2重待ち行列系の情報システムに関する基礎的研究

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  • Study on Information System of Double Queues
  • 2ジュウ マチギョウレツケイ ノ ジョウホウ システム ニ カンスル キソテキ

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In this paper, two models of double queues in a taxi stand are presented and compared from a practical point of views : one is a mathematical model developed by M. W. Sasieni and the other a simulation model by the author. In Sasieni's model, it is assumed that if any queue of customers is observed, no queue of taxis exists and the reverse is also true. These assumptions are only admissible when (1) the service time, 1/μ₀, is extremly short the service is finished in a moment, and/or (2) the number of channels (stands), C, is enough large that empty channels are always available. Therefore a more general simulation model has been newly developed. However, the mathematical model can offer information, at some limited level of strata, in simple way. This simplicity is very attractive for practical men like planners. Then, after verification of the simulation model the domain where the mathematical model is workable has been discussed in the term of ρ ＝λ/Cμ₀（λ: a mean arrival rate of customer or taxi). And the following results are shown: (i) in the domain where ρ≦0.4, the mathematical model can be used safely, (ii) in ρ≧0.8, the simulation model should be used, and (iii) an 0.4<ρ<0.8, the choice should be done according to other practical data.

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