Analytical investigation of a single-channel QS with incoming asynchronous event flow

We consider a single-channel queuing system with an incoming asynchronous double-stochastic two-state request flow (MMPP-flow — Markovian Modulated Poisson Process). We give explicit analytical formulas for the steady-state probability distribution of the system states as well as explicit analytical expressions for the following numerical characteristics of the system: the average queue length, the average number of requests in the system, and the probability of system downtime. We give numerical results, presented in the form of tables, for the characteristics of the system. We consider a special case of an incoming request flow — an asynchronous alternating two-state flow (SPP-flow — Switched Poisson Process).