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The objective of this paper is to treat the solution of network of general queuing system having multi parallel server serial queues and single server non serial queues with balking and reneging considering the concepts of feedback. In this paper we analyze steady – state analysis of a model of a general queuing system having M service channels in series being connected with N nonserial channels having reneging and balking phenomenon, where each of M service channels has identical multiple parallel channels and there is feedback to all the previous channels from the last multiple channels in series with certain probabiliies. Purpose of this model is to allow feedback to all available serial channels and to derive steady – state expressions for such queuing model . Here the queue discipline is random selection for service. Poisson arrivals and exponential holding times are followed. The customer becomes impatient in queue after sometime and may leave the system without getting service. The input process depends upon the queue size in serial and non-serial channels. The two models studied are as follows:
Model-A: There is feedback to all the previous channels from the last multiple channels in series with certain probabiliies. Waiting space is infinite. Model-B: There is feedback to all the previous channels from the last multiple channels in series with certain probabiliies. Waiting space is finite