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Architecture of Computing Systems (Lecture Notes in Computer ...

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The JoSchKa System 79<br />

This results <strong>in</strong> �������� = �240 − 220� �2=40. The average job runtime closest<br />

to this value is ���� =60, the closest mean value is ����� = �<br />

������ ������ =35.<br />

So we get ����� = 35. Because <strong>of</strong> ���� = ����� � rnd�−2,2�, the node gets a job<br />

<strong>of</strong> the (randomly chosen) type ��� or ���. Fig. 2 expla<strong>in</strong>s the example.<br />

|��� − ���|<br />

����1 ����2 ����3 ���1 x<br />

���2 x x<br />

���<br />

����<br />

�������� = |��� − ���| ∙ 2<br />

Fig. 2. Uptime-based distribution example<br />

Due to the usage <strong>of</strong> the mean values and the randomization, the system performs a<br />

stochastic selection between the two best suited job types, if the ideal target value<br />

�������� resides <strong>in</strong> the mean <strong>of</strong> two neighbored job types. The example shows<br />

also, why the largest average runtime (��� �, <strong>in</strong> the example ��� �) is excluded<br />

when calculat<strong>in</strong>g ����. Otherwise, the nodes with the largest rema<strong>in</strong><strong>in</strong>g uptime<br />

would work for the user with the longest runn<strong>in</strong>g jobs only. In other words, a node<br />

gets<br />

• a job <strong>of</strong> type �� � if �������� lies <strong>in</strong> the <strong>in</strong>terval � � or<br />

• a job <strong>of</strong> type �� � or �� ��� (selected randomly), if �������� lies <strong>in</strong> the <strong>in</strong>terval<br />

� �,���.<br />

The <strong>in</strong>terval bounds for the example above are graphically shown <strong>in</strong> Fig. 3. In general,<br />

the <strong>in</strong>tervals are described as follows (� types, � ��1, … , � − 1�):<br />

��� 3<br />

• �� =� �<br />

��������� ������, �<br />

������ ��������, where<br />

�� =�0, �<br />

� ����� �������� • ��,��� =� �<br />

������ �������, �<br />

������� ���������, where<br />

����,� =� �<br />

� ������� ���������,∞� Fig. 3. Interval bounds example<br />

��� 4<br />

� 1 � 1,2 � 2 � 2,3 � 3 � 3,4<br />

��� 3<br />

��� 4<br />

��� ���<br />

����1 ����2 ����3 ���1 x<br />

���2 x x<br />

���

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