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

• Kim, Jeong-Sim
• Published : 2010.11.30
• 45 4

#### 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

#### References

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#### Acknowledgement

Supported by : Chungbuk National University