Earticle

A Krawtchouk polynomial is introduced as the classical Mac-Williams identity, which can be expressed in weight-enumerator-free form of a linear code and its dual code over a Hamming scheme. In this paper we find a new explicit expression for the $p$-number and the $q$-number, which are more generalized notions of the Krawtchouk polynomial in the P-polynomial schemes by using an extended version of a discrete Green's function. As corollaries, we obtain a new expression of the Krawtchouk polynomial over the Hamming scheme and the Eberlein polynomial over the Johnson scheme. Furthermore, we find another version of the MacWilliams identity over a Hamming scheme.

유한버퍼를 갖는 시스템에 대한 분석은 광범위하게 연구되어 왔다. 하지만, 상수 공정시간을 갖는 시스템에 대해서도 안정 대기시간에 대한 고차평균과 꼬리확률에 대한 간결한 표현식은 소개된 적이 없다. 유한버퍼로 인한 차단현상으로 유발되는 복잡성 때문에 일반적인 대기행렬이론은 이를 적절히 다루지 못한다. 본 연구에서는 max-plus 대수를 활용한 기존 연구결과로 부터 상수 공정시간과 DBR (Drum-Buffer-Rope) 재고규칙을 따르는 라인생산시스템에서의 대기시간에 대한 간결한 표현식을 도출하였다.

Although systems with finite capacities have been the topic of much study, there are as of yet no analytic expressions for (higher) moment and tail probability of stationary waiting times in systems with even constant processing times. The normal queueing theory cannot properly handle such systems due to the difficulties caused by finite capacity. In this study, for a DBR (Drum-Buffer-Rope) line production system with constant processing times, we introduce analytic expressions by using previous results obtained using a max-plus algebraic approach.