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CONCAVITY OF THE CONDITIONAL MEAN SOJOURN TIME IN THE PROCESSOR-SHARING QUEUE WITH BATCH ARRIVALS

  • Kim, Jeong-Sim (DEPARTMENT OF MATHEMATICS EDUCATION CHUNGBUK NATIONAL UNIVERSITY)
  • Received : 2009.04.19
  • Published : 2010.11.30

Abstract

For an M/G/1 processor-sharing queue with batch arrivals, Avrachenkov et al. [1] conjectured that the conditional mean sojourn time is concave. However, Kim and Kim [5] showed that this conjecture is not true in general. In this paper, we show that this conjecture is true if the service times have a hyperexponential distribution.

Keywords

processor-sharing queue;batch arrivals;sojourn time;concavity

Acknowledgement

Supported by : Chungbuk National University

References

  1. K. Avrachenkov, U. Ayesta, and P. Brown, Batch arrival processor-sharing with application to multi-level processor-sharing scheduling, Queueing Syst. 50 (2005), no. 4, 459-480. https://doi.org/10.1007/s11134-005-1666-z
  2. N. Bansal, Analysis of the M/G/1 processor-sharing queue with bulk arrivals, Oper. Res. Lett. 31 (2003), no. 5, 401-405. https://doi.org/10.1016/S0167-6377(03)00029-4
  3. H. Feng and V. Misra, Asymptotic bounds for $M^X/G/1$ processor sharing queues, Tech. Rep., CUCS-006-04, Columbia University, 2003.
  4. J. Kim and B. Kim, The processor-sharing queue with bulk arrivals and phase-type services, Perform. Eval. 64 (2007), no. 4, 277-297. https://doi.org/10.1016/j.peva.2006.05.006
  5. J. Kim and B. Kim, Concavity of the conditional mean sojourn time in the M/G/1 processor-sharing queue with batch arrivals, Queueing Syst. 58 (2008), no. 1, 57-64. https://doi.org/10.1007/s11134-007-9058-1
  6. L. Kleinrock, Time-shared systems: A theoretical treatment, J. Assoc. Comput. Mach. 14 (1967), 242-261. https://doi.org/10.1145/321386.321388
  7. L. Kleinrock, R. R. Muntz, and E. Rodemich, The processor-sharing queueing model for time-shared systems with bulk arrivals, Networks 1 (1971), no. 1, 1-13. https://doi.org/10.1002/net.3230010103
  8. K. M. Rege and B. Sengupta, The M/G/1 processor-sharing queue with bulk arrivals, in: Modelling and Performance Evaluation of ATM Technology, Elsevier, Amsterdam, 1993, 417-432.