Optical burst switching is a high-speed data transfer technology where, in place of isolated packets, a bunch of packets known as a burst is sent. However, this mechanism is simple in transmission and reception as bursts propagate on a dedicated path, but burst assembly is a complex problem, and till date, the optimum burst length for data transmission is not fixed. This is the main hurdle in the implementation of OBS. In this paper, a mathematical model is developed to obtain network traffic flow equations and packet/bust drop rates under with and without considering the buffers at various nodes of the switches. The burst length modelling is also detailed, and finally, Monte Carlo simulation is performed to obtain various results. The obtained results clearly reveal that the proposed mathematical model is well in agreement of simulation results.