Busy Period of Random Fuzzy Queueing Systems

The busy period is one of the most important performance indices of random fuzzy queueing systems. In the random fuzzy queueing systems, the interarrival times of customers and service times of servers are random fuzzy variables. Therefore, the busy period is a random fuzzy variable. This paper presents a theorem on the limit value of the average chance of the random fuzzy event "the queueing system is busy at time t". The theorem can be applied to many practical queueing systems with randomness and fuzziness. When the interarrival times and service times degenerate to random variables, the result coincides with the one in traditional queueing systems.