Analysis of an M/G/1 queue with customer impatience and adaptive arrival process

We study an M/G/1 queue with impatience and an adaptive arrival process. The rate of the arrival process changes according to whether an incoming customer is accepted or rejected. We analyse two different models for impatience: (i) based on workload, and (ii) based on queue-length. For the workload-based model, we obtain the Laplace-Stieltjes Transform of the joint stationary workload and arrival rate process, and that of the waiting time. For the queue-length based model we obtain the analogous z-transform. These queueing models might also be useful for capturing the interaction between congestion control algorithms and queue management schemes in the Internet.