time management method for query processing of causality on sensor stream data

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1 "�Òeµ 5

1.1 ���½ 1lxl� . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 ���½ ~½ÓZO� x9� l�#� . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 �7Hë�H_� ½$í . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 ®�Áo> ¥o>Ä© ��� ¥o>Ä© :�¿R� 8

2.1 �'aº�� ���½ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.1 X<s�'� Û¼àÔaË> �'ao� r�Û¼%7� . . . . . . . . . . . . . . . 8

2.1.2 X<s�'� ��s�_ç . . . . . . . . . . . . . . . . . . . . . . 10

2.2 ���½ C��â . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 ���½ ?/6 x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 5���� Ça��+ 15

3.1 s��$�àÔ_� µ1ÏÒqt r�y�� J���� . . . . . . . . . . . . . . . . . . . . 15

3.1.1 s��$�àÔ µ1ÏÒqt í�H"f . . . . . . . . . . . . . . . . . . . . . 15

3.1.2 s��$�àÔ ��ÃÌ í�H"f . . . . . . . . . . . . . . . . . . . . . 16

3.1.3 s��$�àÔ ��ÃÌ 8��â . . . . . . . . . . . . . . . . . . . . . 17

3.1.4 µ1ÏÒqtõ� ��ÃÌ_� �'a>� . . . . . . . . . . . . . . . . . . . 17

3.2 ���õ� �'a>� |9�_� . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2.1 ��6 x�� &ñ_� ½©gË: . . . . . . . . . . . . . . . . . . . . . 22

3.2.2 µ1ÏÒqtõ� ��ÃÌ_� í�H �&³�©�õ� %i���� �&³�©� . . . . . . . . . . 24

4 �¤d"� â«çÃÍÏ� PLl�'aUc"� ê�>ø� ®�N� ���+ %�h� 27

4.1 G'p"f Û¼àÔaË> X<s�'� %�o�\�¦ 0Aô�Ç ½¹כ ���½Ó . . . . . . . . . . 27

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4.2.1 r�çß� �'ao� ~½ÓZO� . . . . . . . . . . . . . . . . . . . . . . 29

4.2.2 ���õ� �'a>� ���� ~½ÓZO� . . . . . . . . . . . . . . . . . . . 33

1

5 ����@ ��� 36

5.1 z�+«> 8��â . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.2 z�+«> ���õ� . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

6 ÚrÒeµ ��� /�×Ññ ¥o>Ä© ø�V� 47

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1 _þt��s�ç �û¶� . . . . . . . . . . . . . . . . . . . . . . . . . . 9

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3 ��� µ1ÏÒqt Êê ��ÃÌ(Êê µ1ÏÒqt ��� ��ÃÌ)_� \V . . . . . . . . . . . . . 19

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1 µ1ÏÒqtí�H"fü< ��ÃÌí�H"f_��'a>�\����Érs��$�àÔ_�µ1ÏÒqtr�y��J���� 20

2 µ1ÏÒqtõ� ��ÃÌ_� í�H �&³�©�õ� %i���� �&³�©�_� µ1ÏÒqt ��0px$í . . . . . . 20

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5 z�+«> 8��â . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

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\�¦%�o�ô�Ç��.�:r���½\�"f��Hs��$�àÔ_� ��ÃÌí�H"f\�%ò�¾Ó�¦p�u���H¹כ���[þt\�

@/ �#� ��6£§õ� °ú s� &ñ_�ô�Ç��.

Ça��+ 3. ��ÃÌ r�y��(Arrival Time)

AT (Ei)��H s��$�àÔ Ei_� ��ÃÌ r�y��s���. ��ÃÌ r�y���Ér s��$�àÔ�� G'p"f W1àÔ0>

ß¼\�¦ :�x �#� G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7�\� ��ÃÌô�Ç r�y��s���.

Ça��+ 4. þj@/ ���²ú� t����(Maximum Propagation Delay)

���²ú� t���� PD(Ei)��H s��$�àÔ Ei_� ��ÃÌ r�y��õ� µ1ÏÒqt r�y��_� �s�s���. þj

@/ ���²ú� t���� MPD��H PD(Ei)_� þjÎ.°úכs���.

PD(Ei) = AT (Ei)− ST (Ei) , MPD = MAX(PD(Ei))

s��$�àÔ_� ��ÃÌ í�H"f��H G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7�\� ��ÃÌô�Ç s��$�

àÔ_� ��ÃÌ r�y��\� _�K� ���&ñ�)a��. ¢ô�Ç, µ1ÏÒqtô�Ç s��$�àÔ��H ���²ú� t����\� _�K�

��ÃÌ r�y��s� ���&ñ�)a��.

µ1ÏÒqtô�Ç s��$�àÔ��H Áº��� W1àÔ0>ß¼_� YO�w� f. ~½Ód��ܼ�Ð G'p"f X<s�'� %�o�

r�Û¼%7�\� ���²ú��)a��. ����"f, ���²ú� t�����Ér Áº��� W1àÔ0>ß¼_� 0A�©� ½� ����o

16

\� _�K� µ1ÏÒqtô�Ç��. �:r ���½\�"f��H s��$�àÔ_� ���²ú� 8��â\� @/ �#� ��6£§õ� °ú 

s� ��&ñô�Ç��.

��Ça� 1. G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7��Ér µ1ÏÒqt r�y��õ� ��ÃÌ r�y��_� �s�

�� þj@/ ���²ú� t���� s�?/��� s��$�àÔ\�¦ ���²ú�~ÃÎ>� �)a��.

3.1.3 l���dçà �¿½ÇÐ ».É¿R�

G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7��Ér z� [j>�_� ����o\� _� �#� \V8£¤ Ô�¦��0px

ô�Ç �ª�_� s��$�àÔ\�¦ ���²ú�~ÃÎ>� �)a��. ¢ô�Ç, G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7�\�

��ÃÌô�Ç þj��H_� s��$�àÔ[þt�Ér r�Û¼%7�\�"f �<Êa� %�o�÷&#Q�� ô�Ç��. �:r ���½\�"f

��H G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7�\� ��ÃÌô�Ç þj��H_� s��$�àÔ[þt\� @/ô�Ç 1lx

r�çß�@/ %�o�\� %ò�¾Ó�¦ p�u���H �\���¹כ @/ �#� ��6£§õ� °ú s� &ñ_�ô�Ç��.

Ça��+ 5. ��ÃÌ çß����(Arrival Rate)

AR��H ���5Åq&h�ܼ�Ð ��ÃÌô�Ç s��$�àÔ Eiü< Ei+1_� ��ÃÌ r�y�� �s�s���.

AR = AT (Ei+1)−AT (Ei)

�:r ���½\�"f��H s��$�àÔ_� ��ÃÌ 8��â\� @/K�"f ��6£§õ� °ú s� ��&ñô�Ç��.

��Ça� 2. G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7��Ér ��ÃÌ çß���� ÅÒl��Ð s��$�àÔ\�¦ ���

²ú�~ÃÎ>� �)a��.

3.1.4 L±Ó�»jø� �¿½ÇÐ�+ ®�N�

G'p"fÛ¼àÔaË>X<s�'�%�o�r�Û¼%7��Érs��$�àÔ_�z�]jµ1ÏÒqtí�H"fü<��H��ØÔ>�s�

�$�àÔ\�¦ ���²ú�~ÃÎ>� �)a��. �:r ���½\�"f��H s��$�àÔ_� µ1ÏÒqt í�H"fü< ��ÃÌ í�H"f_�

�'a>�\� ���� ��6£§õ� °ú s� &ñ_�ô�Ç��.

Ça��+ 6. ��� µ1ÏÒqt ��� ��ÃÌ

G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7�\� ���5Åq&h�ܼ�Ð ��ÃÌô�Ç s��$�àÔ Ei,Ei+1\�

17

@/ �#� ���$� µ1ÏÒqtô�Ç s��$�àÔ�� ���$� ��ÃÌ ô�Ç �âĺ\�¦ �����·p��.

ST (Ei) < ST (Ei+1), AT (Ei) < AT (Ei+1)

ÕªaË> 2��H ��� µ1ÏÒqt ��� ��ÃÌ_� \V\�¦ �Ð#�ÅÒ�¦ e����.

도착 간격도착 시각 = 발생 시각의 최댓값발생 시각의 최솟값최대 전달 지연

이벤트 Ei 발생 시각이벤트 Ei+1 발생 시각이벤트 Ei 발생 구간이벤트 Ei+1 발생 구간t t+a

최대 전달 지연

ÕªaË> 2: ��� µ1ÏÒqt ��� ��ÃÌ_� \V

Ça��+ 7. ��� µ1ÏÒqt Êê ��ÃÌ

G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7�\� ���5Åq&h�ܼ�Ð ��ÃÌô�Ç s��$�àÔ Ei,Ei+1\�

@/ �#� ���$� µ1ÏÒqtô�Ç s��$�àÔ�� 0py>� ��ÃÌô�Ç �âĺ\�¦ �����·p��.

ST (Ei) > ST (Ei+1), AT (Ei) < AT (Ei+1)

Ça��+ 8. Êê µ1ÏÒqt ��� ��ÃÌ

G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7�\� ���5Åq&h�ܼ�Ð ��ÃÌô�Ç s��$�àÔ Ei,Ei+1\�

18

@/ �#� 0py>� µ1ÏÒqtô�Ç s��$�àÔ�� ���$� ��ÃÌ ô�Ç �âĺ\�¦ �����·p��.

ST (Ei) > ST (Ei+1), AT (Ei) < AT (Ei+1)

ÕªaË> 3��H ��� µ1ÏÒqt Êê ��ÃÌõ� Êê µ1ÏÒqt ��� ��ÃÌ_� \V\�¦ �Ð#�ÅÒ�¦ e����.

도착 간격도착 시각 = 발생 시각의 최댓값발생 시각의 최솟값최대 전달 지연

이벤트 Ei 발생 시각이벤트 Ei+1 발생 시각이벤트 Ei 발생 구간이벤트 Ei+1 발생 구간t t+a

최대 전달 지연

ÕªaË> 3: ��� µ1ÏÒqt Êê ��ÃÌ(Êê µ1ÏÒqt ��� ��ÃÌ)_� \V

�:r ���½\�"f��H s��$�àÔ_� µ1ÏÒqt í�H"fü< ��ÃÌ í�H"f_� �'a>�\�¦ �¦�9 �#�, G'p

"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7�\� ��ÃÌô�Ç s��$�àÔ_� µ1ÏÒqt r�y�� J�����¦ ��6£§

õ� °ú s� &ñ_�ô�Ç��.

• µ1ÏÒqtõ� ��ÃÌ_� í�H �&³�©����$� µ1ÏÒqtô�Ç s��$�àÔ�� G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7�\� ���$� ��ÃÌ

ô�Ç��. s��$�àÔ_� ��ÃÌ í�H"f��H s��$�àÔ_� µ1ÏÒqt í�H"fü< °ú ��.

• µ1ÏÒqtõ� ��ÃÌ_� %i���� �&³�©����$� µ1ÏÒqtô�Ç s��$�àÔ�� G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7�\� 0py>� ��ÃÌ

19

ô�Ç��. ¢ô�Ç, 0py>� µ1ÏÒqtô�Ç s��$�àÔ�� G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7�\�

���$� ��ÃÌô�Ç��. s��$�àÔ_� ��ÃÌ í�H"f��H s��$�àÔ_� µ1ÏÒqt í�H"fü< %i�����)a

��.

³ð 1�Ér s��$�àÔ_� µ1ÏÒqt í�H"fü< ��ÃÌ í�H"f_� �'a>�\� ���Ér s��$�àÔ_� µ1ÏÒqt

r�y�� J�����¦ �Ð#�ÅÒ�¦ e����.

³ð 1: µ1ÏÒqt í�H"fü< ��ÃÌ í�H"f_� �'a>�\� ���Ér s��$�àÔ_� µ1ÏÒqt r�y�� J����

µ1ÏÒqt í�H"fü< ��ÃÌ í�H"f_� �'a>� s��$�àÔ_� µ1ÏÒqt r�y�� J����

��� µ1ÏÒqt ��� ��ÃÌ µ1ÏÒqtõ� ��ÃÌ_� í�H �&³�©�

��� µ1ÏÒqt Êê ��ÃÌ, Êê µ1ÏÒqt ��� ��ÃÌ µ1ÏÒqtõ� ��ÃÌ_� %i���� �&³�©�

G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7��Ér s��$�àÔ_� ��ÃÌ í�H"f\�¦ l�ìøÍܼ�Ð |9�

_�\�¦ %�o� �l� M:ë�H\�, |9�_� ���õ���H s��$�àÔ_� µ1ÏÒqt r�y�� J����\� ���� ²ú���

�����. Õª�QÙ¼�Ð µ1ÏÒqtõ� ��ÃÌ_� í�H �&³�©�õ� %i���� �&³�©�_� µ1ÏÒqt ��0px$í�¦ ���½Ó

ܼ�Ð, s��$�àÔ_� µ1ÏÒqt r�y�� J����s� |9�_� ���õ�\� p�u���H %ò�¾Ó�¦ \V�©�½+É Ãº e��

��. ³ð 2��H 3.1.2]X�õ� 3.1.3]X�\�"f &ñ_�ô�Ç s��$�àÔ ��ÃÌ í�H"fü< ��ÃÌ 8��â\�

%ò�¾Ó�¦ p�u���H �_þt]���¹כ �'a>�\� ���Ér ¿º ��t� �&³�©�_� µ1ÏÒqt ��0px$í�¦ �Ð#�

ÅÒ�¦ e����.

³ð 2: µ1ÏÒqtõ� ��ÃÌ_� í�H �&³�©�õ� %i���� �&³�©�_� µ1ÏÒqt ��0px$í

�'a>� ��ÃÌ çß����<þj@/ ���²ú� t���� ��ÃÌ çß����≥þj@/ ���²ú� t����×�æo? ½çß� �>rF� q� �>rF�

µ1ÏÒqtõ� ��ÃÌ_�

í�H �&³�©�

µ1ÏÒqt ��0px µ1ÏÒqt

µ1ÏÒqtõ� ��ÃÌ_�

%i���� �&³�©�

µ1ÏÒqt ��0px µ1ÏÒqt Ô�¦��0px

µ1ÏÒqtõ� ��ÃÌ_� í�H �&³�©�õ� %i���� �&³�©�_� µ1ÏÒqt ��0px$í�Ér þj@/ ���²ú� t����õ�

��ÃÌ çß����_� �'a>�\� ���Ér ×�æo? ½çß�_� �>rF� #�ÂÒ\� _�K� óøÍéß��)a��. Õª s�Ä»

20

��H, s��$�àÔ µ1ÏÒqt ½çß�_� ×�æo? ½çß�\�"f s��$�àÔ_� µ1ÏÒqt r�y�� %i����s� µ1ÏÒqt½+É

ú e��l� M:ë�Hs���. ÕªaË> 4_� a)��H þj@/ ���²ú� t����õ� ��ÃÌ çß����_� �'a>�\� ��

�Ér ×�æo? ½çß� �>rF�_� \V\�¦ b)��H q� �>rF�_� \V\�¦ �Ð#�ÅÒ�¦ e����.

최대 전달 지연

최대 전달 지연도착 간격

도착 간격a) 최대 전달 지연 > 도착 간격

b) 최대 전달 지연 < 도착 간격

이벤트 Ei 발생 구간이벤트 Ei+1 발생 구간

도착 시각 = 발생 시각의 최댓값발생 시각의 최솟값

중첩최대 전달 지연

최대 전달 지연이벤트 Ei 발생 구간이벤트 Ei+1 발생 구간

t t+a

t t+a

ÕªaË> 4: þj@/ ���²ú� t����õ� ��ÃÌ çß���� �'a>�\� ���Ér ×�æo? ½çß� µ1ÏÒqt \V

21

3.2 ê�>ø� ®�N� ���+

�:r ���½\�"f��H ���õ� �'a>� |9�_� ü< ���õ� �'a>� óøÍZ>�_� l�ï�r�¦ &ñ_� ��¦, ���õ�

�'a>� |9�_�_� ���õ�\� %ò�¾Ó�¦ p�u���H ¦¹����כ ×�æd��ܼ�Ð ¶ú�(R�:r��.

3.2.1 ��£� �� Ça��+ ĪÓÏ�

�:r ���½\�"f ���õ� �'a>� |9�_�\�¦ ��6£§õ� °ú s� &ñ_�ô�Ç��.

• ���õ� �'a>� |9�_�s��$�àÔ Ei,EjÞ E \� @/ �#� ���õ� �'a>�\�¦ óøÍéß�ô�Ç��. E��H G'p"f Û¼àÔaË>

X<s�'�_� Áºô�Ç |9�½+Ës���.

s��Qô�Ç ���õ� �'a>� |9�_�\�¦ %�o� ��9���, ���õ� �'a>�_� $íwn� #�ÂÒ\�¦ óøÍZ>� �

l� 0Aô�Ç �|�[þts� ¹כ��9���. {9�ìøÍ&h�ܼ�Ð #Q�"� ��|�s��� �&³�©� ��s�\� ���õ�

�'a>��� $íwn� ��9��� ��A�_� [j �|�s� ëß�7ᤠ�#��� ô�Ç��.[2].

• r�çß�&h� ���'��$í_� "é¶gË:"é¶����Ér ���õ��Ð�� r�çß��©�ܼ�Ð ·ú¡"f�� ô�Ç��.

• /BN1lx ����o_� "é¶gË:"é¶���õ� ���õ���H /BN1lxܼ�Ð ����oK��� ô�Ç��.

• )�0A&h� �'a>�_� C�]j "é¶gË:���õ���H "é¶��� ���ú\� _�K�"fëß� [O�"î÷&#Q�� ��¦, ���Ér ���ú\� _�ô�Ç [O�

"î ��0px$í�Ér C�]j÷&#Q�� ô�Ç��.

G'p"f Û¼àÔaË> X<s�'�\�"f ���õ� �'a>� |9�_� %�o���H s��Qô�Ç [j ��t� �|�[þt

�¦ ìøÍ%òô�Ç ��6 x�� &ñ_� ½©gË:\� ���� ���õ� �'a>�\�¦ óøÍZ>�ô�Ç��. 7£¤, ��6 x�� &ñ

_� ½©gË:�Ér G'p"f Û¼àÔaË> X<s�'�\�"f s��$�àÔ çß�_� ���õ� �'a>�\�¦ óøÍZ>� ���H l�

ï�rs���. �:r ���½\�"f��H ��6 x�� &ñ_� ½©gË:õ� ��6 x�� &ñ_� ]j1 ½©gË:\� K�{©� �

��H r�çß� �|�\� @/K�"f ��6£§õ� °ú s� &ñ_�ô�Ç��.

22

Ça��+ 9. ��6 x�� &ñ_� ½©gË:

s��$�àÔ Ei,EjÞ E \� @/ �#� ���õ� �'a>�\�¦ óøÍéß� ���H l�ï�rs���. ��6 x�� &ñ_�

½©gË: Pk Þ P��H s��$�àÔ �©� (Ei,Ej)\� @/ �#� ½©gË: Pk(Ei,Ej)\�¦ &h�6 x �#�

���õ� �'a>� $íwn��¦ óøÍZ>�ô�Ç��. P��H 3.2.1]X�_� ���õ� �'a>� $íwn��¦ 0Aô�Ç [j ��t�

�|��¦ �¿º ìøÍ%òô�Ç ½©gË:[þt_� |9�½+Ës���.

Ça��+ 10. r�çß�&h� ���'��$í

"é¶��� s��$�àÔ Ei _� µ1ÏÒqt r�y���Ér ���õ� s��$�àÔ Ej_� µ1ÏÒqt r�y���Ð�� ·ú¡�����.

ST (Ei) < ST (Ej) , i6=j

Ça��+ 11. 1lx r�çß�$í

"é¶��� s��$�àÔ Ei ü< ���õ� s��$�àÔ Ej_� µ1ÏÒqt r�y��_� �s���H 1lx r�çß�$í e��>�

°úכ α s�?/s���.

ST (Ej) − ST (Ei) ≤ α ( α > 0)

&ñ_� 10õ� 11��H ��6 x�� &ñ_� ]j1 ½©gË:_� �|�s� 9, ���õ� �'a>� $íwn��¦ 0A

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6£§õ� °ú s� &ño��)a��.

• r�çß�&h� ���'��$í - r�çß�&h� ���'��$í_� "é¶gË:

"é¶���s��$�àÔ_�µ1ÏÒqtr�y��s����õ�s��$�àÔ_�µ1ÏÒqtr�y���Ð��r�çß��©�ܼ�Ð

·ú¡"f��H �âĺ\� ëß�7á¤ô�Ç��.

• 1lx r�çß�$í - /BN1lx ����o_� "é¶gË:\�"f r�çß� �|�

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F� ���H ���õ� s��$�àÔ_� ����o\� %ò�¾Ó�¦ p��2;����H ���]j�� e��#Q�� ô�Ç��.

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ô�Ç��.

23

3.2.2 L±Ó�»jø� �¿½ÇÐ�+ 'K� «Å�(�×ø� �]�¦�> «Å�(�×

µ1ÏÒqtõ� ��ÃÌ_� í�H �&³�©�õ� %i���� �&³�©��Ér G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7�\�

��ÃÌô�Ç s��$�àÔ_� µ1ÏÒqt r�y�� J�����¦ [O�"îô�Ç��. ¢ô�Ç, s��$�àÔ_� µ1ÏÒqt r�y�� J�

����Ér G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7�\�"f |9�_� ���õ�\� %ò�¾Ó�¦ p�u���H s�

�$�àÔ_� ��ÃÌ í�H"f_� :£¤fç�¦ [O�"îô�Ç��. �:r ���½\�"f��H µ1ÏÒqtõ� ��ÃÌ_� í�H �&³

�©�õ� %i���� �&³�©�s� ���õ� �'a>� |9�_� ���õ�\� p�u���H %ò�¾Ó\� @/K�"f ¶ú�(R�:r��.

ÕªaË> 5ü< 6�Ér µ1ÏÒqtõ� ��ÃÌ_� í�H �&³�©�õ� %i���� �&³�©�s� |9�_� ���õ�\� p�u���H

%ò�¾Ó�¦�Ð#�ÅÒ�¦e����.��6 x��&ñ_�½©gË:\���Hr�çß�&h����'��$íõ�1lxr�çß�$í\�

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%i��¦ M:, ���õ� �'a>� |9�_� %�o� ���õ�\�¦ �Ð#�ÅÒ�¦ e����. s� �âĺ\���H 1lx r�çß�

$í e��>�°ú�כ¦ ëß�7ᤠ���H s��$�àÔ[þt ×�æ\�"f ]X�ìøÍs� !Q(�\� �>rF�ô�Ç��.

14 15 8 12 5 10 11 3도착 순서 8 7 6 5 4 3 2 1질의 수행 14 15 8 12 5 10 11 3버퍼 크기 : 4동 시간성 임계값 : 5질의 결과 : (12,14),(14,15)결과 누락 : (11,14),(10,14)버퍼 공간이벤트 발생 시각

ÕªaË> 5: µ1ÏÒqtõ� ��ÃÌ_� %i���� �&³�©�

ÕªaË> 6��H µ1ÏÒqtõ� ��ÃÌ_� í�H �&³�©�s� µ1ÏÒqt �%i��¦ M:, ���õ� �'a>� |9�_� %�o�

���õ�\�¦�Ð#�ÅÒ�¦e����.s��âĺ\���H1lxr�çß�$íe��>�°ú�כ¦ëß�7ᤠ���Hs��$�àÔ[þt

s� �¿º !Q(�\� �>rF�ô�Ç��.

24

15 14 12 11 10 8 5 3도착 순서 8 7 6 5 4 3 2 1질의 수행 15 14 12 11 10 8 5 3버퍼 크기 : 4동 시간성 임계값 : 5질의 결과 : (10,15),(11,15),(12,15),(14,15)버퍼 공간이벤트 발생 시각

ÕªaË> 6: µ1ÏÒqtõ� ��ÃÌ_� í�H �&³�©�

G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7��Ér µ1ÏÒqtõ� ��ÃÌ_� í�H �&³�©�õ� %i���� �&³�©�

_� µ1ÏÒqt\� ���Ér !Q(�_� µ1ÏÒqt r�y�� J�����¦ �Ð�����. �:r ���½\�"f��H !Q(�_� µ1Ï

Òqt r�y�� J�����¦ [O�"î ��¦�� !Q(�_� r�çß� ½çß�õ� r�çß� ���5Åq$í�¦ ��6£§õ� °ú 

s� &ñ_�ô�Ç��.

Ça��+ 12. !Q(�_� r�çß� ½çß�

!Q(�\� $��©��)a s��$�àÔ[þt_� µ1ÏÒqt r�y��_� þj5Åw°úכõ� þjÎ.°úכ_� #3�0As���.

Ça��+ 13. !Q(�_� r�çß� ���5Åq$í

µ1ÏÒqt r�y��s� !Q(�_� r�çß� ½çß�\� �í�<Ê÷&��H s��$�àÔ��H ìøÍ×¼r� !Q(�\� �>rF�ô�Ç

��.

µ1ÏÒqtõ� ��ÃÌ_� í�H �&³�©�s� t�5Åq&h�ܼ�Ð Ä»t�÷&��H �âĺ\���H !Q(�_� r�çß�

���5Åq$í�Ér $íwn��)a��. ìøÍ���\�, µ1ÏÒqtõ� ��ÃÌ_� %i���� �&³�©�s� µ1ÏÒqt �%i��¦ M: !Q

(�_�r�çß����5Åq$í�Ér$íwn�÷&t�·ú§��H��.!Q(�_�r�çß����5Åq$ís�$íwn�÷&��H�âĺ

_� :£¤fç�Ér ��6£§õ� °ú s� .��a(����¹כ

25

• !Q(�\�$��©�÷&��Hs��$�àÔ_�µ1ÏÒqtr�y���Ér!Q(�\�$��©��)as��$�àÔ[þt_�µ1ÏÒqt r�y�� þjÎ.°úכ�Ð�� ß¼��.

• s��$�àÔ_� ��ÃÌ í�H"f��H µ1ÏÒqt í�H"fs���.

• ��ÃÌô�Ç s��$�àÔ_� µ1ÏÒqt r�y��õ� 1lx r�çß�$í e��>�°úכ_� �s��� !Q(�_� r�çß� ½çß�\� �í�<Ê|c M:, 1lx r�çß�$í e��>�°ú�כ¦ ëß�7ᤠ���H s��$�àÔ��H &h�#Q�

��� s��©� �>rF�ô�Ç��.

����"f, 1lx r�çß�@/\� µ1ÏÒqtô�Ç s��$�àÔ��H !Q(�_� r�çß� ���5Åq$ís� $íwn�÷&��H

�âĺ\� �<Êa� %�o��)a��.

26

4 �¤d"� â«çÃÍÏ� PLl�'aUc"� ê�>ø� ®�N� ���+ %�h�

�:r �©�\�"f��H G'p"f Û¼àÔaË> X<s�'� %�o�\�¦ 0Aô�Ç ½¹כ ���½Ó�¦ ¶ú�(R�Ð�¦, G'p"f

Û¼àÔaË> X<s�'�\�"f ���õ� �'a>� |9�_� %�o�\�¦ 0Aô�Ç ~½ÓZO��¦ ]jîß�ô�Ç��.

4.1 �¤d"� â«çÃÍÏ� PLl�'a %�h���· �Dø5� ³ÀÄ© ��/�×

G'p"f Û¼àÔaË> X<s�'���H ���5Åq&h���� ��|¾Ó_� X<s�'�s���. s�%�!3� t�5Åq&h�ܼ�Ð {9�

§4�÷&��H@/|¾Ó_�G'p"fÛ¼àÔaË>X<s�'�\�¦%�o� �l�0Aô�ǹכ½ ���½Ó�Ér��6£§õ�°ú 

s� .a��[10](����¹כ

• í�H"fü< r�çß��¦ l�ìøÍܼ�Ð ���H |9�_��� %�o�÷&#Q�� ô�Ç��.

• |9�_�_� ���õ��Ð ��H�f�°ú�כ¦ )�6 x �#��� ô�Ç��.

• |9�_�\� @/ô�Ç ���õ�\�¦ %3��¦��, {9�§4�÷&��H ���H X<s�'�\�¦ @/�©�ܼ�Ð ���H

�¦�Ð(ç(Blocking) ���íß��¦ ��6 x �t� ·ú§���� ô�Ç��.

• $í0px x9� X<s�'� $��©��è\� @/ô�Ç ]j��� M:ë�H\� X<s�'�\� @/ô�Ç Ñþ�àÔA�(ç(Backtracking)�Ér &h�]X� �t� ·ú§��.

G'p"f Û¼àÔaË> X<s�'�%7�\�"f ���õ� �'a>� |9�_� %�o���H z�r�çß� s�?/\� ¢-a«Ñ

÷&#Q�� ô�Ç��. ����"f, �:r ���½\�"f��H ½�&h���� z�r�çß� %�o�_� ]j��� ���½Ó�¦

��6£§õ� °ú s� ]jîß�ô�Ç��. #�l�"f, z�r�çß� %�o�_� ]j��� #3�0A��H s��$�àÔ_� Òqt$í

ÂÒ'� |9�_� %�o� ¢-a«Ñ��t�s���.

��k�ë5Ñ %�h� V�»ÈÐ 1. ú|9� t���� r�çß� )�6 x °úכ

��ÃÌ r�y�� - µ1ÏÒqt r�y�� < ú|9� t���� r�çß� )�6 x °úכ

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|9�_� %�o� ¢-a«Ñ r�y�� - ��ÃÌ r�y�� < |9�_� %�o� ¢-a«Ñ t���� r�çß� )�6 x °úכ

27

4.2 ê�>ø� ®�N� ���+ %�h���· �Dø5� '�×ß��

G'p"f Û¼àÔaË> X<s�'� %�o�\�¦ 0Aô�Ç ½¹כ ���½Ó�¦ ìøÍ%ò �#�, ���õ� �'a>� |9�_� %�

o�\�¦ 0Aô�Ç ~½ÓZO��Ér ��6£§õ� °ú �Ér :£¤fçܼ�Ð �������.

• s��$�àÔ_� ��ÃÌ í�H"f\�¦ l�ìøÍܼ�Ð |9�_��� %�o��)a��.

• �7H�¦!3�(ç(Non-blocking) ���� ·ú��¦o�7£§�¦ s�6 x �#� ���� ���õ�\�¦ ��ØÔ

>� Òqt$íô�Ç��.

• |9�_� ú'�� r�, s��$�àÔ\�¦ $��©� ���H !Q(���H ô�Ç��� ���Ò�o�)a��.

s��Qô�Ç :£¤fç�¦ �¦�9 �#�, �:r ���½\�"f��H G'p"f Û¼àÔaË> X<s�'�\�"f ���õ�

�'a>� |9�_�\�¦ %�o�\�¦ 0Aô�Ç ¿º ��t� ~½ÓZO��¦ ]jîß�ô�Ç��.

• r�çß� �'ao� ~½ÓZO�s��$�àÔ_� ��ÃÌ í�H"f\�¦ ����â �#� Dh�Ðî�r ��ÃÌ í�H"f\�¦ ÂÒ#�ô�Ç��.

• ���õ� �'a>� ���� ~½ÓZO����õ� �'a>� óøÍZ>��¦ 0Aô�Ç s��$�àÔ �©�_� Òqt$í ��¦, ��6 x�� &ñ_� ½©gË:�¦ l�

ìøÍܼ�Ð ���õ� �'a>�\�¦ óøÍZ>�ô�Ç��.

ÕªaË> 7õ� ·ú��¦o�7£§ 1�Ér ���õ� �'a>� |9�_� %�o�_� õ�&ñ�¦ �Ð#�ÅÒ�¦ e����.

Algorithm 1: CausalityQueryProcessorinput: E is incoming eventbegin1

/∗ method1 is method of incoming order ∗/2

/∗ method2 is method of chronological order ∗/3

if method1 then4

IncomingOrder(E)5

if method2 then6

ChronologicalOrder(E)7

end8

28

인과 관계조인 방법 응용프로그램사용자 정의규칙센서 스트림데이터

인과 관계 질의 처리 과정인과 관계질의 결과시간 관리방법

ÕªaË> 7: ���õ� �'a>� |9�_� %�o� õ�&ñ

4.2.1 k�ë5Ñ ®�h� '�×ß��

���õ� �'a>� |9�_� %�o�\�¦ 0Aô�Ç r�çß� �'ao� ~½ÓZO��Ér G'p"f Û¼àÔaË> X<s�'� %�o� r�

Û¼%7�\� ��ÃÌô�Ç s��$�àÔ_� µ1ÏÒqt r�y�� J�����¦ �'ao� ��¦�� s��$�àÔ_� ��ÃÌ í�H"f

\�¦ ����â ���H �.���sכ ��ÃÌ í�H"f\�¦ ����â ���H s�Ä»��H ���õ� �'a>� |9�_�_� ���õ�

�� s��$�àÔ_� ��ÃÌ í�H"f\� ���� ²ú���t�l� M:ë�Hs���. �:r �7Hë�H\�"f��H ��6£§õ�

°ú s� r�çß� �'ao� ~½ÓZO��¦ ]jîß�ô�Ç��.

• ��ÃÌ í�H"f(Incoming order) ~½ÓZO�

µ1ÏÒqtõ� ��ÃÌ_� í�H �&³�©�õ� %i���� �&³�©��¦ )�6 xô�Ç��. ����"f, ����â �t� ·ú§

�Ér s��$�àÔ_� ��ÃÌ í�H"f\�¦ l�ìøÍܼ�Ð |9�_�\�¦ %�o�ô�Ç��.

• ���@/ í�H"f(Chronological order) ~½ÓZO�

µ1ÏÒqtõ� ��ÃÌ_� %i���� �&³�©��¦ µ1ÏÒqtõ� ��ÃÌ_� í�H �&³�©�ܼ�Ð ����âô�Ç��. ��

��"f, s��$�àÔ_� ��ÃÌ í�H"f\�¦ s��$�àÔ_� µ1ÏÒqt r�y��_� �2£§�í�Hܼ�Ð ���

�â �#� |9�_�\�¦ %�o�ô�Ç��.

29

���õ� �'a>� |9�_� %�o�\�¦ 0Aô�Ç ��ÃÌ í�H"f ~½ÓZO�_� :£¤fç�Ér ��6£§õ� °ú s� ���¹כ

÷&#Q�����.

• s��$�àÔ_� ��ÃÌ í�H"f��H ����â÷&t� ·ú§��H��.

• G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7�\� ��ÃÌô�Ç s��$�àÔ_� µ1ÏÒqt r�y�� J�����Ér µ1ÏÒqtõ� ��ÃÌ_� í�H �&³�©�õ� %i���� �&³�©�s� �¿º µ1ÏÒqt ��0px ���.

• !Q(�_� r�çß� ���5Åq$í�Ér µ1ÏÒqtõ� ��ÃÌ_� %i���� �&³�©�s� µ1ÏÒqt �t� ·ú§�¦ M:$íwn��)a��.

·ú��¦o�7£§ 2�Ér ���õ� �'a>� |9�_� %�o�\�¦ 0Aô�Ç ��ÃÌ í�H"f ~½ÓZO�_� õ�&ñ�¦ �Ð

#�ï�r��.

Algorithm 2: IncomingOrderinput: E is incoming eventbegin1

CausalityJoin(E)2

end3

���õ� �'a>� |9�_� %�o�\�¦ 0Aô�Ç ���@/ í�H"f ~½ÓZO�_� :£¤fç�Ér ��6£§õ� °ú s� ���¹כ

�)a��.

• s��$�àÔ_� ��ÃÌ í�H"f��H s��$�àÔ_� µ1ÏÒqt í�H"f\� ����"f ����â�)a��.

• G'p"f Û¼àÔaË> X<s�'� %�o� r�Û¼%7�\� ��ÃÌô�Ç s��$�àÔ_� µ1ÏÒqt r�y�� J�����Ér µ1ÏÒqtõ� ��ÃÌ_� í�H �&³�©�ëß�s� µ1ÏÒqt ��0px ���.

• !Q(�_� r�çß� ���5Åq$ís� $íwn��)a��.

���@/ í�H"f ~½ÓZO�_� éß�&h��Ér ���H s��$�àÔ_� ��ÃÌ í�H"f\�¦ ����â ���H 1lxîß�\�

���õ��'a>�|9�_�_�%�o���t�����)a����H���Qô�Çéß�&h��¦K��s���.sכ�� �l�0AK�

"f �:r �7Hë�H\�"f��H ÂÒì�r&h�ܼ�Ð ��ÃÌ í�H"f\�¦ ����â ���H >h¥Æ��¦ ]jîß�ô�Ç��.

30

Ça��+ 14. ��ÃÌ í�H"f ����â s��$�àÔ Ãº

��ÃÌ í�H"f\�¦ µ1ÏÒqt í�H"f�Ð ����â½+É s��$�àÔ_� >hús���.

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����â s��$�àÔ Ãº\�¦ &h�6 xô�Ç ���@/ í�H"f ~½ÓZO��Ér !Q(�_� r�çß� ���5Åq$ís� $íwn�÷&

t� ·ú§��H��. ����"f, ÂÒì�r&h�ܼ�Ð s��$�àÔ_� ��ÃÌ í�H"f\�¦ µ1ÏÒqt í�H"f\� ���� ���

�â ���� s��$�àÔ\�¦ !Qo���H �âĺ�� µ1ÏÒqtô�Ç��. 7£¤, ��ÃÌ í�H"f ����â s��$�àÔ Ãº\�¦

&h�6 xô�Ç ���@/ í�H"f ~½ÓZO�\�"f��H !Q(�_� r�çß� ���5Åq$ís� $íwn�÷&�¦�� s��$�àÔ �<H

z�s� µ1ÏÒqtô�Ç��.

ÕªaË> 8�Ér ��ÃÌ í�H"f ����â s��$�àÔ Ãº\�¦ &h�6 xô�Ç ���@/ í�H"f ~½ÓZO�\�"f, !Q(�

_� r�çß� ���5Åq$ís� $íwn�÷&�¦�� s��$�àÔ�� �<Hz�÷&��H \V\�¦ �Ð#�ÅÒ�¦ e����. �<H

z�÷&��H s�Ä»��H, !Q(� ?/\� �>rF� ���H s��$�àÔ[þt_� þj@/ µ1ÏÒqt r�y�� 12�Ð�� 8õ�

11s� ��ØÔl� M:ë�Hs���.

도착 순서 8 7 6 5 4 3 2 1이벤트 발생 시각 14 15 8 11 5 10 12 3도착 순서 변경이벤트 발생 시각 15 14 12 10 5 3인과 관계 조인버퍼 크기 : 4동 시간성 임계값 : 5도착 순서 변경 이벤트 수 : 4이벤트 손실 : 8,11 ( < 12 )질의 결과 : (10,15),(12,15),(14,15)결과 누락 : (11,15)

버퍼 공간8 7 6 5 4 3 2 115 14 11 8 12 10 5 3

ÕªaË> 8: ��ÃÌ í�H"f ����â s��$�àÔ Ãº\�¦ &h�6 xô�Ç ���@/ í�H"f ~½ÓZO�

31

·ú��¦o�7£§ 3�Ér ��ÃÌ í�H"f ����â s��$�àÔ Ãº\�¦ &h�6 xô�Ç ���@/ í�H"f ~½ÓZO��¦ �Ð

#�ÅÒ�¦ e����.

Algorithm 3: ChronologicalOrderinput: E is incoming eventbegin1

/∗ buf1 is memory-based storage for adjusting arrival order ∗/2

/∗ buf2 is memory-based storage for join ∗/3

/∗ MaxSize(buf1) is number of events sorted by sensing time ∗/4

AddEvent(buf1,E)5

/∗ make an array for accommodated events on sensing time ∗/6

SortEvent(buf1)7

if MaxSize(buf1) == GetSize(buf1) then8

for i = 1 To MaxSize(buf1) do9

/∗ fetchs an event which has adjusted arrival order ∗/10

E1=GetEvent(buf1,i)11

DelEvent(buf1,i)12

if GetSize(buf2)== 0 then13

AddEvent(buf2,E)14

else15

/∗ fetchs an event which has maximum sensing time in16

buf2 ∗/E2=GetEventMaxSensingT ime(buf2)17

if ST(E1) > ST(E2) then18

CausalityJoin(E)19

/∗ stores event E in buf2 ∗/20

AddEvent(buf2,E)21

end22

��ÃÌ í�H"f ����â s��$�àÔ Ãº\�¦ &h�6 xô�Ç ���@/ í�H"f ~½ÓZO�\�"f��H ��ÃÌ í�H"f ���

�â s��$�àÔ Ãº\� _�K�"f |9�_� %�o� ¢-a«Ñ t����s� µ1ÏÒqtô�Ç��. Õª�Q�� |9�_� %�o�

¢-a«Ñ t���� r�çß��Ér z�r�çß� %�o� ]j��� 2 s�?/\�"f )�6 x�)a��. �:r ]X�\�"f��H �

�ÃÌí�H"f����âs��$�àÔú\�¦&h�6 xô�Ç���@/í�H"f~½ÓZO�_�|9�_�%�o�¢-a«Ñt����r�

çß��¦ ��&ñ 3\�"f ]jîß�ô�Ç��. ¢ô�Ç, �:r ���½\�"f��H z�r�çß� %�o� ]j��� 2 s�?/\�

"f )�6 x÷&��H ��ÃÌ í�H"f ����â s��$�àÔ Ãº\�¦ ]jîß�ô�Ç��.

32

��Ça� 3. |9�_� %�o� ¢-a«Ñ t���� r�çß�

|9�_� %�o� ¢-a«Ñ t���� r�çß� = s��$�àÔ n >h_� ��ÃÌ í�H"f ����â r�çß� + s��$�àÔ

n >h_� |9�_� %�o� r�çß�

��Ça� 4. s��$�àÔ n >h_� ��ÃÌ í�H"f ����â r�çß�

s��$�àÔ n >h_� ��ÃÌ í�H"f ����â r�çß� = ��ÃÌ çß���� × (n-1)

��Ça� 5. s��$�àÔ n >h_� |9�_� %�o� r�çß�

s��$�àÔ n>h_� |9�_� %�o� r�çß� < ��ÃÌ çß����

��k�ë5Ñ %�h� V�»ÈÐ 3. ��ÃÌ í�H"f ����â s��$�àÔ Ãº

|9�_� %�o� ¢-a«Ñ t���� r�çß� )�6 x °úכ��ÃÌ çß����

≥ ��ÃÌ í�H"f ����â s��$�àÔ Ãº

4.2.2 ê�>ø� ®�N� �¿ê�> '�×ß��

�:r �7Hë�H\�"f��H G'p"f Û¼àÔaË> X<s�'�\�"f s��$�àÔ çß�_� ���õ� �'a>�\�¦ óøÍZ>� ���H

���õ� �'a>� ���� ~½ÓZO��¦ ]jîß�ô�Ç��. ���õ� �'a>� ���� ~½ÓZO�_� õ�&ñ�Ér ��6£§õ� °ú 

��.

1. s��$�àÔ �©� Òqt$í

G'p"f Û¼àÔaË> X<s�'��ÐÂÒ'� s��$�àÔ �©��¦ Òqt$íô�Ç��.

2. ���õ� �'a>� óøÍZ>�

��6 x�� &ñ_� ½©gË:�¦ l�ìøÍܼ�Ð ���õ� �'a>�\�¦ ëß�7ᤠ���H s��$�àÔ �©��¦ óøÍ

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n∑

k=1

Pk(Ei, Ej) , Pk(Ei, Ej) =

1 for true

0 for false

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Algorithm 4: CausalityJoininput : E is incoming eventoutput: pairs consists of pairs as (event,event)begin1

/∗ P is a set of user-defined rules ∗/2

/∗ buf2 is memory-based storage for join ∗/3

/∗ joins the incoming event with events in buf2 ∗/4

/∗ pairs is result of Causality Join ∗/5

for i = 1 To GetSize(buf2) do6

Bi = GetEvent(buf2,i)7

pair = CreatePair(E,Bi)8

for j = 1 To GetSize(P ) do9

/∗ determinates causality with pair on user-defined rule ∗/10

if Pj(pair) == 1 then11

count++12

/∗ pair has causality relationship∗/13

if count == GetSize(P ) then14

/∗ add pair to pairs ∗/15

AddPair(pairs,pair)16

/∗ buf2 is no enough memory to accommodate E ∗/17

if MaxSize(buf2) == GetSize(buf2) then18

/∗ flush the event which has minimum arrival time into out of19

buf2 ∗/DelEventMinArrivalT ime(buf2)20

end21

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44

63 58 41 59 42 52 48 34도착 순서 8 7 6 5 4 3 2 1인과 관계 조인 63 58 41 59 42 52 48 34버퍼 크기 : 4동 시간성 임계값 : 20

버퍼 공간63 59 58 41 52 48 42 34도착 순서 변경 8 7 5 4 3 2 1

인과 관계 조인 63 58 52 48 42 34도착 순서 변경 이벤트 수 : 4이벤트 손실 : 41 ( < 52 )질의 결과 : (48,63),(52,63),(58,63),(59,63)버퍼 공간

이벤트 발생 시각

이벤트 발생 시각a) 도착 순서 방법( 재현율 0.5 )

b) 연대 순서 방법( 재현율 1.0 )

질의 결과 : (59,63),(58,63)결과 누락 : (48,63),(52,63)659

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45

63 50 45 59 58 41 48 34도착 순서 8 7 6 5 4 3 2 1인과 관계 조인 63 50 45 59 58 41 48 34버퍼 크기 : 4동 시간성 임계값 : 20

버퍼 공간63 59 50 45 58 48 41 34도착 순서 변경 8 7 5 4 3 2 1

인과 관계 조인 63 59 58 48 41 34도착 순서 변경 이벤트 수 : 4이벤트 손실 : 45,50 ( < 58 )질의 결과 : (48,63),(58,63),(59,63)결과 누락 : (45,63),(50.63)

버퍼 공간

이벤트 발생 시각

이벤트 발생 시각a) 도착 순서 방법( 재현율 0.8 )

b) 연대 순서 방법( 재현율 0.6 )

질의 결과 : (58,63),(59,63),(45,63),(50,63)결과 누락 : (48,63)6

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51

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52

Time Management Method for QueryProcessing of Causality on Sensor Stream

Data

Lee Sang-Hyun

Department of Computer Engineering, Pusan National University

Abstract

According to the disseminate of sensor network and development of re-

lated technology, analysis of sensor stream data is beginning to make its

appearance. So, Causality is necessary in extracting meaningful informa-

tion.

Query processing of causality requires sensing time of sensor in determi-

nating causal relationships between events on sensor stream data, because

cause precedes effect.

To raise performance of query processing of causality, events that have

consecutive orders for sensing time of event should be conducted continu-

ously. But, the event has arrival order which is different from occurrence

order in system for processing sensor stream data. This research suggests

time management method, which event is conducted continuously in consec-

utive order in sensing time of event, to change arrival order into occurrence

order.

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