- Volume 47 Issue 6
DOI QR Code
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
For an M/G/1 processor-sharing queue with batch arrivals, Avrachenkov et al.  conjectured that the conditional mean sojourn time is concave. However, Kim and Kim  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.
processor-sharing queue;batch arrivals;sojourn time;concavity
Supported by : Chungbuk National University
- 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
- 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
H. Feng and V. Misra, Asymptotic bounds for
$M^X/G/1$processor sharing queues, Tech. Rep., CUCS-006-04, Columbia University, 2003.
- 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
- 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
- L. Kleinrock, Time-shared systems: A theoretical treatment, J. Assoc. Comput. Mach. 14 (1967), 242-261. https://doi.org/10.1145/321386.321388
- 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
- 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.