Mathematical model for calculating and analyzing characteristics of optical switch in transient mode

The article considers a transient behavior of an optical switch described using a single-channel finite buffer queuing system with Poisson input stream and exponential service time distribution. To solve the Kolmogorov equations system and find the probabilities of states in the transition mode, the apparatus of the Laplace transform was used. Analytical expressions are found for determining the probability of losses and the throughput of an optical switch at a given point in time. In a numerical example, the performance metrics of an optical switch with a buffer size of two packets are analyzed for different network loads in transient and stationary modes. The stationary performance metrics obtained using the proposed approach coincided with the known results, which confirms the correctness of the conclusions. The optical switch transient behavior analyses at different network load showed that with a decreasing service rate the transition mode time increases.