There is a case about a system comprising two queues of M/M(a)/1/K with a due date with FCFS service policy in each queue. Using the methods of simulation and mathematical analysis, the solution diagrams were illustrated for the fixed due date Ɵ=1 second at the phase of due date up to the commencement of the service, limited capacity K₁=5 and K₂=4, for both scenarios of different service management rate resulted. For the analytical solution, first, a SAN model from the system was created in the Mobius tool. For simulation, a java discrete systems simulation code was used. Adjustment of the initial values, selection of the scenarios for service rate, the number of the consumers in the simulation, etc. were all carried out in the simulation code.