Neutrosophic Theory and Its Application in Various Queueing Models: Case Studies

Abstract

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.