Abstract:

 A GI／G／1 queue with setup times was modelled to describe the automatic repeat request (ARQ) protocol in communication network. First, a functional lower and upper bound for the idle time was constructed, and then the bound relation was used to obtain the diffusion approximations for the queue length, workload and busy time processes.

Key words:  GI／G／1 queue with setup times; fluid approximation; diffusion approximation