The Time Independent Analysis of Finite Waiting Space Generalised Multichannel Mixed Queuing System with Balking and Reneging Due to Long Queue and Some Urgent Message

Abstract

The Proposed queuing model comprises of M serial service channels connected to N non-serial service channels. Inside every serial as well as non-serial service channel multiple parallel servers are allocated. Customers are allowed to balk as well as renege at any server inside the queuing model. Along with welsh because of long queue, reneging due to some urgent phone call or text information received, while waiting in the queue is applied in this queuing model. Using (Kelly, F.P., 1975. Networks of queues with customers of different types. Journal of Applied Probability, 12(3), pp.542–554) the difference-differential equations of the proposed model are obtained. Considering the system to be time independent, the time independent equations and corresponding solutions for various cases in the proposed queuing model are obtained. Further, it is submitted that the appearance process is Poisson, the administration time circulation is exponential, waiting space is finite, arrival of the customer depends upon the queue size at every service channel (serial/nonserial) and Service is done in random order rather than First come first serve principle.