Abstract: This paper studies a random fuzzy queueing system
that the interarrival times of customers arriving at the server and
the service times are independent and identically distributed random
fuzzy variables. We match the random fuzzy queueing system with
the random fuzzy alternating renewal process and we do not use from
α-pessimistic and α-optimistic values to estimate the average chance
of the event ”random fuzzy queueing system is busy at time t”, we
employ the fuzzy simulation method in practical applications. Some
theorem is proved and finally we solve a numerical example with
fuzzy simulation method.
Abstract: The modern queueing theory is one of the powerful
tools for a quantitative and qualitative analysis of communication systems, computer networks, transportation systems, and many other technical systems. The paper is designated to the analysis of queueing
systems, arising in the networks theory and communications theory
(called open queueing network). The authors of this research in the
sphere of queueing theory present the theorem about the law of the iterated logarithm (LIL) for the queue length of a customers in open
queueing network and its application to the mathematical model of
the open message switching system.