Probability Characteristics of Queuing Systems with Two Different Threshold-Based Stochastic Drop Mechanisms⋆

In this article for the queuing system with recurrent input flow and exponentially distributed service time two different stochastic threshold-based mechanisms for dropping of incoming or already accepted into the queue requests are presented. The dropping occurs for either at arrival moments or at moments of the end of service. The threshold parameter Q in the queue not only determines the moment when the stochastic dropping of tasks is enabled, but also sets the safe area in the queue from which accepted into the system tasks cannot be dropped. The formulas for the main probability characteristics (such as the stationary distribution of the number of tasks in the system, the probabilities for arriving tasks to be served or to be dropped (lost)) are given. For the case of a Poisson incoming flow the obtained probabilistic characteristics are compared for different values of drop probability q, system load ρ and threshold Q. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.