The Analysis of Queueing System with Two Input Flows and Stochastic Drop Mechanism

The queueing system with two independent flows of requests with different types of priorities is considered. The incoming flows are Poisson flows with different (non equal) rates. The service times of each type requests are independent and exponentially distributed. The priority requests at the end of its service can drop non-priority ones with probability q (renovation probability) or just leaves the system with probability p = 1 - q. For general case the two-dimensional Markov process is introduced and the system of equilibrium equations for steady-state probability distribution is presented. For special case, when drop probability q is equal to one, some probabilistic characteristics as the steady-state probability distribution of priority requests, the probability of idle period are obtained. Also the analytical expressions for some characteristics of non-priority requests, such as probability of being dropped (or serviced), waiting time distribution for non-priority requests (in terms of Laplace-Stieltjes transformation and generating function) and mean waiting time, are obtained.

queueing system, two input flows, renovation probability, stochastic drop mechanism, time-probability characteristics