Multi-channel fuzzy queuing systems and membership functions of related fuzzy services and fuzzy inter-arrival times

Queuing models need well defined knowledge on arrivals and service times. However, in real applications, because of some measurement errors or some loss of information, it is hard to achieve deterministic knowledge. Non-deterministic knowledge interferes or complicates analysis of the queuing model. Additionally, when the customers are asked about their impressions on waiting times or service times, mostly the answers are linguistic expressions like ‘I waited too much’, ‘service was fast’, and that the responses are. Linguistic statements and ill defined data make the sense of imprecision in the model. In this study, arrivals and service times are defined as fuzzy numbers in order to represent this imprecision. Fuzzy multi-channel queuing systems and membership functions are introduced in defining the arrivals and service times. Besides, a new membership function based on a probability function is studied. Fuzzy queuing characteristics are calculated via different membership functions and the results are compared on simulations. Among models it is found that Generalized Beta Distribution membership function is the one that minimized the queuing characteristics.