Analysis of the GI/E<sub>k</sub>/1 queue with finite waiting room by the supplementary variable approach

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公開日
1984-01
権利情報
  • http://onlinelibrary.wiley.com/termsAndConditions#vor
DOI
  • 10.1002/ecja.4400670103
公開者
Wiley

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<jats:title>Abstract</jats:title><jats:p>This paper combines the supplementary variable method and the phase method to analyze the steady‐state of GI/E<jats:sub>k</jats:sub>/1 with finite waiting room. Although there have been many studies made on the queue with finite waiting room, there has not been a study of GI/Ek/<jats:sub>1</jats:sub>which determines the characteristic quantities and discusses the characteristics by numerical computation. This paper defines first the residual arrival time as the supplementary variable and derives steady‐state basic equations for the joint probability density functions of that variable and the total remaining number of phases in the system. Using Laplace transform, the solutions are represented by the joint probability densities for the remaining number of phases and the zero remaining arrival time. the value of joint probability densities is determined, if the distribution function of arrival interval is given, by solving a system of linear equations by numerical computation. Using that solution, various characteristic quantities are represented such as number of customers in the system, actual waiting time, response time, distribution of busy period length, distribution of idle period length, loss probability and power. Finally, the analytical result for GI/M/1/N is found to be equal to the known result, and as a numerical example characteristic quantities of GI/E4/1/4* are illustrated, together with the discussion for the characteristics.</jats:p>

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