Regularly varying tail of the waiting time distribution in M/G/1 retrial queue

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.