CN105743980A - Constructing method of self-organized cloud resource sharing distributed peer-to-peer network model - Google Patents

Abstract

The invention relates to a self-organized model constructing method of a cloud resource sharing peer-to-peer network, a distributed peer-to-peer network for short. The topology structure of the distributed peer-to-peer network is constructed through adoption of a space division concept. Physically closed cloud noses are self-organized. A reachable routing table is extended. The cloud peer-to-peer network which takes data as a core and is equipped with performances such as low delay and extensibility is realized. According to the method, in a large scale cloud resource distributed sharing environment, cloud node information is managed in real time, rapid resource positioning is carried out to the computing resource demand of each user, and an inquiring result is returned. Compared with the prior art, the method has the advantages that the method has clear average cloud resource inquiring delay advantage, the computing capabilities of the nodes are utilized fully, the actual performance of the cloud computing application is satisfied, and the method has wide application prospects in cloud resource sharing aspects.

Description

A kind of cloud resource-sharing distributed p 2 p model construction method of self-organizing

Technical field

The present invention relates to a kind of computer distribution type peer-to-peer network technical field, particularly to the cloud resource-sharing distributed p 2 p model construction method of a kind of self-organizing.

Background technology

Traditional distributed peer-to-peer network strategy can not shake down under cloud application demand.Hardware resource is probably " rare " resource, is no longer reproducible shared file；Available cloud resource is dynamically change, supplying inquiry on the resource information backup on cloud node to other node and unwise, because substantial amounts of renewal expense can be brought.For another example, the server resource in cloud peer-to-peer network is high stability, generally can work long hours so that need not excessively worry the dynamic change of node topology；The computing capability of cloud node, available memory space, the handling capacity of network broadband is all significantly increased, and has the storage capacity of relatively powerful Resource TOC information and neighbor information, but the search performance of cloud resource requires also higher.

Classical peer-to-peer network based on distributed hashtable DHT (distributedhashtables).Such as Chord and Kademlia, can quickly position the resource of dispersion storage, but resource is by, while disperseing storage to reach optimization collocation, causing its actual physical location of node adjacent to be in logic likely to far apart, the communication with low jumping figure is not meant to must be low latency.And also result in resource itself management difficulty, it is impossible to be directly used in solve cloud application faced by problem.By contrast, the peer network architecture of mixed model, not only can effectively utilize the isomerism of node, it is achieved shorter query latency, reduce its network overhead.And some local area datas can be processed more concentratedly.

Summary of the invention

The present invention be directed to now cloud peer-to-peer network Problems existing used, it is proposed that the cloud resource-sharing distributed p 2 p model construction method of a kind of self-organizing, it is ensured that the computational resource requirements of each user is carried out fast resource location and returns Query Result.

The technical scheme is that the cloud resource-sharing distributed p 2 p model construction method of a kind of self-organizing, specifically include following steps:

1) network is divided into two-layer distributed frame: ground floor, and the close cloud node rendezvous of physics, to collectively forming cloud cluster, filters out a Centroid in each cloud node cluster, and this Centroid is responsible for and is safeguarded other ordinary nodes in oneself cloud cluster；The second layer, the Centroid set of N number of cloud cluster, the Centroid information of 2 times of square logical reach of record, constitute the distributed p 2 p structure with trunk function, each Centroid is all each responsible for a region of search S in management distributed p 2 p_{[Start, End]}, Start, End is that this responsible search volume of cloud node starts mark and terminates mark respectively, it is reduced to S, it is expressed as the search volume that current cloud node is responsible for, stores the directory information of data object in its region of search, and response is for the inquiry request of data object in the region of search；

2) cloud node adds and leaves:

Cloud node adds: new cloud node is intended to add cloud peer-to-peer network, notice is sent firstly the need of to the Centroid on adjacent distributions formula core network, calculate oneself position in a network, find new node cloud cluster of optimum low latency in each Centroid, send to the Centroid of this cluster and add request, Centroid response is submitted its cloud nodal information to Centroid, just can be joined in this cloud cluster after adding request；

Cloud node leaves: the inefficacy of partial node or leave two kinds of situations, if the ordinary node of a cloud cluster lost efficacy or left, only need to update the cloud Resource TOC information on corresponding cluster centers node on peer-to-peer network；If cluster centers node normally leaves network, it is necessary to specify new Centroid, replicate cloud Resource TOC information and the routing iinformation updating peer-to-peer network；If cluster centers node catastrophic failure, that cloud Resource TOC information also will be lost, and its search volume cluster centers node that will front be continued reclaims, and other nodes in its cloud cluster are also required to rejoin network；

3) routing table optimization: on the basis of Chord routing table algorithm, retains known node information, is called up to node route list, obtains up to the collection of node from query manipulation；It is update to expand routing table in inquiry request: when node receives a certain inquiry request, can find in up to routing table than Chord routing table nodal distance object identifier closer to node quote, in the way of message iteration, forwarding inquiries is asked to nearest up to node, and increase in former routing table this closer to the information up to node；

4) network divides: along with a large amount of cloud nodes add or the growth of directory information data on cloud node, the cloud cluster that Centroid performance in distributed p 2 p is gradually reduced is repartitioned, mark off a part of cloud node, form new cloud cluster, and be responsible for the search volume of part；This network partition process comprises two parts, the division of cloud node cluster and the division of catalogue data,

A: node assemblage classification, step is as follows:

First, it is assumed that each cloud cluster set is distributed on virtual ring in whole distributed p 2 p, in the direction of the clock, the cluster before the node cluster being divided continues before becoming cluster, and the cluster after the node cluster being divided becomes follow-up cluster；In like manner, cluster centers node above continues before being referred to as Centroid, and cluster centers node below is referred to as follow-up Centroid, by calculating each node p and follow-up Centroid respectively, with the ratio of the network delay of the Centroid that front continuesEstimate each node physical location in network rings,

Computing formula is expressed asWherein delay Delay computing function, next represents follow-up Centroid, and continue before pre representative Centroid, if itsRatio, more than 1, illustrates that node is the closer to the Centroid that front continues, then this node should be retained in current cluster,Ratio, less than 1, illustrates that node is the closer to follow-up Centroid, then this node will divide away, belongs to new follow-up cluster；

Then, new clustered node filters out the node with stronger ability, as the Centroid of new cluster, cloud node capacity is estimated, utilize the area formula of Weight to express the integration capability W of this node p_p, weigh integration capability W_pEstimation formulas: W_p=w₁T_p+w₂C_p+w₃D_p+w₄B_p, wherein, T_pFor available average line duration, C_pFor available computational capacity, D_pFor free hard resource, B_pFor available bandwidth, w₁,w₂,w₃,w₄For corresponding weight parameter vector；

B: search volume catalogue partitioning algorithm:

Calculating current search interval directory information capacity is V_s, to find group search interval optimal partition point Best, distribute the region of search S that new cluster is responsible for, it specifically comprises the following steps that

Define and start to the mark End region of search S terminated from mark Start, for wherein certain keyword k, its resource access temperature t_k, t_kFor this resource hit-count in certain period, catalogue data information size d_k, then the directory information capacity definition of this region of search S is V_s, its V_sComputing formula is as follows:

$V_s=\underset{k=Start}{\overset{End}{\Σ}}{t}_k\·d_k$

It is considered that the optimal partition point Best of search volume is: will produce two new search with suitable region of search capacity interval, new search interval capacity is close to the half V of initial search interval capacity_[Start,Best]=V_[Best,End], now will bring the effect of comparatively equally loaded and comparatively ideal search performance,

$V_{\[Start,Best\]}=\underset{k=Start}{\overset{Best}{\Σ}}{t}_k\·d_k=\frac{1}{2}{V}_S,S\∈\[Start,End\].$

The beneficial effects of the present invention is: the cloud resource-sharing distributed p 2 p model construction method of self-organizing of the present invention, from assembling physically closely located node, adopt the strategy that cloud cluster space divides, self-organization nodes cluster, optimize web search path as far as possible, form the distributed p 2 p of a kind of low latency.By comparing with traditional distributed network technology, the present invention has with the obvious advantage on mean cloud resource query postpones, meet the actual performance demand of cloud computing application, and the computing capability of node can be made full use of, future can between scattered cloud computing center, contractile cloud peer-to-peer network can be formed, make the sale of calculating resource, rent and become convenient, have wide practical use.

Accompanying drawing explanation

Fig. 1 is cloud peer to peer topology structure chart of the present invention；

Fig. 2 is that new node of the present invention adds cloud peer-to-peer network figure；

Fig. 3 is the present invention routing mechanism instance graph up to node；

Fig. 4 is that cloud cluster of the present invention divides schematic diagram；

Fig. 5 is that one directory information of the present invention divides example figure；

Fig. 6 is search volume of the present invention capacity schematic diagram.

Detailed description of the invention

The present invention adopts space to divide concept to build distributed p 2 p topological structure, and the cloud node that self-organizing is physically close, extension is up to routing table, it is achieved the cloud peer-to-peer network with the performance such as low latency, scalability being core with data.Future between scattered cloud computing center, can form contractile cloud peer-to-peer network, makes the sale of calculating resource, rents and become convenient, has wide practical use.

The cloud resource-sharing distributed p 2 p model of a kind of self-organizing, specifically includes following feature:

1, network is divided into two-layer distributed frame.Ground floor, the close cloud node rendezvous of physics, to collectively forming cloud cluster, filters out a Centroid in each cloud node cluster, and this Centroid is responsible for and is safeguarded other ordinary nodes and resource information thereof in oneself cloud cluster.The second layer, the set of the Centroid of N number of cloud cluster, the Centroid information (similar classical Chord, with Kademlia structure) of 2 times of square logical reach of record, constitute the distributed p 2 p structure with trunk function.Each Centroid is all each responsible for one section of region of search S in management distributed p 2 p_{[Start, End]}(Start, End is that this responsible search volume of cloud node starts mark respectively, identify with end, that is, start to the mark End one section of region of search terminated from mark Start, it is expressed as the search volume that current cloud node is responsible for, in order to convenient, it be reduced to S, be expressed as the search volume that current cloud node is responsible for), store the directory information of data object in its region of search, and response is for the inquiry request of data object in the region of search.

As shown in Fig. 1 cloud peer to peer topology structure, 4 cloud clusters being represented by dashed line in figure, wherein open circles is its common cloud node, and filled circles is the Centroid of cloud cluster.The Centroid of 4 clusters connects into the distributed network of ring-type trunk structure.

2, cloud node adds and leaves: new node is intended to add cloud peer-to-peer network, need to send notice to the Centroid on adjacent distributions formula core network, calculate oneself position in a network, find new node cloud cluster of optimum low latency in each Centroid, send to the Centroid of this cluster and add request, Centroid response is submitted its cloud nodal information to Centroid, just can be joined in this cloud cluster after adding request.

As in figure 2 it is shown, a new node adds cloud peer-to-peer network example, node D is by accessing the Centroid C of cluster B_BSeek to add cloud peer-to-peer network, know the Centroid C of cluster A contiguous on core network_A, the Centroid C of cluster C_c, and communicate with them the computing relay time.It is exactly a communication delay that Frame comes and goes the half of time used, uses repeatedly transmission timing to visit frame and takes average to calculate communication delay.If communication delay respectively 10ms, 22ms, 25ms of the Centroid of node D and cluster A, cluster B, cluster C, the Centroid selected and oneself postpone minimum cluster A sends and adds request message, after cluster A Centroid responds and replys permission message, the ordinary node of the cluster A that namely node D becomes.The shared information of oneself is issued by cluster A Centroid.If neighbor set group center is all unsatisfactory for the condition (within desired delay period 20ms) of low latency, that will access farther cluster centers node or the cluster centers node selecting now time delay minimum when reaching the detection upper limit.

Cloud node leaves: the situation losing efficacy or leaving of node is more complicated, in two kinds of situation: if the ordinary node of a cloud cluster lost efficacy or left, its inefficacy or leave and have any impact all without on whole network structure, it is only necessary to update the cloud Resource TOC information on corresponding cluster centers node on peer-to-peer network；If cluster centers node normally leaves network, it is necessary to specify new Centroid, replicate cloud Resource TOC information and the routing iinformation updating peer-to-peer network；If cluster centers node catastrophic failure, that cloud Resource TOC information also will be lost, and its search volume cluster centers node that will front be continued reclaims, and other nodes in its cluster are also required to rejoin network.This is very undesirable situation, but Cloud Server is relatively stable, and failure conditions odds is only small.

3, traditional structure distributed network supposes that node is dynamically change, and inquiry request is random distribution.Wanting the jumping figure that inquiry request is forwarded more few, it is more many that maintains structurized neighbor node number, and the quantity of information that node to store is more big, and network operation cost is more high.Chord network, the identifier of the node that continues before the distance of its routing table maintenance 2 power times and IP information, be sized to O (logN), the time complexity O (logN) of route, it is clear that reached the optimal node in a space and time compromise.

But, not such restriction in cloud equity distributed network environment, also cloud node have good performance and bigger memory space, also can go out the existence of " heat " cloud node and " heat " path.In the present invention, on the basis of Chord routing algorithm, we reach performance requirement in cloud peer-to-peer network up to node route list at increase.Each node retains up-to-date N number of up to nodal information, and composition is up to node route list.Can obtain from query manipulation up to the collection of node, such as, the initiation node of inquiry, the node set of upper hop or the destination node of inquiry.When node receives a certain inquiry request time, can find in up to routing table than Chord routing table nodal distance object identifier closer to node quote, in the way of message iteration, forwarding inquiries is asked to nearest up to node.Once fail to respond at the appointed time up to node, then carried out recursive search by Chord method for routing.

The original routing table of Chord up to routing table extension, constructs " shortcut " of network, and route time quickly trends towards the shorter time, the route time of the destination node for frequently occurring can be reduced to 1 jumping.

As shown in Figure 3 up to the routing mechanism instance graph of node, one by 8 node standard chord networks, each node route list safeguards the nodal information (position of x is for up to node) of 2 powers times, if there being a request finding mark 0 to send from 3 nodes, so from chord routing table lookup immediate node clockwise be node 7, request message issues node 7, node 7 routing table exists the node 0 being responsible for mark 0, node 0 returns Query Result to node 3, this poll-final, and node 0, node 3 finds each other, supplementing in respective routing table and adding the other side is the information up to node.

If it follows that there is a request to identify 2 from node 3 set off in search, being used alone Chord routing algorithm, according to Chord routing rule, issue node 7, be transmitted to node 1, finally arrive node 2, return result, produce path (b) shown in solid, if used up to node route list, in node 3 route from the nearest node of mark 2 be node 0, node 0 should be issued, relay to node 2, produce path (c) shown in dotted line.Obviously, the route time of query path (c) reduces by 1 jumping than query path (b).

4, network divides: along with a large amount of cloud nodes add or the growth of directory information data on cloud node, some cloud cluster Centroid performance in distributed p 2 p will be gradually reduced, it is necessarily required to mark off a part of cloud node, to form new cloud cluster, and is responsible for the search volume of part.This network partition process comprises two parts, the division of cloud node cluster and the division of catalogue data.

It not when cloud node joins and departs from, just dynamically adjust topology of networks, and be based on the size of data of physical directory information, visit capacity, and what the load capacity of Centroid determined.Additionally also attempt to be integrated together less for some data volumes search volume, to shorten the searching route of inquiry, improve the location efficiency of resource.So also make full use of node can calculating resource, optimize systematic entirety energy.

A: node assemblage classification, step is as follows:

Definition: assuming that whole cloud peer-to-peer network cluster set is distributed on virtual ring, in the direction of the clock, the cluster before the node cluster being divided continues before becoming cluster, and the cluster after the node cluster being divided becomes follow-up cluster；In like manner, cluster centers node above continues before being referred to as Centroid, and cluster centers node below is referred to as follow-up Centroid.Cluster centers node continues the information of Centroid before and after being responsible for safeguarding.1) by calculating each node p and follow-up Centroid respectively, with the ratio of the network delay of the Centroid that front continuesEstimate each node physical location in network rings,

Computing formula is represented by(delay Delay computing function, next represents follow-up Centroid, and continue before pre representative Centroid), thus, this ratio of ascending sort will obtain new clustered node position queue, it is concluded that have cloud node if appropriate for being divided into new cluster.

If itsRatio, more than 1, illustrates that node is the closer to the Centroid that front continues, then this node should be retained in current cluster.But,Ratio, less than 1, illustrates that node is the closer to follow-up Centroid, then this node will divide away, belongs to new cluster (new follow-up cluster), if difference is little, considers further that according to balanced both sides cloud number of nodes to decide whether that division is gone out.

Cloud cluster divides schematic diagram as shown in Figure 4, and cluster B separates the relation forming the new cluster D at virtual ring original position, cluster B, continuing before cluster B is cluster A, and the follow-up of cluster B is cluster C, and new cluster D is the new cluster produced in cluster B, after division, it is follow-up is cluster C, and front continuing is cluster B.As shown in table 1, compare and cluster C Centroid C_cWith cluster A Centroid C_ARatio time delay time delay.That is, compare away from cluster A, from cluster C apart from close to node all divide away, generate new cluster D.Especially, node 8, the time delay comparing both sides is identical, now just by principle of equipartition, is also divided in D cluster.

Table 1

Label	CA	Cc	Whether division is gone out
				1	6ms	2ms	It is
2	3ms	5ms
				3	8ms	6ms	It is 5-->
4	3ms	6ms
				5	0ms	2ms
6	8ms	4ms	It is
				7	2ms	0ms	It is
8	6ms	6ms	It is

2) in new clustered node, the node with stronger ability is filtered out, as the Centroid of new cluster.Cloud node capacity is estimated by we, utilizes the area formula of Weight to express the integration capability W of this node p_p。

Weigh integration capability W_pEstimation formulas: W_p=w₁T_p+w₂C_p+w₃D_p+w₄B_p, wherein, T_pFor available average line duration, C_pFor available computational capacity, D_pFor free hard resource, B_pFor available bandwidth, w₁,w₂,w₃,w₄For corresponding weight parameter vector.

B: search volume catalogue partitioning algorithm:

It is different from legacy network, the node ID of random assortment so that data are dispersed between network nodes.The search key that the cloud node of the present invention is responsible for is distributed by self-organizing strategy, and the node object distributed is cloud cluster Centroid.The shared data message of quantity of cloud cluster will keep an efficient work ratio.The method of salary distribution being so core with data, can make full use of Internet resources, and can effectively process the data message of storage.

Calculating current search interval directory information capacity is V_s.Find group search interval optimal partition point Best, distribute interval, the search volume S that new cluster is responsible for.It specifically comprises the following steps that

Definition 1 starts in mark End certain specific region of search S terminated from mark Start, for wherein certain keyword k, its resource access temperature t_k(this resource hit-count in certain period), catalogue data information size d_k, then the directory information capacity definition of this region of search S is V_s, its V_sComputing formula is as follows

$V_s=\underset{k=Start}{\overset{End}{\Σ}}{t}_k\·d_k.$

It is considered that the optimal partition point Best of search volume, by producing, two new search with suitable region of search capacity are interval, are namely that new search interval capacity should close to the half V of initial search interval capacity_[Start,Best]=V_[Best,End], now will bring the effect of comparatively equally loaded and comparatively ideal search performance.

Thus we have formula: $V_{\[Start,Best\]}=\underset{k=Start}{\overset{Best}{\Σ}}{t}_k\·d_k=\frac{1}{2}{V}_S,S\∈\[Start,End\].$

A directory information divides example figure as shown in Figure 5, lifts a simplified example.One simple network having 2 Centroids, the search volume of Centroid A is belonging to interval [0000-1000], and the search volume of Centroid B is belonging to interval [1000-0000].Search volume capacity distribution (Fig. 6) according to Centroid A, Centroid A will determine that the search volume isolating the 3rd Centroid C is interval.

Search volume capacity schematic diagram as shown in Figure 6, by calculating the search volume capacity known, [0000-0110] field capacity accounts for 48%, and [0110-1000] accounts for 52%, and finding best key value is 0110, is precisely the half of former capacity.The C node so marked off, the interval of its search volume will be [0000-0110], [0110-1000].

Along with the segmentation of search volume, comprising keyword and gradually decrease in search volume, corresponding corresponding storage data and visit capacity thereof, also can greatly reduce with it, and system would tend to relatively stable state.

Claims (1)

1. the cloud resource-sharing distributed p 2 p model construction method of a self-organizing, it is characterised in that specifically include following steps:

1) network is divided into two-layer distributed frame: ground floor, and the close cloud node rendezvous of physics, to collectively forming cloud cluster, filters out a Centroid in each cloud node cluster, and this Centroid is responsible for and is safeguarded other ordinary nodes in oneself cloud cluster；The second layer, the Centroid set of N number of cloud cluster, the Centroid information of 2 times of square logical reach of record, constitute the distributed p 2 p structure with trunk function, each Centroid is all each responsible for a region of search S in management distributed p 2 p_{[Start, End]}, Start, End is that this responsible search volume of cloud node starts mark and terminates mark respectively, it is reduced to S, it is expressed as the search volume that current cloud node is responsible for, stores the directory information of data object in its region of search, and response is for the inquiry request of data object in the region of search；

2) cloud node adds and leaves:

Cloud node adds: new cloud node is intended to add cloud peer-to-peer network, notice is sent firstly the need of to the Centroid on adjacent distributions formula core network, calculate oneself position in a network, find new node cloud cluster of optimum low latency in each Centroid, send to the Centroid of this cluster and add request, Centroid response is submitted its cloud nodal information to Centroid, just can be joined in this cloud cluster after adding request；

Cloud node leaves: the inefficacy of partial node or leave two kinds of situations, if the ordinary node of a cloud cluster lost efficacy or left, only need to update the cloud Resource TOC information on corresponding cluster centers node on peer-to-peer network；If cluster centers node normally leaves network, it is necessary to specify new Centroid, replicate cloud Resource TOC information and the routing iinformation updating peer-to-peer network；If cluster centers node catastrophic failure, that cloud Resource TOC information also will be lost, and its search volume cluster centers node that will front be continued reclaims, and other nodes in its cloud cluster are also required to rejoin network；

3) routing table optimization: on the basis of Chord routing table algorithm, retains known node information, is called up to node route list, obtains up to the collection of node from query manipulation；It is update to expand routing table in inquiry request: when node receives a certain inquiry request, can find in up to routing table than Chord routing table nodal distance object identifier closer to node quote, in the way of message iteration, forwarding inquiries is asked to nearest up to node, and increase in former routing table this closer to the information up to node；

4) network divides: along with a large amount of cloud nodes add or the growth of directory information data on cloud node, the cloud cluster that Centroid performance in distributed p 2 p is gradually reduced is repartitioned, mark off a part of cloud node, form new cloud cluster, and be responsible for the search volume of part；This network partition process comprises two parts, the division of cloud node cluster and the division of catalogue data,

A: node assemblage classification, step is as follows:

First, it is assumed that each cloud cluster set is distributed on virtual ring in whole distributed p 2 p, in the direction of the clock, the cluster before the node cluster being divided continues before becoming cluster, and the cluster after the node cluster being divided becomes follow-up cluster；In like manner, cluster centers node above continues before being referred to as Centroid, and cluster centers node below is referred to as follow-up Centroid, by calculating each node p and follow-up Centroid respectively, with the ratio of the network delay of the Centroid that front continuesEstimate each node physical location in network rings,

Computing formula is expressed asWherein delay Delay computing function, next represents follow-up Centroid, and continue before pre representative Centroid, if itsRatio, more than 1, illustrates that node is the closer to the Centroid that front continues, then this node should be retained in current cluster,Ratio, less than 1, illustrates that node is the closer to follow-up Centroid, then this node will divide away, belongs to new follow-up cluster；

Then, new clustered node filters out the node with stronger ability, as the Centroid of new cluster, cloud node capacity is estimated, utilize the area formula of Weight to express the integration capability W of this node p_p, weigh integration capability W_pEstimation formulas: W_p=w₁T_p+w₂C_p+w₃D_p+w₄B_P,Wherein, T_pFor available average line duration, C_pFor available computational capacity, D_pFor free hard resource, B_pFor available bandwidth, w₁,w₂,w₃,w₄For corresponding weight parameter vector；

B: search volume catalogue partitioning algorithm:

Calculating current search interval directory information capacity is V_s, to find group search interval optimal partition point Best, distribute the region of search S that new cluster is responsible for, it specifically comprises the following steps that

Define and start to the mark End region of search S terminated from mark Start, for wherein certain keyword k, its resource access temperature t_k, t_kFor this resource hit-count in certain period, catalogue data information size d_k, then the directory information capacity definition of this region of search S is V_s, its V_sComputing formula is as follows:

$V_s=\underset{k=Start}{\overset{End}{\Σ}}{t}_k\·d_k$

It is considered that the optimal partition point Best of search volume is: will produce two new search with suitable region of search capacity interval, new search interval capacity is close to the half V of initial search interval capacity_[Start,Best]=V_[Best,End], now will bring the effect of comparatively equally loaded and comparatively ideal search performance, $V_{\[Start,Best\]}=\underset{k=Start}{\overset{Best}{\Σ}}{t}_k\·d_k=\frac{1}{2}{V}_S,S\∈\[Start,End\].$