Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
권호 표지

POISSON ARRIVAL QUEUE WITH ALTERNATING SERVICE RATES

  • KIM JONGWOO (Statistical Research Center for Complex Systems, Seoul National University) ;
  • LEE EUI YONG (Department of Statistics, Sookmyung Women’s University) ;
  • LEE HO WOO (Department of Systems Management Engineering, Sungkyunkwan University)
  • Published : 2005.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

We adopt the P/sub λ, T//sup M/ policy of dam to introduce a service policy with alternating service rates for a Poisson arrival queue, in which the service rate alternates depending on the number of customers in the system. The stationary distribution of the number of customers in the system is derived and, after operating costs being assigned to the system, the optimization of the policy is studied.

Keywords

References

  1. ABDEL-HAMEED, M. (2000). 'Optimal control of a dam using $P_{\lambda}^M,{\gamma}$ policies and penalty cost when the input process is a compound Poisson process with positive drift', Journal of Applied Probability, 37, 408-416 https://doi.org/10.1239/jap/1014842546
  2. BAE, J., KIM, S. AND LEE, E. Y. (2003). 'Average cost under the $P_{\lambda}^M,{\gamma}$ policy in a finite dam with compound Poisson inputs', Journal of Applied Probability, 40, 519-526 https://doi.org/10.1239/jap/1053003561
  3. FADDY, M. J. (1974). 'Optimal control of finite dams: Discrete (2-stage) output procedure', Journal of Applied Probability, 11, 111-121 https://doi.org/10.2307/3212588
  4. KARLIN, S. AND TAYLOR, H. M. (1975). A First Course in Stochastic Processes, 2nd edition, Academic Press, New York
  5. LEE, E. Y. AND AHN, S. K. (1998). '$P_{\lambda}^M$ -policy for a dam with input formed by a compound Poisson process', Journal of Applied Probability, 35, 482-488 https://doi.org/10.1239/jap/1032192863
  6. LI, S.-Q. (1989). 'Overload control in a finite message storage buffer', IEEE Transactions on Communications, 37, 1330-1338 https://doi.org/10.1109/26.44204
  7. YEH, L. (1985). 'Optimal control of a finite dam: Average-cost case', Journal of Applied Probability, 22, 480-484 https://doi.org/10.2307/3213793