Tandem system with retrials and impatient customers

Consideration was given to the tandem queuing system with multiple-line phases and a stationary Poisson flow. The customer arriving with the input flow and finding all first-phase servers occupied goes to an infinite-size orbit from which it retries to be serviced. Between the phases there is a finite buffer. The customers passing to the second phase have different priorities. For the highest-priority customers, second-phase servers are foreseen. If all places permitted for the given customer at the second phase are occupied, it either discharges the queuing system underserviced or returns to the first-phase orbit and retries to get a server at this phase. The impatient customers leaving the intermediate buffer behave in a similar manner. The stationary characteristics of system performance were established. Numerical examples, including the problem of optimal selection of the number of reserved servers, were presented.