A queueing model with mutually independent service times whose distributions are not necessarily identical

The queueing model discussed in this paper relaxes the requirement that the service times be mutually independent and have identical distribution in a GI/G/1 queue. It only requires that the restriction on service process be reduced to the degree that the service times be mutually independent. It follows that this queueing model is more rational than GI/G/1 queue in simulating real-world systems. Under the relaxed restriction, the transient distribution of the queue length of the queueing system discussed is obtained by means of supplementary variables.