Flexible M/G/1 queueing system with state dependent service rate

In this paper, we propose the extended Poisson distribution which unifies some well-known models in finite queues that have been used to model congestion in vehicular, pedestrian traffic networks as well as the Conway–Maxwell Poisson distribution (Kadane et al., 2006). The main issue is to formulate a M/G/1 queue wherein the service distribution is the Exponential Conway–Maxwell Poisson distribution (Cordeiro et al., 2012) which uses a new defense mechanism against long waiting time. A Bayesian simulation study and an example with a real dataset are provided.