Queueing theory is an important technique to study and evaluate the performance of system. Queueing theory is applied in many applications such as logistics, finance, emergency services and project management, etc. In this research we apply neutrosophic philosophy in queueing theory. We deal with several queue models such as M/M/1 queue, M/M/s queue and M/M/1/b queue. We illustrate, solve, and find the performance measures of M/M/1, M/M/s, and M/M/1/b crisp queue models via examples with exact arrival rate and service rate. Queueing models affect by many factors such as arrival rate, service rate, number of servers, etc. These factors are not constantly expressed by accurate times; hence we express the parameters of queueing system by the neutrosophic. We express arriving rates and serving rates by neutrosophic values. We also illustrate, solve, and find the performance measures of NM/NM/1, NM/NM/s, and NM/NM/1/b neutrosophic queue models via examples. We concluded that the performance measures of neutrosophic queue models is more accurate than crisp queue models. Keywords: Neutrosophic Set, Queueing Theory, Poisson Process, Exponential Distribution.