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ABSTRACT. We design a queuing model comprised of M serial service channels connected to N non-serial service channels both characterized with balking as well as reneging due to long queue. We introduce multiple parallel servers in serial as well as non-serial channels. The difference-differential equations for this model are formulated and the steady-state solutions for various cases are obtained. Here, the input process is Poisson and depends upon the queue size in serial and non-serial channels. The service time distribution is exponential and the service discipline follows SIRO-rule instead of FIFO-rule. Waiting space is finite.