Time independent analysis of biserial and parallel queuing models with batch arrival

In the present paper we have derived the steady-state solutions for a complex network queuing model consisting of bi-serial and parallel queuing subsystems commonly connected with a single server. The customers soliciting services at bi-serial queuing subsystem arrive in batches of fixed size while at parallel queuing subsystem customer arrives one at a time. Finally after getting services at either of the subsystem the customer moves to the single server for completion of services. The mean queue length and average waiting time for customers have been calculated using generating function technique, laws of calculus and statistical tools. The numerical illustration is provided to order to validate the theoretical results.