CN114374698A - Ingress-based automatic NodePort pool switching system - Google Patents

Ingress-based automatic NodePort pool switching system Download PDF

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CN114374698A
CN114374698A CN202210279758.8A CN202210279758A CN114374698A CN 114374698 A CN114374698 A CN 114374698A CN 202210279758 A CN202210279758 A CN 202210279758A CN 114374698 A CN114374698 A CN 114374698A
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access
service
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CN114374698B (en
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张卫平
米小武
李显阔
张伟
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Global Digital Group Co Ltd
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L67/00Network arrangements or protocols for supporting network services or applications
    • H04L67/01Protocols
    • H04L67/10Protocols in which an application is distributed across nodes in the network
    • H04L67/1001Protocols in which an application is distributed across nodes in the network for accessing one among a plurality of replicated servers
    • H04L67/1004Server selection for load balancing
    • H04L67/1008Server selection for load balancing based on parameters of servers, e.g. available memory or workload
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F9/00Arrangements for program control, e.g. control units
    • G06F9/06Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
    • G06F9/44Arrangements for executing specific programs
    • G06F9/455Emulation; Interpretation; Software simulation, e.g. virtualisation or emulation of application or operating system execution engines
    • G06F9/45533Hypervisors; Virtual machine monitors
    • G06F9/45558Hypervisor-specific management and integration aspects
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L67/00Network arrangements or protocols for supporting network services or applications
    • H04L67/01Protocols
    • H04L67/10Protocols in which an application is distributed across nodes in the network
    • H04L67/1001Protocols in which an application is distributed across nodes in the network for accessing one among a plurality of replicated servers
    • H04L67/1036Load balancing of requests to servers for services different from user content provisioning, e.g. load balancing across domain name servers
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F9/00Arrangements for program control, e.g. control units
    • G06F9/06Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
    • G06F9/44Arrangements for executing specific programs
    • G06F9/455Emulation; Interpretation; Software simulation, e.g. virtualisation or emulation of application or operating system execution engines
    • G06F9/45533Hypervisors; Virtual machine monitors
    • G06F9/45558Hypervisor-specific management and integration aspects
    • G06F2009/45562Creating, deleting, cloning virtual machine instances
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F9/00Arrangements for program control, e.g. control units
    • G06F9/06Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
    • G06F9/44Arrangements for executing specific programs
    • G06F9/455Emulation; Interpretation; Software simulation, e.g. virtualisation or emulation of application or operating system execution engines
    • G06F9/45533Hypervisors; Virtual machine monitors
    • G06F9/45558Hypervisor-specific management and integration aspects
    • G06F2009/45591Monitoring or debugging support
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F9/00Arrangements for program control, e.g. control units
    • G06F9/06Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
    • G06F9/44Arrangements for executing specific programs
    • G06F9/455Emulation; Interpretation; Software simulation, e.g. virtualisation or emulation of application or operating system execution engines
    • G06F9/45533Hypervisors; Virtual machine monitors
    • G06F9/45558Hypervisor-specific management and integration aspects
    • G06F2009/45595Network integration; Enabling network access in virtual machine instances

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Abstract

The invention provides an Ingress-based automatic NodePort pool switching system, which comprises an external access module, an Ingress rule module, an Ingress control module, a monitoring module and a rear-end service module, wherein the rear-end service module is used for providing a Pod, the external access module is used for submitting an access application, the Ingress rule module is used for recording an access rule, the Ingress control module forwards the access application to a corresponding Pod according to the access rule, the monitoring module is used for monitoring the Pod operation state of the rear-end service module, and the access rule in the Ingress rule module is automatically updated according to the operation state of the Pod; the system can process a large number of Pod service access problems in the container cloud, and enables a user to access the most appropriate Pod by automatically changing the binding relationship between the Ids of the NodePort and the Pod.

Description

Ingress-based automatic NodePort pool switching system
Technical Field
The present disclosure relates generally to the field of container clouds, and more particularly to an Ingress-based automatic nodoport pool switching system.
Background
The container cloud is a very popular service framework at present, can provide lightweight and easy-to-transfer service, and the Pod is a collection of a plurality of containers, and for safety, the Pod service is not directly exposed to an external network, and meanwhile, the id of the Pod can be changed all the time due to frequent creation and logout, and the Pod service is often accessed in a reverse proxy manner, while Ingress is an efficient reverse proxy manner, and when Ingress is used, an effective switching system is needed to switch the accessed Pod, so that the access efficiency is improved, and the stability of the system is guaranteed;
now, many switching systems have been developed, and through a lot of search and reference, it is found that the existing authorization systems, such as the systems disclosed in publication nos. KR100950744B1, KR101828424B1, CN111181968B and KR101454678B1, use a listener configured to monitor whether the configuration file corresponding to the Pod changes; setting an initial trigger variable for triggering Pod and executing synchronous operation of the configuration file; the monitor synchronizes the monitoring result of the configuration file to the APIServer; and the label selector built in the Kubelet component does not wait for whether the synchronization operation between the configuration file of the last version of the current configuration file and the Pod is completed or not, and injects the current configuration file into the Pod to complete the synchronization operation between the Pod and the current configuration file and restore the initial trigger variable. However, in the system, the access efficiency of the system needs to be improved in order to optimize specific Pod handover.
Disclosure of Invention
The invention aims to provide an Ingress-based automatic NodePort pool switching system,
the invention adopts the following technical scheme:
an Ingress-based automatic NodePort pool switching system comprises an external access module, an Ingress rule module, an Ingress control module, a monitoring module and a back-end service module, wherein the external access module is used for providing a NodePort port for a user to access the system, the back-end service module is used for providing a Pod for service, the Ingress rule module is used for recording the binding relationship between an access domain name and the Id of the Pod, the monitoring module is used for monitoring the Id change of the Pod, and the Ingress control module is used for realizing the flow forwarding from the NodePort to the Pod according to the binding relationship between the access domain name and the Id of the Pod;
a user submits an access application containing an access domain name through the NodePort port, one or one access domain name corresponds to one Pod service, one Pod service comprises a plurality of pods running at different nodes, and the Ingress control module selects one Pod for switching;
the Ingress control module calculates the viscosity index of the j-th Pod service accessed by the user through the i-th NodePort port according to the historical access data
Figure DEST_PATH_IMAGE001
Figure 749777DEST_PATH_IMAGE002
Wherein,
Figure DEST_PATH_IMAGE003
indicating the number of times the user selects the jth Pod service,
Figure 860559DEST_PATH_IMAGE004
indicating the number of times the user selects the i < th > NodePort port for access,
Figure DEST_PATH_IMAGE005
representing the number of times that the user accesses the jth Pod service through the ith NodePort port;
the Ingress control module calculates the candidate indexes of all the Pods in the jth Pod service
Figure 741927DEST_PATH_IMAGE006
Figure DEST_PATH_IMAGE007
Wherein,
Figure 363402DEST_PATH_IMAGE008
in order to be the first conversion factor,
Figure DEST_PATH_IMAGE009
in order to be the second conversion coefficient,
Figure 30137DEST_PATH_IMAGE010
the function is a network communication cost estimation function for estimating the network delay cost from the ith NodePort port to the kth Pod in the jth Pod service,
Figure DEST_PATH_IMAGE011
represents the load capacity of the node where the kth Pod of the jth Pod service is located,
Figure 891914DEST_PATH_IMAGE012
representing the number of times that the user obtains a service by accessing a kth Pod in a jth Pod service;
the Ingress control module selects a to-be-selected index
Figure DEST_PATH_IMAGE013
The largest Pod is used as the object of flow forwarding;
further, the monitoring module monitors a new Pod created in the node and a cancelled old Pod and obtains an update event, and the Ingress control module matches the update event to obtain three types of synchronization tasks: the Ingress rule module updates binding data of Id of the Pod according to the synchronous task;
furthermore, the Ingress control module generates link data of Id of a user, namely NodePort, Pod and Pod, when the user accesses the network, and the Ingress control module obtains historical access data according to the link data statistics and stores the historical access data in a database;
further, the first conversion coefficient
Figure 650792DEST_PATH_IMAGE014
The calculation formula of (2) is as follows:
Figure DEST_PATH_IMAGE015
wherein,
Figure 630949DEST_PATH_IMAGE016
the average load of all nodes in the whole system in a fixed time,
Figure DEST_PATH_IMAGE017
the time average value from each NodePort port to all nodes is obtained;
further, the second conversion coefficient
Figure 870301DEST_PATH_IMAGE018
The calculation formula of (2) is as follows:
Figure DEST_PATH_IMAGE019
wherein,
Figure 214563DEST_PATH_IMAGE020
for intermediate times, for all of the whole system
Figure DEST_PATH_IMAGE021
The median value over a fixed time.
The beneficial effects obtained by the invention are as follows:
the system adopts the Ingress frame to carry out anti-proxy, can solve the problem that the Id of the Pod changes due to drift, can also easily deal with the problem of creating a new Pod, and selects the most appropriate Pod for flow forwarding according to the historical access data of the user and the running state of the Pod in each node under the current state when the Pod accessed by the user is switched, so that the access efficiency is improved, and the stability of the system is ensured.
For a better understanding of the features and technical content of the present invention, reference should be made to the following detailed description of the invention and accompanying drawings, which are provided for purposes of illustration and description only and are not intended to limit the invention.
Drawings
FIG. 1 is a schematic view of the overall structural framework of the present invention;
FIG. 2 is a schematic diagram illustrating an Ingress rule change flow according to the present invention;
FIG. 3 is a diagram illustrating readable data in an update time pool according to the present invention;
FIG. 4 is a schematic diagram of a rule package according to the present invention;
FIG. 5 is a schematic diagram of chain data accessed by a user according to the present invention.
Detailed Description
The following is a description of embodiments of the present invention with reference to specific embodiments, and those skilled in the art will understand the advantages and effects of the present invention from the disclosure of the present specification. The invention is capable of other and different embodiments and its several details are capable of modification in various other respects, all without departing from the spirit and scope of the present invention. The drawings of the present invention are for illustrative purposes only and are not intended to be drawn to scale. The following embodiments will further explain the related art of the present invention in detail, but the disclosure is not intended to limit the scope of the present invention.
The first embodiment.
The embodiment provides an Ingress-based automatic node port pool switching system, which, with reference to fig. 1, includes an external access module, an Ingress rule module, an Ingress control module, a monitoring module, and a back-end service module, where the external access module is configured to provide a node port for a user to access the system, the back-end service module is configured to provide a Pod for service, the Ingress rule module is configured to record a binding relationship between an access domain name and an Id of the Pod, the monitoring module is configured to monitor Id change of the Pod, and the Ingress control module is configured to implement traffic forwarding from the node port to the Pod according to the binding relationship between the access domain name and the Id of the Pod;
a user submits an access application containing an access domain name through the NodePort port, one or one access domain name corresponds to one Pod service, one Pod service comprises a plurality of pods running at different nodes, and the Ingress control module selects one Pod for switching;
the Ingress control module calculates the viscosity index of the j-th Pod service accessed by the user through the i-th NodePort port according to the historical access data
Figure 273786DEST_PATH_IMAGE022
Figure DEST_PATH_IMAGE023
Wherein,
Figure 4107DEST_PATH_IMAGE024
indicating the number of times the user selects the jth Pod service,
Figure DEST_PATH_IMAGE025
indicating the number of times the user selects the i < th > NodePort port for access,
Figure 816074DEST_PATH_IMAGE026
representing the number of times that the user accesses the jth Pod service through the ith NodePort port;
the Ingress control module calculates the candidate indexes of all the Pods in the jth Pod service
Figure DEST_PATH_IMAGE027
Figure 347550DEST_PATH_IMAGE028
Wherein,
Figure DEST_PATH_IMAGE029
in order to be the first conversion factor,
Figure 48396DEST_PATH_IMAGE030
in order to be the second conversion coefficient,
Figure DEST_PATH_IMAGE031
the function is a network communication cost estimation function for estimating the network delay cost from the ith NodePort port to the kth Pod in the jth Pod service,
Figure 408839DEST_PATH_IMAGE032
represents the load capacity of the node where the kth Pod of the jth Pod service is located,
Figure DEST_PATH_IMAGE033
representing the number of times that the user obtains a service by accessing a kth Pod in a jth Pod service;
the Ingress control module selects a to-be-selected index
Figure 888362DEST_PATH_IMAGE034
The largest Pod is used as the object of flow forwarding;
the monitoring module monitors a new Pod created in a node and a cancelled old Pod and obtains an update event, and the Ingress control module matches the update event to obtain three types of synchronous tasks: the Ingress rule module updates binding data of Id of the Pod according to the synchronous task;
the Ingress control module generates link data of Id of a user, namely NodePort-Pod, when the user accesses the network every time, and the Ingress control module obtains historical access data according to the link data statistics and stores the historical access data in a database;
the first conversion coefficient
Figure DEST_PATH_IMAGE035
The calculation formula of (2) is as follows:
Figure 279154DEST_PATH_IMAGE036
wherein,
Figure DEST_PATH_IMAGE037
the average load of all nodes in the whole system in a fixed time,
Figure 234341DEST_PATH_IMAGE038
the time average value from each NodePort port to all nodes is obtained;
the second conversion coefficient
Figure DEST_PATH_IMAGE039
The calculation formula of (2) is as follows:
Figure 618049DEST_PATH_IMAGE040
wherein,
Figure DEST_PATH_IMAGE041
for intermediate times, for all of the whole system
Figure 705740DEST_PATH_IMAGE042
The median value over a fixed time.
Example two.
The embodiment includes the whole content of the first embodiment, and provides an Ingress-based automatic nodoport pool switching system, which includes an external access module, an Ingress rule module, an Ingress control module, a monitoring module, and a back-end service module, where the back-end service module is configured to provide a Pod, the external access module is configured to submit an access application, the Ingress rule module is configured to record an access rule, the Ingress control module forwards the access application to a corresponding Pod according to the access rule, the monitoring module is configured to monitor a Pod operation state of the back-end service module, and the access rule in the Ingress rule module is automatically updated according to the operation state of the Pod;
the access rule binds an access domain name and the Id of the Pod, a user submits an access application in the external access module in a mode of inputting the domain name, and the Ingress control module acquires the Id of the Pod corresponding to the domain name and then forwards the access flow to the corresponding Pod;
with reference to fig. 2, since a node where a Pod works in a container cloud changes, and an Id of the Pod also changes, the monitoring module monitors the change of the Id of the Pod in real time, and feeds back the change information to the Ingress rule module, and the Ingress rule module updates the Id of the access domain name and the bound Pod according to the change information, and the specific process includes the following steps:
s1, the monitoring module establishes monitoring connection in each main node;
s2, the monitoring module sets a trigger thread, and when a logout Pod or a creation Pod appears on the master node, the event is written into an update event pool;
s3, the control process reads the update event from the update event pool, and when the update event is read, a synchronization task is added into the synchronization queue;
s4, the task processing thread acquires the synchronous task from the synchronous queue periodically;
s5, the task processing thread judges whether the synchronous task is reloaded, if yes, the step is jumped to S6, and if not, the step is jumped to S7;
s6, the Ingress rule module reloads and switches the recorded access rules;
s7, the Ingress rule module binds the access domain name and the Id of the new Pod again, constructs POST data and uploads the POST data to the pairing reading unit;
s8, the Ingress control module acquires corresponding Id information of Pod in the paired reading unit when receiving the access application;
in the process, a control process, a task processing thread, an update event pool and a synchronous queue all belong to the Ingress control module;
in step S2, the triggering thread corresponding to each master node records the number of Pod running on the master node and the Id of the corresponding Pod, and when the Pod decreases in number due to logout or increases in number due to creation, the triggering thread starts a query unit, and the query unit compares the Id of the existing Pod with the Id of the recorded Pod to find the logged Pod or the created Pod, and then writes the event into an update pool, and updates the Id of the recorded Pod at the same time, where it is noted that the update event includes only two types of events, namely logout Pod and creation Pod;
with reference to fig. 3, the update event pool is provided with a pairing unit, the pairing module performs content scanning on a previous logout Pod event and a subsequent created Pod event, when the function descriptions of the pods in the events are consistent, the two events are paired to form readable data, for the logout Pod event, a pairing time is set, when a pairable created Pod event does not occur within the pairing time, the logout Pod event is separately formed into readable data, for the created Pod event, when there is no previous logout Pod event in the update event pool, the created Pod event is directly and separately formed into readable data;
when the control process in step S3 reads the update events in the update event pool, only the three types of readable data can be read;
in step S5, the paired synchronization task corresponding to the logout Pod event and the creation Pod event and the synchronization task corresponding to the individual logout Pod event need to be reloaded, and the synchronization task corresponding to the individual creation Pod event does not need to be reloaded;
with reference to fig. 4, the Ingress rule module includes a plurality of rule packages, each rule package records one or more access domain names pointing to the same service name and ids of a plurality of bound Pod, the ids of the pods in the same rule package are ids of pods distributed in different nodes but providing the same service, and the rule packages with similar types are integrated into a cluster;
the Ingress control module switches and selects an Id of a Pod from Ids of a plurality of pods in a corresponding rule packet according to NodePort submitted with an access application and IP information of a user to forward the flow;
with reference to fig. 5, when accessing Pod services, a user can submit an access application through different nodoports, and access different Pod services, and select one Pod of the Pod services for final access, where each access generates link data of Id of the user, nodoport-Pod, and the Ingress control module obtains historical access data according to the link data statistics, and selects an Id of a proper Pod for the next access of the user according to the historical access record data;
for the same user, the historical access data comprises:
Figure DEST_PATH_IMAGE043
indicating the number of times the user selects the jth Pod service;
Figure 438073DEST_PATH_IMAGE044
indicating the times of the user selecting the ith NodePort port to access;
Figure DEST_PATH_IMAGE045
indicating the number of times that the user accesses the jth Pod service through the ith NodePort port;
Figure 755922DEST_PATH_IMAGE046
indicating the number of times that the user obtains the service by accessing the kth Pod in the jth Pod service;
the Ingress control module calculates the viscosity index of the j-th Pod service accessed by the user through the i-th NodePort port according to the historical access data
Figure DEST_PATH_IMAGE047
Figure 694053DEST_PATH_IMAGE048
The Ingress control module obtains the load capacity of a node where a kth Pod of a jth Pod service is located, and uses the load capacity
Figure DEST_PATH_IMAGE049
Showing that the Ingress control module calculates the index to be selected of each Pod
Figure 351431DEST_PATH_IMAGE050
Figure DEST_PATH_IMAGE051
Wherein,
Figure 848140DEST_PATH_IMAGE052
in order to be the first conversion factor,
Figure DEST_PATH_IMAGE053
for the second conversion factor, the specific value is obtained by actual testing,
Figure 856547DEST_PATH_IMAGE054
the function is a network communication cost estimation function and is used for estimating the network delay cost from the ith NodePort port to the kth Pod in the jth Pod service;
the Ingress control module selects a to-be-selected index
Figure DEST_PATH_IMAGE055
The largest Pod is used as the object of flow forwarding;
the second conversion coefficient
Figure 267544DEST_PATH_IMAGE056
The acquisition method comprises the following steps:
testing the time from each NodePort port to all nodes and obtaining the average value as
Figure DEST_PATH_IMAGE057
Then, then
Figure 294274DEST_PATH_IMAGE056
Comprises the following steps:
Figure 306093DEST_PATH_IMAGE058
wherein,
Figure DEST_PATH_IMAGE059
intermediate times, as in the whole systemIs provided with
Figure 270638DEST_PATH_IMAGE060
A median value over a fixed time;
the first conversion coefficient
Figure DEST_PATH_IMAGE061
The calculation formula of (2) is as follows:
Figure 816151DEST_PATH_IMAGE062
wherein,
Figure DEST_PATH_IMAGE063
the average load of all nodes in the whole system in a fixed time is obtained.
The disclosure is only a preferred embodiment of the invention, and is not intended to limit the scope of the invention, so that all equivalent technical changes made by using the contents of the specification and the drawings are included in the scope of the invention, and further, the elements thereof can be updated as the technology develops.

Claims (5)

1. An Ingress-based automatic NodePort pool switching system is characterized by comprising an external access module, an Ingress rule module, an Ingress control module, a monitoring module and a back-end service module, wherein the external access module is used for providing a NodePort port for a user to access the system, the back-end service module is used for providing a Pod for service, the Ingress rule module is used for recording the binding relationship between an access domain name and the Id of the Pod, the monitoring module is used for monitoring the Id change of the Pod, and the Ingress control module is used for realizing the flow forwarding from the NodePort to the Pod according to the binding relationship between the access domain name and the Id of the Pod;
a user submits an access application containing an access domain name through the NodePort port, one access domain name corresponds to one Pod service, one Pod service comprises a plurality of pods running at different nodes, and the Ingress control module selects one Pod for switching;
the Ingress control module calculates the viscosity index of the j-th Pod service accessed by the user through the i-th NodePort port according to the historical access data
Figure 610261DEST_PATH_IMAGE001
Figure 664804DEST_PATH_IMAGE002
Wherein,
Figure 45714DEST_PATH_IMAGE003
indicating the number of times the user selects the jth Pod service,
Figure 428285DEST_PATH_IMAGE004
indicating the number of times the user selects the i < th > NodePort port for access,
Figure 234567DEST_PATH_IMAGE005
representing the number of times that the user accesses the jth Pod service through the ith NodePort port;
the Ingress control module calculates the candidate indexes of all the Pods in the jth Pod service
Figure 533830DEST_PATH_IMAGE006
Figure 806679DEST_PATH_IMAGE007
Wherein,
Figure 66759DEST_PATH_IMAGE008
in order to be the first conversion factor,
Figure 99569DEST_PATH_IMAGE009
in order to be the second conversion coefficient,
Figure 4071DEST_PATH_IMAGE010
the function is a network communication cost estimation function for estimating the network delay cost from the ith NodePort port to the kth Pod in the jth Pod service,
Figure 306876DEST_PATH_IMAGE011
represents the load capacity of the node where the kth Pod of the jth Pod service is located,
Figure 913307DEST_PATH_IMAGE012
representing the number of times that the user obtains a service by accessing a kth Pod in a jth Pod service;
the Ingress control module selects a to-be-selected index
Figure 61391DEST_PATH_IMAGE013
The largest one Pod is the subject of traffic forwarding.
2. The system as claimed in claim 1, wherein the monitoring module monitors a new Pod created in a node and a revoked old Pod and obtains an update event, and the Ingress control module matches the update event to obtain three types of synchronization tasks: and the Ingress rule module updates binding data of the Id of the Pod according to the synchronous task.
3. The system as claimed in claim 2, wherein the Ingress control module generates a link data of Id of user-nodoport-Pod at each access of the user, and the Ingress control module obtains historical access data according to the link data statistics and stores the historical access data in the database.
4. The method as claimed in claim 3, wherein the Ingress-based automatic NodePort pool switchingSystem characterized in that said first conversion coefficient
Figure 820400DEST_PATH_IMAGE014
The calculation formula of (2) is as follows:
Figure 294107DEST_PATH_IMAGE015
wherein,
Figure 700684DEST_PATH_IMAGE016
the average load of all nodes in the whole system in a fixed time,
Figure 527826DEST_PATH_IMAGE017
the time average of each nodoport port to all nodes.
5. The Ingress-based automatic NodePort pool switching system as claimed in claim 4, wherein said second conversion factor
Figure 265975DEST_PATH_IMAGE018
The calculation formula of (2) is as follows:
Figure 35217DEST_PATH_IMAGE019
wherein,
Figure 163710DEST_PATH_IMAGE020
for intermediate times, for all of the whole system
Figure 919176DEST_PATH_IMAGE021
The median value over a fixed time.
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