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

Abstract

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.

Keywords

References

  1. Management Science v.39 Second Derivative Sample Path Estimators for the GI/G/m Queue Fu, M.C.;Hu, J.Q.
  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.
  6. Korean Journal of Management Science v.17 Sensitivity Analysis for the Busy Cycle in M/M/1 Queue Park, H.S.
  7. Journal of the Korean Statistical Society v.25 Smoothed Perturbation Analysis for Performance Measures in a Markov Renewal Process Park, H.S.