A single-server queueing system with modified service mechanism

We consider a single-server GI/G/1 queueing system with modified service mechanism. By modified service mechanism, we mean that the service time distribution (H₀) for the customers arriving to find the system idle may be different from the service time distribution (H₁) for the customers arriving to find the system busy. We present qualitative relationships among the performance measures in the system. Approximating the virtual waiting time process via the diffusion process and combining the qualitative relationships, we propose a new approximate formula for the mean performance measures. For special cases, our approximation is seen to be consistent with the previously-obtained exact results for the M/G/1 queueing system with modified service mechanism, and it is further seen to be consistent with the previously-proposed approximate results for the GI/GI/1 queueing system with standard (H₀ = H₁) service mechanism.