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 etźal., 2006). The main issue is to formulate a M/G/1 queue wherein the service distribution is the Exponential Conway-Maxwell Poisson distribution (Cordeiro etźal., 2012) which uses a new defense mechanism against long waiting time. A Bayesian simulation study and an example with a real dataset are provided.