Analysis of cocoon feeding system with a priority order of seniority

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  • 先任優先権をもった繭補充システムの解析
  • 先任優先権をもった繭補充システムの解析I : 空バスケット連の確率分布
  • センニン ユウセンケン オ モッタ マユ ホジュウ システム ノ カイセキ 1
  • I. Probability distribution of the size of empty baskets run
  • I. 空バスケット連の確率分布

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We dealt with the probability distribution of the size of empty baskets run in the feeling process of newly-cooked cocoons with a priority order of seniority.<br>We now define each notation as follows;<br>Z(j); random variable on the size of empty baskets run at the j th's store box of cooked cocoons, <br>k; number of the empty units, <br>q; probability that a store box requiring cocoons accepts the cocoon of one unit from the basket series, p=1-q, <br>P(Z(j)=k); probability of (Z(j)=k).<br>From our analysis, the next relation was led.<br>P(Z(1)=k)=qkp, P(Z(2)=k)=∑kl=0(k+l 2l)p2(pq)k<br>As a general rule, <br>P(Z(j+1)=k)=P(Z(j)=k)pk+1+∑k-1i=0P(Z(j)=i)P(Z(j)=k-i-1)(k+1 2)qpk/(k 1)<br>+∑k-2i=0∑k-2-Il=0P(Z(j)=i)P(Z(j)=l)P(Z(j)=k-i-l-2)(k+2 4)q2pk-1/(k 2)<br>+……+[P(Z(j)=0)]k+1(k+k 2k)qkp/(k k)<br>where j=2, 3, ……, N-1. These theoretical results were verified by means of Monte-Carlo procedures and the validity was certified.

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