Abstract
We consider an M/G/1 retrial queue where the service time distribution has a regularly varying tail with index −β, β>1. The waiting time distribution is shown to have a regularly varying tail with index 1−β, and the pre-factor is determined explicitly. The result is obtained by comparing the waiting time in the M/G/1 retrial queue with the waiting time in the ordinary M/G/1 queue with random order service policy.
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J. Kim’s research was supported by the Korea Research Foundation (KRF) grant funded by the Korea government (MEST) (2009-0076674). B. Kim’s research was supported by the Korea Research Foundation (KRF) grant funded by the Korea government (MEST) (2009-0076600).
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Kim, J., Kim, J. & Kim, B. Regularly varying tail of the waiting time distribution in M/G/1 retrial queue. Queueing Syst 65, 365–383 (2010). https://doi.org/10.1007/s11134-010-9180-3
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DOI: https://doi.org/10.1007/s11134-010-9180-3
Keywords
- M/G/1 retrial queue
- Regular variation
- Waiting time distribution
- Stochastic comparison
- Random order service