This paper has been developed by dynamic system of communication flow in the presence of queueing theory under control chart with fuzzy environment. Also we discuss the application of bulk arrival queue model to communication network under vague data where the arrival rate and service rate are fuzzy in nature. Fuzzy queues are more realistic than the crisp conventional queues. The basic idea of this paper depends on Zadeh’s extension law. The objective is transform fuzzy control chart of mean arrival length to a family if crisp modal by α-cut approach. We derive the membership function for triangular and trapezoidal fuzzy numbers followed by Parametric (NLP) Non-linear program approach, numerical example is illustrated.

Mean arrival, Membership function, Fuzzy control chart, parametric non-linear program and α-cuts