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CN101895952B - Multi-route establishment method and parallel data transmission method of wireless sensor network - Google Patents

Multi-route establishment method and parallel data transmission method of wireless sensor network Download PDF

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Publication number
CN101895952B
CN101895952B CN2010102283238A CN201010228323A CN101895952B CN 101895952 B CN101895952 B CN 101895952B CN 2010102283238 A CN2010102283238 A CN 2010102283238A CN 201010228323 A CN201010228323 A CN 201010228323A CN 101895952 B CN101895952 B CN 101895952B
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route
node
destination node
multirouting
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CN101895952A (en
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郭强
陈长英
徐向华
魏诺
刘瑞霞
孔祥龙
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Shandong Computer Science Center
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Abstract

The invention provides a low-delay transmission based multi-route establishment method and a multi-route parallel data transmission method of a wireless sensor network. The multi-route establishment method comprises the following steps: judging whether existing routes arriving at the destination node exist by a forwarding node; retaining the existing routes and carrying out bidirectional route confirmation if the existing routes exist; further judging whether the new routes exist if the existing routes do not exist; and further establishing multiple routes. The data transmission method comprises the following steps: selecting a plurality of routes containing least nodes from a plurality of established routes and simultaneously transmitting data; a source node detecting the state of each route and transmitting the data packet to be transmitted to a destination node along the route which is free in advance until all the data are transmitted. The two methods of the invention reduce the data transmission time and realize low-delay transmission of the data from the source node to the destination node.

Description

The multirouting method for building up and the parallel data transmission method of wireless sensor network
Technical field
The present invention relates to a kind of multirouting method for building up and parallel data transmission method of wireless sensor network; In particular; Relate in particular to the multirouting method that a kind of wireless sensor network low delay of realizing in network layer transmits, and a kind of method of utilizing above-mentioned multirouting to realize the data parallel transmission.
Background technology
Wireless sensor network is through adopting the node with perception distributed way to be deployed in the place that needs perception or monitoring; The physical quantity that need carry out perception or monitoring adopts mode wireless, multi-hop to pass to aggregation node usually, thereby realizes the short-distance wireless communication technology to surrounding environment wireless aware purpose.
The core of wireless sensor network technology is the design of communication protocol stack.At present still most at home in the world concrete communication protocol stacks of using all are to adopt the mode that combines based on IEEE 802.15.4 standard and ZigBee standard to design.IEEE 802.15.4 standard is the physical layer of corresponding wireless senser and the protocol stack design of MAC layer; And the ZigBee standard is the protocol stack design of map network layer and application layer.Wherein, the effect of network layer protocol stack is: set up a network, provide equipment to add and administrative mechanism, route discovery and the route maintenance of deviated from network, discovery and the preservation of adjacent node information, the mechanism of network layer transmission data etc. of a hop neighbor.
Wherein, The mechanism of the discovery of existing route discovery and route maintenance, a hop neighbor and transmission data all be support single channel by set up and single channel by transfer of data; Because like this can be so that the node in current activation route keeps operating state; And the node in current activation route does not keep resting state, thus the power consumption that can save node, the useful life of improving node.Though the forward node between from the source node to the destination node is also preserved multirouting information, this is in order when current route breaks down, to set up up-to-date route as early as possible, and from seeing in essence, or single channel is by data-transmission mode.Forward node quantity in the middle of from the source node to the destination node more for a long time; The Network Transmission time-delay will be very big; This just can't satisfy the low delay transmission requirement of some application scenarios; Such as transmission of intrusion detection, alert data etc., just be difficult to satisfy the transfer of data requirement of its low delay, real-time.
Summary of the invention
The present invention is in order to overcome the shortcoming of above-mentioned technical problem, and a kind of multirouting method for building up of the wireless sensor network low delay transmission that realizes in network layer and a kind of based on this route parallel data transfer approach is provided.
Wireless sensor network multirouting method for building up of the present invention, described wireless sensor network adopt response mode to set up the transmission mode of network layer, and its special feature is that described multirouting method for building up may further comprise the steps:
A. sent the source node of data by needs, the forward node around it sends to the route requests order of destination node;
B. whether forward node is to existing the existing route that arrives destination node to judge; If have existing route, then execution in step c; If there is not existing route, execution in step g then;
C. keep the existing route of judging as the part in the multirouting from the source node to the destination node; Carry out the forward node of judging and send the route replies order, carry out two-way route and confirm to its even higher level of node; Then, carry out following steps d;
D. whether forward node is to existing the new route that arrives destination node to judge; There are new route, then execution in step e if judge; If judge and do not have new route then execution in step f;
E. new route keeps as the part of the multirouting from the source node to the destination node;
F. cancel other new routes of this forward node are set up, carry out the route requests of next stage;
G. whether forward node is to existing the new route that arrives destination node to judge; There are new route, then execution in step h if judge; If judge and do not have new route then execution in step i;
H. new route keeps as the part of the multirouting from the source node to the destination node;
I. cancel the route of this forward node is set up.
Forward node described in the said method is the node around the source node, promptly with the node of source node direct communication.In the process that route is set up, the forward node around the source node sends to after the route requests order of destination node, and at first whether forward node has the judgement of existing route, and then whether the judgement of new route is arranged.Between source node and destination node, set up many routes, can realize the low delay transmission of data from the source node to the destination node.
Further, wireless sensor network multirouting method for building up of the present invention, whether the forward node described in steps d and the step g exists the determination methods of new route may further comprise the steps:
1) forward node sends to the route requests order of destination node to the next stage forward node around it;
2) judge that whether forward node receives the route replies order of next stage node in pre-set time interval, if in pre-set time interval, receive the route replies order, then exist the route that arrives destination node; If in pre-set time interval, do not receive the route replies order, then do not have the route that arrives destination node;
Forward node between described source node and the destination node is identical with the method for building up from source node to the destination node route described in the claim 1 to the method for building up of destination node route.
Above-mentioned further qualification to technical scheme has provided the determination methods whether forward node has new route, makes more perfect to the method for building up of destination node route from source node.At source node under the many situation of the forward node between the destination node; Forward node between regulation source node and the destination node is identical with the method for building up that source node arrives the destination node route to the method for building up of destination node route; Can between source node and destination node, set up many routes according to identical method.Set up in the process to the route of destination node at source node, the forward node of source node around it sends the route requests order, and this forward node has judged whether that at first existing route exists, and sends the route requests order to its subordinate's forward node again; Subordinate's forward node judges whether that at first existing route exists, and sends the route requests order to its subordinate's forward node again, and goes on successively according to the method; The forward node that sends to destination node or do not get in touch until route requests order with destination node; After destination node receives the route requests order, send the route replies order directly for last forward node in the route, forward node sends the route replies order more one by one to higher level's forward node then; If finally receiving the node of route requests order is the forward node of not getting in touch with destination node, then destination node can not sent the route replies order to this forward node, and this forward node also can not send the route replies order to its superior node.
Further; Wireless sensor network multirouting method for building up of the present invention; If the forward node between described source node and the destination node is a destination node; Then corresponding forward node directly sends the route replies order to its even higher level of node, and whether the judgement that arrives the destination node route is not arranged.
Further; Wireless sensor network multirouting method for building up of the present invention; The command format of network layer is based on ZigBee network layer order foundation in the described multirouting method for building up; The combined value of bit in the frame control format of ZigBee network layer order 6 and bit 7 is defined as the route discovery sign, the combination of bit 13, bit 14 and bit 15 in the frame control format of ZigBee network layer order is defined as the routing number of the multirouting of discovery; Bit in the route requests command format 0 is defined as the route requests sign, and being used for mark is that single channel is by request or multirouting request; The combination of bit 0, bit 1 and the bit 2 of the command selection territory field in the route response order is defined as routing number, is used to represent current route response from which bar route is returned.Bit 6 and bit 7 in the described frame control format; Bit 13 in the frame control format, bit 14 and bit 15, the bit 0 in the route requests command format, and bit 0, bit 1 and the bit 2 of the command selection territory field in the route response order are the reservation position of existing order; These undefined reservation positions are defined; And other everybody definition all remains unchanged, and does not increase new order, and this has just guaranteed well and the compatibility of existing ZigBee standard.
Further; Wireless sensor network multirouting method for building up of the present invention, the bit 6 in the described frame control format and the meaning that is combined as 00,01,10 or 11 interval scales of bit 7 are respectively forbids that route discovery, permission route discovery, permission multirouting are found, reservation; Bit 0 in the described route requests command format is 1 expression multirouting request, is that 0 expression single channel is by request.
Of the present invention based on wireless sensor network multirouting parallel data transmission method; Might as well establish total route bar number of being set up to destination node by source node is the m bar; Needing data packets for transmission is n, and its special feature is levied and is: described parallel data transmission method may further comprise the steps:
A. from m bar route, choose the j bar and comprise the minimum route of node number;
No. 1 packet in the n that B. will the send packet is routed to the j route through No. 1 respectively to the j packet and sends;
C. the source node detection is routed to the state of j route for No. 1, detects which bar route and frees out earlier, and send to destination node to packet to be sent along the route that frees out earlier;
D. repeating step C finishes until whole transmission of n packet;
E. destination node is spliced the n that a receives packet according to package successively, can revert to source node the data that will send.
Data transmission method based on the wireless sensor network multirouting recited above is compared with existing transmission method, has the advantage of low delay.Because only carrying out data through a route in the transfer of data in the existing wireless sensor network transmits; And the data transmission method based on the wireless sensor network multirouting among the present invention relies on many routes to carry out the transmission of data; Data to be transferred for equal number; Utilize data transferring method of the present invention in the less time, can accomplish data and transmit, make it can satisfy the occasion of many low delay transmission requirements.
Further, the data transmission method based on the wireless sensor network multirouting of the present invention is supposed N MaxBe the node number that the longest route in the m bar route comprises, the maximum average transfer delay time that from the source node to the destination node, allows is T, and be τ maximum processing time of delay that each forward node is handled a packet Max, it is characterized in that: the numerical value of said j can be confirmed through following formula:
j ≥ n T τ max N max
After calculating through following formula, if the value of above-mentioned inequality right-hand member less than the value of m, then j gets the smallest positive integral value that satisfies above-mentioned inequality condition; If the value of above-mentioned inequality right-hand member is more than or equal to the value of m, then the value of j is m.Above-mentioned inequality has provided the value computational methods of counting j to destination node route bar from source node, and the route that obtains through following formula calculating can realize the low delay requirement of transfer of data when carrying out transfer of data.
The invention has the beneficial effects as follows: utilize multirouting method for building up of the present invention; Can between source node and destination node, set up many routes; Thereby make the data from the source node to the destination node to carry out parallel transmission, help realizing the low delay transmission of data along many routes; In the method for routing foundation of the present invention, the route of forward node node to the destination is set up and to be comprised that existing route and two new of routes set up process, makes that the process of setting up of route is more convenient.Data parallel transmission method based on the wireless sensor network multirouting of the present invention, described data can be transmitted through many routes of choosing simultaneously, have realized the low delay transmission from source node to the destination node data.
Description of drawings
Fig. 1 sets up the process sketch map for multirouting of the present invention;
Fig. 2 carries out the principle schematic of data parallel transmission for the present invention utilizes multirouting;
Fig. 3 sets up the program principle figure of process for multirouting of the present invention.
Embodiment
Below in conjunction with accompanying drawing and embodiment the present invention is described further.
Solid arrow RREQ illustrated in figures 1 and 2 representes the route requests order, and dotted arrow RREP representes the route replies order.
Fig. 1 and Fig. 3 have provided the program diagram that route of the present invention is set up process sketch map and route foundation respectively; Fig. 3 has provided the flow chart that route is set up process synoptically; The process that can be drawn route foundation by Fig. 3 may further comprise the steps: a. sends the source node of data by needs, and the forward node around it sends to the route requests order of destination node; B. whether forward node is to existing the existing route that arrives destination node to judge; If have existing route, then execution in step c; If there is not existing route, execution in step g then; C. keep the existing route of judging as the part in the multirouting from the source node to the destination node; Carry out the forward node of judging and send the route replies order, carry out two-way route and confirm to its even higher level of node; Then, carry out following steps d; D. whether forward node is to existing the new route that arrives destination node to judge; There are new route, then execution in step e if judge; If judge and do not have new route then execution in step f; E. new route keeps as the part of the multirouting from the source node to the destination node; F. cancel the new route of this forward node is set up, carry out the route requests of next stage; G. whether forward node is to existing the new route that arrives destination node to judge; There are new route, then execution in step h if judge; If judge and do not have new route then execution in step i; H. new route keeps as another part of the multirouting from the source node to the destination node; I. cancel the route of this forward node is set up.When the forward node between source node and the destination node was destination node, corresponding forward node directly carried out the route replies order to its superior node and confirms.Whether the forward node described in steps d and the step g exists the determination methods of new route may further comprise the steps: 1) forward node sends to the route requests order of destination node to the subordinate's forward node around it; 2) judge that whether forward node receives the route replies order of next stage node in pre-set time interval, if in pre-set time interval, receive the route replies order, then exist the route that arrives destination node; If in pre-set time interval, do not receive the route replies order, then do not have the route that arrives destination node; Forward node between described source node and the destination node is identical with the method for building up from source node to the destination node route described in the claim 1 to the method for building up of destination node route.
Above-described method for routing foundation has briefly provided the multirouting method for building up from the source node to the destination node, below in conjunction with the process of the bright specifically route foundation of Fig. 1.
As shown in Figure 1, comprise 9 nodes among Fig. 1, wherein, No. 1 node is a source node, is used to initiate initial route requests order; No. 6 nodes are destination node, can only initiate the route replies order; Remaining node is the forward node between from the source node to the destination node.
When setting up by source node in the destination node routing procedure, at first source node 1 No. 2 nodes and No. 8 nodes around it send route requests order RREQ, and whether after No. 8 nodes receive this order, searching earlier has the existing route that arrives No. 6 nodes to exist; Because not existing route exists, No. 8 nodes continue to send the route requests order to No. 9 nodes, see if there is new route and exist; Do not exist because current No. 9 nodes arrive the existing route of destination node, No. 9 nodes continue to send forward route requests order RREQ and carry out pathfinding; Because destination node 6 can't be sent route replies order RREP to No. 9 nodes; No. 9 node can't receive route replies order RREP in pre-set time interval, carries out two-way route affirmation so No. 9 nodes also can't be beamed back route replies order RREP to No. 8 nodes; And then No. 1 node can't receive route replies order RREP from No. 8 nodes in pre-set time interval, will cancel the foundation to destination node 6 these routes of No. 8 nodes.
Suppose the existing route from No. 2 node to destination node 6 of 2-3-5-6 for having set up; After No. 2 nodes receive the route requests order RREQ from source node 1; Whether 2 pairs of forward node exist existing route to judge; Owing to there is existing route 2-3-5-6 to exist; Then No. 2 nodes are beamed back route replies order RREP to source node 1, just set up from the two-way route of No. 1 node to 2 node like this, simultaneously with the existing route of 2-3-5-6 as a part of route of 6 keeps and stores from source node 1 to destination node.Then; No. 2 node continues to send forward route requests order RREQ; The new route of seeking No. 6 destination nodes of arrival that whether also have other exists; As shown in Figure 1,2-4-7-6 is the new route from No. 2 node to 6 destination nodes, and there are not the existing route that arrives destination node 6 in No. 4 nodes and No. 7 nodes; So No. 2 nodes can receive the route replies order RREP that beams back from No. 4 nodes, then this new route of 2-4-7-6 will be as another part route of 6 keeps and stores from source node 1 to destination node.
Suppose to exist to the not existing route of destination node 6 from No. 2 nodes; Then No. 2 nodes are initiated route requests RREQ to No. 3 nodes and No. 4 nodes simultaneously; In pre-set time interval, respectively return a route replies order RREP from No. 3 nodes and No. 4 nodes; Such No. 2 nodes can respectively be received a route replies order RREP from No. 3 nodes and No. 4 nodes in pre-set time interval, the link that No. 2 nodes will arrive No. 3 nodes and No. 4 nodes all keeps as new-found two-way route and stores.
It is identical that the route of other forward node between source node 1 and the destination node 6 is set up process, sets up after the process through such route, and many routes that arrive destination node from source node have just been set up.
Below in conjunction with Fig. 2, the method for parallel data transmission is carried out in narration based on the multirouting of setting up:
As shown in Figure 2, the total number of routes that might as well establish from the source node to the destination node to be set up is the m bar, needs data packets for transmission to draw together n packet, carries out the parallel transmission of data according to following steps:
At first, confirm to carry out j (the bar route of j≤m) of transfer of data according to following inequality (1);
j ≥ n T τ max N max - - - ( 1 )
Wherein, N MaxBe the node number that the longest route in the m bar route comprises, the maximum average transfer delay time of T for allowing, τ MaxBe the maximum processing time of delay of a packet of each node processing.When the value of inequality (1) right-hand member during less than m, j gets the smallest positive integral value that satisfies inequality (1); When the value of inequality (1) right-hand member during more than or equal to m, the value of j is got m.
Certainly, for for simplicity, the route bar is counted confirming of j value, also can in m bar route, get to comprise the minimum j bar route of node number and carry out transfer of data.
Then, No. 1 packet in the n bag packet to be sent is routed to the j route along No. 1 simultaneously to the j packet and sends to destination node; Simultaneously, source node detects the state that is routed to the j route for No. 1, judges that which bar route frees out earlier, and sends to destination node to packet to be sent along the route that frees out earlier, all sends until n packet to finish.
At last, destination node is spliced the n that a receives packet according to package successively, just can revert to source node the data that will send.
So both can guarantee that all n that will transmit data wrap in is sent to destination node in the official hour, total node energy that transfer of data is consumed is not too big.
Correspondingly, if set some parameter amount, also can provide and utilize multirouting to carry out the mathematic(al) representation of the network average transfer delay time of transfer of data.Total m bar route between supposing from the source node to the destination node, current source node has selected j bar route wherein to carry out the transfer of data from the source node to the destination node, and total n the packets need of source node sent, and No. 1 route comprises N 1Individual node, No. 2 route comprises N 2Individual node ..., the j route comprises N jIndividual node, the processing time-delay of node i is τ i, and the data packet number that supposition is sent through each bar route is equal, then sends the average latency time of n packets need and can represent that wherein E representes average through following formula (2),
n j E [ Σ i = 1 N 1 τ i , Σ i = 1 N 2 τ i , · · · , Σ i = 1 N j τ i ] - - - ( 2 )
Top expression formula also can be expressed as
Figure BSA00000192862300092
And for adopting single channel for the situation of transmission, if selected be that (1≤l≤j) carries out the transmission of packet to the l route, and this route comprises N lIndividual node then sends the network delay time of n packets need and can be represented by following (3) formula,
n Σ i = 1 N l τ i - - - ( 3 )
If (2) average in the formula is
Figure BSA00000192862300094
then (2) formula can be expressed as (4) formula
n j Σ i = 1 N l τ i - - - ( 4 )
Through comparing (3) formula and (4) formula, it is big more that the route bar that can obtain selecting is counted j, and the averaging network propagation delay time used from source node to the destination node transfer of data is few more.It is big more that the route bar of choosing is counted j, and the forward node quantity of participating in transfer of data is just many more, and the energy of consumption comparatively speaking will be many more.
The command format of network layer has also been set up in the network layer order that the present invention is based on ZigBee; It has utilized the reservation position of existing form; And other every definition all remains unchanged, and does not increase new order, has realized the compatibility with existing ZigBee standard well.
As shown in table 1, the combined value 10 of bit in the frame control format of ZigBee network layer order 6 and bit 7 is defined as allows multirouting to find sign, the combination definition of bit 6 and bit 7 is as shown in table 2; The combination of bit 13, bit 14 and bit 15 in the frame control format of ZigBee network layer order is defined as the routing number of the multirouting of discovery.
Table 1 frame control format (bit)
Figure BSA00000192862300101
The definition of 6,7 bits in the table 2 frame control format
Find the value of routed domain The meaning of expression
00 Forbid route discovery
01 Allow route discovery
10 The permission multirouting is found
11 Keep
Bit in the route requests command format 0 is defined as the route requests sign, and being used for sign is single channel request or multichannel request, and bit 0 is 1 expression multirouting request, bit 0 be 0 expression single channel by request, as shown in table 3; The combination of bit 0, bit 1 and the bit 2 of the command selection territory field in the route response order is defined as routing number, is used to represent current route response from which bar route is returned, as shown in table 4.
Table 3 route requests command format (bit)
0 1-2 3-4 5 6 7
Single (many) route requests Keep Many-one Purpose IEEE address Throw more Keep
Table 4 command selection territory field format (bit)
Figure BSA00000192862300102

Claims (7)

1. wireless sensor network multirouting method for building up, described wireless sensor network adopt response mode to set up the transmission mode of network layer, it is characterized in that described multirouting method for building up may further comprise the steps:
A. sent the source node of data by needs, the forward node around it sends to the route requests order of destination node;
B. whether forward node is to existing the existing route that arrives destination node to judge; If have existing route, then execution in step c; If there is not existing route, execution in step g then;
C. keep the existing route of judging as the part in the multirouting from the source node to the destination node; Carry out the forward node of judging and send the route replies order, carry out two-way route and confirm to its even higher level of node; Then, carry out following steps d;
D. whether forward node is to existing the new route that arrives destination node to judge; There are new route, then execution in step e if judge; If judge and do not have new route then execution in step f;
E. new route keeps as the part of the multirouting from the source node to the destination node;
F. cancel the new route of this forward node is set up, carry out the route requests of next stage;
G. whether forward node is to existing the new route that arrives destination node to judge; There are new route, then execution in step h if judge; If judge and do not have new route then execution in step i;
H. new route keeps as another part of the multirouting from the source node to the destination node;
I. cancel the route of this forward node is set up.
2. wireless sensor network multirouting method for building up according to claim 1 is characterized in that: whether the forward node described in steps d and the step g exists the determination methods of new route may further comprise the steps:
1) forward node sends to the route requests order of destination node to the next stage forward node around it;
2) judge that whether forward node receives the route replies order of next stage node in pre-set time interval, if in pre-set time interval, receive the route replies order, then exist the route that arrives destination node; If in pre-set time interval, do not receive the route replies order, then do not have the route that arrives destination node;
Forward node between described source node and the destination node is identical with the method for building up from source node to the destination node route described in the claim 1 to the method for building up of destination node route.
3. wireless sensor network multirouting method for building up according to claim 2; It is characterized in that: if the forward node between described source node and the destination node is a destination node; Then corresponding forward node directly sends the route replies order to its even higher level of node, and whether the judgement that arrives the destination node route is not arranged.
4. wireless sensor network multirouting method for building up according to claim 1 and 2; It is characterized in that: the command format of network layer is based on ZigBee network layer order foundation in the described multirouting method for building up; The combined value of bit in the frame control format of ZigBee network layer order 6 and bit 7 is defined as the route discovery sign, the combination of bit 13, bit 14 and bit 15 in the frame control format of ZigBee network layer order is defined as the routing number of the multirouting of discovery; Bit in the route requests command format 0 is defined as the route requests sign, and being used for mark is that single channel is by request or multirouting request; The combination of bit 0, bit 1 and the bit 2 of the command selection territory field in the route response order is defined as routing number, is used to represent current route response from which bar route is returned.
5. wireless sensor network multirouting method for building up according to claim 4 is characterized in that: the bit 6 in the described frame control format and the meaning that is combined as 00,01,10 or 11 interval scales of bit 7 are respectively forbids that route discovery, permission route discovery, permission multirouting are found, reservation; Bit 0 in the described route requests command format is to represent the multirouting request at 1 o'clock, is to represent that single channel was by request at 0 o'clock.
6. the multirouting parallel data transmission method of a wireless sensor network of setting up based on the said multirouting method for building up of claim 1; What might as well establish in the claim 1 to be set up be the m bar by source node to the total route bar number of destination node; Needing data packets for transmission is n, and it is characterized in that: described parallel data transmission method may further comprise the steps:
A. from m bar route, choose the j bar and comprise the minimum route of node number;
No. 1 packet in the n that B. will the send packet is routed to the j route through No. 1 respectively to the j packet and sends;
C. the source node detection is routed to the state of j route for No. 1, detects which bar route and frees out earlier, and send to destination node to packet to be sent along the route that frees out earlier;
D. repeating step C finishes until whole transmission of n packet;
E. destination node is spliced the n that a receives packet according to package successively, can revert to source node the data that will send.
7. multirouting parallel data transmission method according to claim 6 is supposed N MaxBe the node number that the longest route in the m bar route comprises, the maximum average transfer delay time that from the source node to the destination node, allows is T, and be τ maximum processing time of delay that each forward node is handled a packet Max, it is characterized in that: the numerical value of said j can be confirmed through following formula:
Figure 2010102283238100001DEST_PATH_IMAGE002
After calculating through following formula, if the value of above-mentioned inequality right-hand member less than the value of m, then j gets the smallest positive integral value that satisfies above-mentioned inequality condition; If the value of above-mentioned inequality right-hand member is more than or equal to the value of m, then the value of j is m.
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