,
It is the formation average length.
3), can calculate the response time of each branch according to The above results
:
Wherein,
Be the B of branch
iThe service centre's number that comprises.
4) from all branches, select have the longest response time as trunk.
Fig. 2 has described based on the closed bifurcated of the single class of horizontal decomposition-compile queueing network to find the solution flow process:
1. to the closed bifurcated of single class-compiling queueing network's usage level decomposes, thus obtain 1 closure and
The queueing network of the product type of individual opening.
2. according to known system request number
NWith the service time of each service centre
D i , use the MVA method to calculate the throughput of system of closed model, and the response time of each service centre.
3. with the throughput of system of closed model request arriving rate, thereby can use the MVA method to calculate other as other open model
The response time of each service centre in the individual open model.
4. according to the response time of each service centre of calculating gained, recomputate each branch response time of (comprising trunk) according to prior art.
5. if the trunk of selecting in the first step has the longest response time, then the selection before the explanation is correct, finds the solution flow process and finishes.
Otherwise, the branch that the response time is the longest is chosen as trunk, and decomposes original model again, returns for second step then to re-execute, and has the longest response time up to the trunk of selecting.
Pass through above-mentioned steps, can approximate calculation go out the closed bifurcated of single class-compile the throughput of system of queueing network and the response time of each service centre, other parameter (as utilance, queue length etc.) of service centre can be calculated based on above 2 values.
The above only is a preferred implementation of the present invention; should be pointed out that for those skilled in the art, without departing from the inventive concept of the premise; can also make some improvements and modifications, these improvements and modifications also should be considered within the scope of protection of the present invention.
Claims (5)
1. the closed bifurcated of single class of horizontal decomposition compiles the analytical method of queuing network performance, it is characterized in that, may further comprise the steps:
1), sets request number N according to the load scale of system, and obtain D service time in the historical record of corresponding computational resource to a class request only being arranged and comprise in the system of bifurcated-integration operations
iDescribed system is set up single class closed queuing network model in computer, corresponding service centre of each computational resource wherein will request number N and D service time of each service centre
iTwo input parameters as this model;
2) computer decomposes the model usage level of described foundation, with the parallel processing of bifurcated-between compiling
The subtask decompose obtain 1 trunk and
The queuing network of individual branch product type;
3) count D service time of N and each service centre according to described system request
i, use the mean value analytical method to calculate the throughput of system of closed trunk, and the response time of each service centre;
4), use the mean value analytical method to calculate other with the throughput of system of described trunk request arriving rate as other branch
The response time of each service centre in the individual branch;
5) response time of each service centre that calculates according to step 3) and step 4), recomputate each the service centre's response time in trunk and each branch;
6) determining step 4) the longest response time, if the trunk of selecting in step 3) has the longest response time, then the selection before the explanation is correct, flow process finishes; Otherwise the branch that the response time is the longest is chosen as trunk, and decomposes original model again, returns step 3) then and re-executes, and has the longest response time up to the trunk of selecting;
Described trunk is closed queuing network's model; The described open queuing network's model that branches into.
2. the closed bifurcated of single class of horizontal decomposition according to claim 1 compiles the analytical method of queuing network performance, it is characterized in that described step 2) in, definite method of trunk is the average queue length for each service centre
A rational initial value is provided
Thereby, estimate response time of each subtask, and the subtask execution route that the response time is the longest is set at trunk; Described
NBe the sum of asking in closed queuing network's model,
KSum for service centre in closed queuing network's model.
3. the closed bifurcated of single class of horizontal decomposition according to claim 2 compiles the analytical method of queuing network performance, it is characterized in that, uses in the described closed queuing network model
When estimating the average queue length of each service centre, the response time of each service centre
Can calculate by following formula:
Described
Be the queue length of request due in, described
It is the formation average length.
4. the closed bifurcated of single class of horizontal decomposition according to claim 3 compiles the analytical method of queuing network performance, it is characterized in that the response time of described trunk and described each branch
Can calculate by following formula:
Described
Be the B of branch
iThe service centre's number that comprises.
5. the analytical method of compiling the queuing network performance according to the closed bifurcated of single class of any described horizontal decomposition of claim 1 ~ 4, it is characterized in that other parameter of described service centre is to calculate by the response time of described throughput of system and described each service centre.
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| CN101110841A (en) * | 2007-08-24 | 2008-01-23 | 清华大学 | Mixed strategy method for optimizing aggregative indicator under service oriented architecture SOA |
| WO2008021470A2 (en) * | 2006-08-17 | 2008-02-21 | Dolby Laboratories Licensing Corporation | Transient analysis of packet queuing loss in a broadcast network |
| CN101557608A (en) * | 2009-05-14 | 2009-10-14 | 北京航空航天大学 | Node identity protection method of mobile wireless sensor network on basis of message time delay condition |
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| WO2008021470A2 (en) * | 2006-08-17 | 2008-02-21 | Dolby Laboratories Licensing Corporation | Transient analysis of packet queuing loss in a broadcast network |
| CN101110841A (en) * | 2007-08-24 | 2008-01-23 | 清华大学 | Mixed strategy method for optimizing aggregative indicator under service oriented architecture SOA |
| CN101557608A (en) * | 2009-05-14 | 2009-10-14 | 北京航空航天大学 | Node identity protection method of mobile wireless sensor network on basis of message time delay condition |
Non-Patent Citations (1)
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Application publication date: 20110817 Assignee: Tianjin Shenzhou General Data Co., Ltd. Assignor: Zhejiang University Contract record no.: 2014330000025 Denomination of invention: Method for analyzing performances of single closed fork-join queuing network based on horizontal decomposition Granted publication date: 20130619 License type: Common License Record date: 20140303 |
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