JP2005117468A - Packet loss rate estimation method and apparatus, program thereof, and recording medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To estimate a packet loss rate of each portion with accuracy higher than the conventional method and apparatus by using an estimation expression based on a conditional probability more approximate to "1" while using a unicast probe packet without changing the amount of test packets from the conventional test packets. <P>SOLUTION: Continuous transmission is performed in an arrow direction like a set of R, L, a set of L, R and a set of R, L so that the orders of transmission transmission destinations do not become the same. In order to measure a packet loss rate (or an arrival rate) thereof, and unicast packets of different transmission destinations are continuously transmitted a plurality of times as one group so that the orders of transmission destinations for the packets to be transmitted as one group do not become the same at all the time. In a receiving apparatus, these packets are received and the number of received packets and the number of transmitted packets are counted, thereby estimating the packet loss rate (or the arrival rate) of a link through which the packets are transmitted in common or a link through which the packets are transmitted for each destination. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a method and an estimation device for estimating a packet loss rate (or arrival rate) of a link in a network, a program for causing a computer to execute a procedure for estimating a packet loss rate of a link in the network, and the program The present invention relates to a computer-readable recording medium on which is recorded.

(Prior art 1)
Here, a measurement technique based on multicast will be described.
The following non-patent literature (R. Caceres et al: Multicast-based inference of network-internal loss charac- teristics, IEEE Trans. In Information Thory, 45 (1999) 2462-2480.) Will be described.
FIG. 1 is a diagram showing a logical tree structure.
In FIG. 1, the node that transmits the maltast probe packet is the root, and this is represented by O. Let the receiving node of the final Malchast probe packet be a leaf, and let E be the set. Let V be a set of nodes including O and E. Here, a logical tree structure is targeted. In other words, a node whose link is not branched by a node is treated as not present. In this logical tree structure, it is assumed that a certain node i is connected to nodes O, j, and k.

In this case, nodes j and k are called children for node i, and node i is called a parent for nodes j and k. Not only when directly connected to the root, but through the directly connected nodes, the side close to the root is called the parent and the side close to the leaf is called the child.
N probe packets are transmitted from the root O. Now consider the following random variables.
X = (X _k ) _k∈V (1)
Here, when X _k = 1 probe packet arrives at node k X _k = 0 when probe packet does not arrive at node k
... (2)
It is. Therefore,
X _O = 1 (3)
It is.

For nodes other than the root O, the value of X _j is determined according to the following rules.
If X _k = 0, X _j = 0 (where node j is a child of node k) (4)
If X _k = 1, X _j = 1 (with independent probability α _j ) (5)
If X _k = 1, X _j = 1 (with independent probability 1−αj) (6)
Random variable vector X _(E)
X _(E) = (X _k ) _kεE (7)
Toki,
x ∈ Ω (8)
Ω = {0,1} ^E ... (9)
And The distribution of trials (X _k ) _kεE for the probability of arrival α = (α _k ) _kεV between a given set of links shall be represented by P _α . further,
P (x; α) = P _α (X _(E) = x) (10)
Write.

となる。ここで、ｎ（ｘ）は、観測値ｘが得られた回数である。以上の定式化から求めるべき各リンクのパケット到達率α
α＝（α_ｋ）_ｋ∈Ｖ・・・・・・・・・・ （１２）
は、最尤法によって求められる。最尤方程式は、

である。なお、パケット到達率とパケット損失率との間には、
パケット損失率＝１−パケット到達率・・・・・（１４）
という関係がある。 Assuming that the observation values x ¹ ,..., x ⁿ by the transmission of n probe packets are independent,

It becomes. Here, n (x) is the number of times the observed value x is obtained. Packet arrival rate α of each link to be obtained from the above formulation
α = (α _k ) _k∈V (12)
Is obtained by the maximum likelihood method. The maximum likelihood equation is

It is. In addition, between the packet arrival rate and the packet loss rate,
Packet loss rate = 1-packet arrival rate (14)
There is a relationship.

(Conventional technology 2)
Here, a measurement technique based on Striped Unicast Probes will be described.
In Non-Patent Document 2 (NG Duffield et al: Inferring link lost using striped unicast prbes, Proceedings of IEEE INFOCOM 2001. (Anchorage 2001) 915-923.) ing. This technique is a technique that replaces the multicast probe packet used in the prior art 1 with a unicast probe packet.
The unicast probe packet is called a striped unicast probe, and continuously transmits a plurality of unicast probe packets as a group. A packet composed of two packets is called binary strips, and a packet composed of n (n> 2) packets is called n-packet strips. First, binary stripes will be described.

  FIG. 2 shows a tree structure branching at the node C when a packet is transmitted from the root S to the leaves R and L. In the prior art 1, a multi-chest probe packet is transmitted from the root to the leaf. Here, a binary strips probe packet is transmitted. The destinations of the two binary stripes probe packets are L for the first packet and R for the second packet. When multicast is used, it is only whether or not the packet arrives from the root O to the node C. However, in the case of the binary stripes probe packet, two packets are sent continuously so that the same behavior as multicast is obtained. It is possible that one of the two packets will be lost.

Assuming that Zi is a random variable in which the i-th packet of binary stripes probe packets reaches the destination and is 1 and the other is 0, the probability that the first packet reaches the destination L is E [Z ₁ ] The probability that the second packet reaches the destination R is represented as E [Z ₂ ], and is represented by the following equation.
E [Z ₁ ] = α _C (1) α _L (1) (15)
E [Z ₂ ] = α _C (2) α _R (2) (16)
Here, α _k (i) is a packet arrival rate (arrival rate is 1−loss rate) of the link from the parent node to the child node k of the i-th packet of the binary stripes probe packet. Here, the value of α _k (i) may be changed by i. If β _k (i / j) (i ≠ j) is a conditional probability that the packet i reaches the node k under the condition that the packet j arrives at the node k, the case of FIG.
β _C (2 | 1) = α _C ({1,2}) α _C (1) ≦ 1 (17)
β _C (1 | 2) = α _C ({1,2}) α _C (2) ≦ 1 (18)
It is.

The probability E [Z ₁₂ ] that both the first packet and the second packet are their destination is
E [Z ₁₂ ] = α _C ({1,2}) α _L (1) α _R (2) (19)
It is. From these, the packet arrival rate of each link is as follows.

となる。ここで、Ｅの上付文字は推定値を意味する。例えば、αの推定値はα^Ｅで表す。 If the following equation is assumed:
β _C = (1 | 2) = 1 (23)
β _C = (2 | 1) = 1 (24)
Then, the packet arrival rate of each link to be obtained can be obtained as follows by measuring E [Z ₁ ], E [Z ₂ ], E [Z ₁₂ ].

It becomes. Here, the superscript of E means an estimated value. For example, the estimated value of alpha is expressed by alpha ^E.

となる。α_Ｂ ^Ｅを求めるためには、３つのパケットの宛先が、それぞれＲ，Ｌ，Ｌで構成される３−ｐａｃｋｅｔ ｓｔｒｉｐｅｓを使用することにより同様に求められる。非特許文献２（Ｎ．Ｇ．Ｄｕｆｆｉｅｌｄ ｅｔ ａｌ： Ｉｎｆｅｒｒｉｎｇ ｌｉｎｋ ｌｏｓｓ ｕｓｉｎｇ ｓｔｒｉｐｅｄ ｕｎｉｃａｓｔ ｐｒｐｂｅｓ，Ｐｒｏｃｅｅｄｉｎｇｓ ｏｆ ＩＥＥＥ ＩＮＦＯＣＯＭ ２００１．（Ａｎｃｈｏｒａｇｅ２００１）９１５〜９２３．）では、４−ｐａｃｋｅｔ ｓｔｒｉｐｅｓを使用することによって、さらに精度が向上するとある。 Next, a packet loss rate estimation method for each link by n-packet stripes will be described.
Basically, it is the same as binary stripes, and the probe packet is composed of a larger number of packets so that the conditional probabilities such as assumptions (23) and (24) are closer to 1. Here, an example composed of three packets is shown. The destinations of the three packets are L, R, and R, respectively. These three packets are transmitted continuously. By transmitting three packets rather than two in this way, the probability that the first packet arrives at the destination L under the condition that both the second packet and the third packet arrive at the destination R is increased. , Higher than binary stripes. As a result, the packet loss rate of each link is

It becomes. In order to obtain α _B ^E , the destinations of the three packets are similarly obtained by using 3-packet stripes composed of R, L, and L, respectively. In Non-Patent Document 2 (NG Duffield et al: Inferring link lost using striped unicast prbes, Processeds of IEEE INFOCOM 2001. (Anchorage 2001) 915-923.), It is further assumed that 4-p. There is an improvement.

R. Caceres et al: Multicast-based inference of network-internal loss charactaristics, IEEE Trans. in Information Story, 45 (1999) 2462-2480. N. G. Duffield et al: Inferring link loss using striped unicast rpbes, Proceedings of IEEE INFOCOM 2001. (Anchorage 2001) 915-923.

Although the prior art 1 has improved the technique for estimating the behavior inside the network, there are the following two problems. One of them is that an important part in the Internet does not support multicasting to the network level.
Another is that measurement by multicast packets is often very different from measurement by unicast packets. This is a very important issue considering that most traffic in the Internet is unicast.
Prior art 2 uses a unicast probe packet to solve the problems of prior art 1 and continuously transmits the unicast packets that make up the probe packet, so that a plurality of constituent packets propagate on the same link. When a multicast probe packet is used, it is devised so that one of them does not cause a packet loss.

However, although the conventional technique 2 is devised so that the behavior is the same as that of the multicast probe packet by the unicast probe packet, the probability of the previous equation (23) is larger than the probability of the previous equation (24). Since both are estimated as 1, the accuracy of the estimation formula (formula (27)) approximated with the probability of the formula (24) as 1 is low. In order to make these approximations accurate, in the prior art 2, a probe packet is composed of a larger number of packets, but this has the problem that it increases the accuracy and also causes more bursty traffic. is there.
Even if a probe packet is composed of a large number of packets, the probability corresponding to the previous equation (23) remains the same as the probability corresponding to the previous equation (24), and other links depend on the estimated link. The problem that the arrival rate is estimated to be higher (the packet loss rate is lower) than that is not solved.

(the purpose)
The object of the present invention is to solve these problems and to use a unicast probe packet without changing the amount of the conventional test packet and the test packet, that is, a condition closer to 1 without placing a heavy burden on the network. It is an object to provide a packet loss rate estimation method and an estimation device that can estimate the packet loss rate of each part with higher accuracy than before by using an estimation formula based on the attached probability.

In the packet loss rate estimation method of the present invention, the configuration of unicast probe packets is continuously transmitted as a group in the order of destination L and destination R, and the next probe packet is grouped in the order of destination R and destination L. Send continuously. The interval between the pair of destinations L and R and the pair of destinations R and L is set to be sufficiently larger than the interval inside the set of those packets, and by measuring these probe packets, the accuracy is improved. Correct the estimation result bias.
Specifically, in order to measure the packet loss rate (or arrival rate), a plurality of unicast packets with different destinations are continuously transmitted a plurality of times as a group, and the destination order of the packets to be transmitted as a group Are not always in the same order, receive those packets, and count the number of received and transmitted packets, so that the packet loss rate of the link through which the packet was routed in common and the link through each destination (or (Arrival rate) is estimated.

  According to the present invention, an estimation equation with a conditional probability closer to 1 can be obtained using a unicast probe packet without changing the amount of the conventional test packet and the test packet, that is, without placing a heavy burden on the network. By using it, it becomes possible to estimate the packet loss rate of each part with higher accuracy than before.

Embodiments of the present invention will be described below in detail with reference to the drawings.
FIG. 3 is a configuration diagram of a packet loss rate estimation system according to an embodiment of the present invention, and FIG. 4 is a test packet image diagram of the present invention.
In FIG. 3, 10 is a test packet transmitting device, 11 and 12 are test packet receiving devices, and 13 is a test packet counting device. First, a test packet is transmitted from the test packet transmitter 10. Here, a case where two packets are transmitted as a test packet will be described.
As shown in FIG. 4, the test packet transmitter 10 transmits packets of different destinations as a group. That is, in FIG. 4, since the right direction is the traveling direction, R1-1 and L1- are transmitted as the first set, L2-1 and R2-2 are transmitted as the next set, and R3-1, L3-2 is transmitted as the next batch and thereafter transmitted in the reverse order. Here, this is called a test packet pair. Each packet in FIG. 4 has a serial number and a child number described below. Further, a serial number is assigned to the test packet pair, and the same number is assigned to each packet constituting the test packet pair. This serial number is incremented by 1 up to a predetermined number and assigned to the test packet pair. When the predetermined number is exceeded, a number is assigned from 1 again.

In addition to the serial number, the test packet pair is assigned a number (child number) indicating the number of the packet in the test packet pair. As shown in FIG. 4, the test packet pairs are transmitted so that the destinations are alternated.
Here, let us consider a case where the measurement section can be expressed by a basic tree structure having two leaves (see FIG. 2). By performing a plurality of basic measurements at the same time, the packet loss rate of each section of a more complicated network can be estimated.

FIG. 5 is an operation flowchart of a packet loss rate estimation method according to an embodiment of the present invention, FIG. 7 is a processing flowchart of a receiving terminal according to an embodiment of the present invention, and FIG. 8 is an embodiment of the present invention. It is a block block diagram of the receiving terminal which concerns on an example.
The test packet receivers 11 and 12 in FIG. 3 are receiving terminals 511 configured as shown in FIG. The received packet is received by the packet receiver 516 of the receiving terminal 511 in FIG. The received packet is recorded in the data storage unit 517 of FIG. 8 with the serial number and child number written in the content of the received test packet. Unless the predetermined maximum number of serial numbers is exceeded, the recording of serial numbers and child numbers and reception of test packets are repeated many times.
When the maximum number is exceeded, the recorded data is transmitted to the totalization device 13 by the measurement data transmission unit 518 of FIG.
The operation of the receiving terminal will be described with reference to FIG. When the test packet is received (step 111), the received packet is recorded in the data storage unit 517 with a serial number and a child number (step 112). Until the maximum number of serial numbers is reached, the process returns to step 111 (step 113), and the reception of the test packet and the recording of the communication number and the child number are repeated (steps 111 and 112).
If the maximum number is exceeded, the recorded data is transmitted from the measurement data transmission unit 518 to the counting device (step 114).

FIG. 6 is a block diagram of a counting device according to an embodiment of the present invention.
The aggregation device 13 in FIG. 3 is a device 501 configured as shown in FIG. The measurement data reception unit 507 in FIG. 6 receives the measurement data results from the receiving devices 11 and 12. Based on the received measurement data, the E [Z ₁₂ ] counting unit 506 performs E [Z ₁₂ ], E [Z ₁ ^LR ], E [Z ₂ ^LR ], E [Z ₁ ^RL ], E [Z ₂ ^RL ]. ] Is calculated. E _{[Z 12]} obtained E by the counting unit 506 _{[Z 12],} E _[Z ^{1 LR],} E _[Z ^{2 LR],} E _[Z ^{1 RL],} based on E _[Z ^{2 RL],} packets The loss rate counting unit 508 obtains the packet loss rate in each section and displays the result. In FIG. 6, 502 is a CPU (central processing unit) that controls the totalizing apparatus 501, 503 is a memory, 504 is an I / O control unit, and 505 is a keyboard.

FIG. 5 is an operation flowchart of the counting device according to the embodiment of the present invention.
The measurement data results sent from the receiving terminals 11 and 12 are received by the measurement data receiving unit 507 (step 101). Then, based on the received measurement data, the E [Z ₁₂ ] counting unit 506 uses the E [Z ₁₂ ], E [Z ₁ ^LR ], E [Z ₂ ^LR ], E [Z ₁ ^RL ], E [Z ₂ ^RL ] are calculated (step 102). Based on these equations, the packet loss rate estimation unit 508 calculates the packet loss rate in each section (step 103). Then, the calculated result is displayed (step 104).

Here, a method for setting the destination of a test packet, each probability, and a random variable will be described.
The destination of the test packet pair is written as “first packet destination, second packet destination”. For example, if the first is L and the second number is R, << L, R >>.
Based on the notation of Non-Patent Document 2 (NG Duffield et al: Inferring link lost striped unicast prbes, Proceedings of IEEE INFOCOM 2001. (Anchorage 2001) 915-923.).
X _k (d)... 1 when packet d reaches destination node k, 0 otherwise
Z _d ^k1k2 ... When the destination of the packet pair is ^<< k ₁ , k ₂ >>, the random variable Z { _{d1, d1} is 1 when the packet with the child number d reaches the destination, and 0 otherwise _{. d2, ...} dn} child numbers _d 1 in ... test _packet, d 2, ... _{d n} 1 where a packet respectively reach the destination, the random variable to the others and 0

α _C (d _i )... C is the node where each packet branches depending on the destination of the packet constituting the test packet pair, and the probability that the packet with child number d _i reaches node C α _k. Node C is a node where each packet branches depending on the destination of the packet constituting the test packet pair, and C is the probability β _C (d ₁ | d ₂ ) that the packet of child number d _i will reach node C. Probability that a packet with child number d ₁ will reach C under the condition that a packet with child number d ₂ has arrived at branch node C.

In the case of FIG. 2, each probability and random variable are expressed as follows.
E [Z ₁ ^LR ] = α _L α _C (1) (30)
E [Z ₂ ^LR ] = α _R α _C (2) (31)
E [Z ₁ ^RL ] = α _R α _C (1) (32)
E [Z ₂ ^RL ] = α _L α _C (2) (33)
E [Z ₁₂ ] = α _C ({1,2}) α _L α _R = α _C (2) β _C (1 | 2) α _L α _R
... (34)
Here, α _C ({1,2}) is the probability that both the packets of the child numbers 1 and 2 will reach the branch node C.

From the above equation, the following equation is obtained.

The formula obtained as the probability of arrival has been given above.
For consecutive packets, the following equation holds because the subsequent packets are more likely to be discarded within the continuous packets.
β _C (2 | 1) <β _C (1 | 2) (<1) (41)
From these, the present invention approximates βC (1 | 2) to 1 without approximating β _C (2 | 1) as 1 as in the prior art 2, and is more accurate than the prior art 2, and is more uniform. Α _C (1), α _C (2), α _R , α _L can be estimated using the cast probe packet.

In the embodiment, when there are two destinations, transmission is performed so that the order of the destinations is not the same as LR, RL, LR,..., But when there are three or more destinations, AB, BA, AB, BC, CB, BC or AC, CA, AC is transmitted. That is, it is not applied unless there are two destinations.
The number of packets in a group can be three or more. There are restrictions on the pattern.
That is, in the case of three, ABB, BAA, ABB,..., In the case of four, ABBB, BAAA, ABBB,..., In the case of five, ABBBBB, BAAAA, ABBBBB,. Become. The estimation accuracy is improved by increasing the number of packets in a group. This improvement in accuracy is described in Non-Patent Document 2 described above.

  If the operation flow of the counting device shown in FIG. 5 and the operation flow of the receiving terminal shown in FIG. 7 are programmed and stored in a recording medium such as a CD-ROM, the program for carrying out the present invention can be bought and sold. Convenient and easy to realize the present invention in the network by installing and executing the program by attaching the recording medium to the computer in the terminal as the transmitting terminal, receiving terminal or totaling device in the network can do.

It is a figure which shows a logical tree structure. It is a figure which shows the structure of the tree with two leaves used as the premise of this invention. It is a system configuration | structure figure of the packet loss rate estimation apparatus which concerns on one Example of this invention. It is an image figure of the test packet which concerns on one Example of this invention. It is a flowchart of the processing operation by the totalization apparatus which concerns on one Example of this invention. It is a block diagram of the totalization apparatus which concerns on one Example of this invention. It is a flowchart of the processing operation by the receiving terminal which concerns on one Example of this invention. It is a block diagram of the receiving terminal which concerns on one Example of this invention.

Explanation of symbols

O ... transmitting node (root), j, k ... receiving node (leaf), S ... transmitting terminal, C ... relay node,
L, R ... receiving terminal, 10 ... transmitting device, 11, 12 ... receiving device, 13 ... counting device,
501 ... Totaling device, 502 ... CPU, 503 ... Memory, 504 ... I / O control unit,
505 ... Keyboard, 506 ... E [Z ₁₂ ] counting unit, 507 ... Measurement data receiving unit,
508: Packet loss rate counting unit, 511: Receiving terminal, 512: CPU,
513: Memory, 514: I / O control unit, 515: Keyboard,
516: Packet receiving unit, 517: Data storage unit, 518: Measurement data transmitting unit.

Claims (12)

In a method for estimating a packet loss rate of a link in a packet network,
In order to measure the packet loss rate or the packet arrival rate, the transmitting device transmits a plurality of unicast packets with different destinations as a group, and transmits a plurality of times.
Send the destinations of the packets to be sent as a group in a different order,
The receiving device receives the packet and counts the number of receptions and transmissions to estimate the packet loss rate or arrival rate of the link through which the packet passes in common and the link through each destination. A characteristic packet loss rate estimation method. In a method for estimating a packet loss rate of a link in a packet network,
In order to measure the packet loss rate or the packet arrival rate, the transmitting device collects a plurality of unicast packets with different destinations and assigns serial numbers to the different packet packages with different destinations,
Furthermore, a child number indicating the number of each packet among the plurality of packets is given,
Send multiple packets of the above multiple times so that the destination order of the packets to be sent is always different,
The receiving device receives the packet and counts the number of receptions and transmissions to estimate the packet loss rate or arrival rate of the link through which the packet passes in common and the link through each destination. A characteristic packet loss rate estimation method. In the transmitting device among the devices that estimate the packet loss rate of the link in the packet network,
In order to measure the packet loss rate, a means for creating a plurality of unicast packets with different destinations;
Means for giving a serial number to a group of different packets of the plurality of destinations, and giving a child number indicating what number each packet is among the plurality of packets in the group;
And a means for transmitting the packets so that the plurality of packets are grouped in succession and the destinations of the packets to be transmitted as a group are always in different orders. In the receiving device among the devices that estimate the packet loss rate of the link in the packet network,
Means for receiving a packet transmitted from the transmission device;
Means for recording serial number and child number information;
A receiving apparatus comprising: a link through which packets are commonly routed from received information; and a means for estimating a packet loss rate or a packet arrival rate of a link through each destination. A recording medium recording a program for causing a computer to execute a processing procedure for estimating a packet loss rate or an arrival rate of a link in a packet network,
In order to measure the packet loss rate, means for transmitting a plurality of unicast packets with different destinations in succession and collectively, and transmitting the packets so that the destinations of the packets to be transmitted are always in a different order. Program for causing a computer to function as a means, a means for receiving the packet, a means for measuring based on the received information, and a means for estimating a packet loss rate of a link through which the packet is commonly passed and a link through which the packet is routed for each destination A computer-readable recording medium on which is recorded. A recording medium storing a program for causing a computer to execute a processing procedure for estimating a packet loss rate or an arrival rate of a link in a packet network,
Means for creating a plurality of unicast packets with different destinations for measuring the packet loss rate, means for assigning serial numbers to the packets, and indicating the number of each packet among the plurality of packets The computer functions as a means for assigning a child number, a means for transmitting the plurality of packets in succession and collectively, and a means for transmitting the addresses of the packets to be transmitted as a group in such a way that they are always in different orders. A computer-readable recording medium on which a program for causing the program to be recorded is recorded. A recording medium recording a program for causing a computer to execute a processing procedure for measuring a packet loss rate or an arrival rate of a link in a packet network,
A computer-readable recording medium storing a program for causing a computer to function as means for receiving a packet transmitted by a transmission device and means for recording serial number and child number information. A recording medium recording a program for causing a computer to execute a processing procedure for measuring a packet loss rate or an arrival rate of a link in a packet network,
A computer-readable recording of a program for causing a computer to function as means for receiving measured information, and means for estimating a packet loss rate of a link through which a packet passes in common and a link through each destination from the information. recoding media. A program for causing a computer to execute a processing procedure for estimating a packet loss rate or an arrival rate of a link in a packet network,
In order to measure the packet loss rate, a means for transmitting a plurality of unicast packets with different destinations in a continuous and collective manner so that the destinations of the packets to be transmitted in a collective order are always in a different order. Causes the computer to function as a means for transmitting, a means for receiving the packet, a means for measuring by receiving, a means for estimating the packet loss rate or the arrival rate of the link through which the packet has passed in common and the link through which the packet has been routed for each destination A program for estimating packet loss rate or reachability. A program for causing a computer to execute a processing procedure for estimating a packet loss rate or an arrival rate of a link in a packet network,
Means for creating a plurality of unicast packets with different destinations for measuring the packet loss rate, means for assigning a serial number to the plurality of packets, and indicating the number of each packet among the plurality of packets Let the computer function as a means for assigning a child number, a means for transmitting the plurality of packets in succession and collectively, and a means for transmitting the destinations of the packets to be transmitted as a group in a different order at all times A program for estimating packet loss rate or reachability. A program for causing a computer to execute a processing procedure for estimating a packet loss rate or an arrival rate of a link in a packet network,
A packet loss rate or arrival rate estimation program for causing a computer to function as means for receiving a packet transmitted by a transmission device and means for recording serial number and child number information. A program for causing a computer to execute a processing procedure for estimating a packet loss rate or an arrival rate of a link in a packet network,
Packet loss rate or arrival rate estimation program for causing a computer to function as a means for receiving measured information, a link through which packets are commonly passed, and a means for estimating a packet loss rate of a link through each destination from the information .

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