Second Derivative Estimation for Performance Measures in a Markov Renewal Process

  • Heung Sik Park (Staff of Natural Sciences, Sejong University, Seoul, 143-747, Korea)
  • Published : 1997.08.01


In this paper, we find the second derivative of mean busy cycle with respect to a parameter of inter-arrival time distribution. We show that this derivative can be estimated from single sample path. We do the similar thing for the mean number of arrivals during busy cycle.



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  2. Queueing Systems v.18 Perturbation Analysis of the GI/G/1 Queue Zazanis, M.A.;Suri, R.
  3. Management Science v.34 Perturbation Analysis Gives Strongly Consistent Sensitivity Estimates for the M/G/1 Queue Suri, R.;Zazanis, M.A.
  4. IEEE Transactions on Automatic Control v.37 Extensions and Generalizations of Smoothed Perturbation Analysis in a Generalized Semi-Markov Process Framework Fu, M.C.;Hu, J.Q.
  5. IEEE Transactions on Automatic Control v.35 Smoothed Perturbation Analysis for a Class of Discrete Event Systems Glasserman, P.;Gong, W.B.
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  7. Journal of the Korean Statistical Society v.25 Smoothed Perturbation Analysis for Performance Measures in a Markov Renewal Process Park, H.S.