The present paper deals with the mathematical and graphical study of mean queue length of a queueing system of a developed queuing model in which three servers are connected in parallel in tri-cum biserial way with a common server. The arrival and service pattern are assumed to follow the Poisson process. Variation in Mean queue length of the system have been studied mathematically and graphically by changing the values of different queueing characteristics keeping the remaining variables constant.

Keywords: Four Servers, Mathematical and Graphical Study, Mean Queue Length, Queueing Characteristics.