Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ANALYSIS OF QUEUEING MODEL WITH PRIORITY SCHEDULING BY SUPPLEMENTARY VARIABLE METHOD

  • Choi, Doo Il (Department of Applied Mathematics, Halla University)
  • Received : 2012.07.03
  • Accepted : 2012.11.05
  • Published : 2013.01.30
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Abstract

We analyze queueing model with priority scheduling by supplementary variable method. Customers are classified into two types (type-1 and type-2 ) according to their characteristics. Customers of each type arrive by independent Poisson processes, and all customers regardless of type have same general service time. The service order of each type is determined by the queue length of type-1 buffer. If the queue length of type-1 customer exceeds a threshold L, the service priority is given to the type-1 customer. Otherwise, the service priority is given to type-2 customer. Method of supplementary variable by remaining service time gives us information for queue length of two buffers. That is, we derive the differential difference equations for our queueing system. We obtain joint probability generating function for two queue lengths and the remaining service time. Also, the mean queue length of each buffer is derived.

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References

  1. N. K. Jaiswal, priority queues, Academic Press, New York, (1968).
  2. R. Chipalkatti, J. F. Kurose, and D. Towsley, Scheduling policies for real-time and nonrealtime traffic in a statistical multiplexer, Proceedings of the IEEE INFOCOM'89, Ottawa (1989), 774-783.
  3. A. Sugahara, T. Takine, Y. Takahashi, T. Hasegawa, Analysis of a nonpreemptive priority queue with SPP arrivals of high class, Perf. Eval. 21 (1995), 215-238. https://doi.org/10.1016/0166-5316(93)E0044-6
  4. D. I. Choi and Y. Lee, Performance analysis of a dynamic priority queue for traffic control of bursty traffic in ATM networks, IEE Proc. - Commun. 148 (2001), No. 3 181-187. https://doi.org/10.1049/ip-com:20010115
  5. C. Knessl, D. I. Choi and C. Tier, A dynamic priority queue model for simultaneous service of two traffic types, SIAM J. APPL. MATH. 63(2002), No. 2 398-422. https://doi.org/10.1137/S0036139901390842
  6. D. I. Choi, B. D. Choi and D. K. Sung, Performance analysis of priority leaky bucket scheme with queue-length-threshold scheduling policy, IEE Proc.- Comm. 145 (1998), No. 6 395-401. https://doi.org/10.1049/ip-com:19982287
  7. B. D. Choi, D. I. Choi, An analysis of M,MMPP/G/1 queue with QLT scheduling policy and Bernoulli schedule, IEICE Tran. on Comm. E81-B (1998), No. 1 13-22.
  8. D. S. Lee and B. Sengupta, Queueing analysis of a threshold based priority scheme for ATM networks, IEEE/ACM Tran. on Networking 1(1993), No. 6 709-717. https://doi.org/10.1109/90.266058
  9. D. I. Choi, Transient analysis of a queueing system with Markov-modulated Bernoulli arrivals and overload control, Journal of Applied Mathematics and Computing 15(2004), No.1-2 405-414.
  10. D. I. Choi, Analysis of a queueing system with overload control by arrival rates, Journal of Applied Mathematics and Computing 18(2005), No.1-2 455-464.