The overflow process from a state-dependent queue

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The interoverflow time distribution is explicitly obtained as a power series for a finite-state queueing system with general state-dependent arrival and service rates. This can be expressed as a hyper-exponential distribution in closed form for specific constant, linear and quadratic arrival and service rates. Further, we obtain an explicit formula for the rth moment of the overflow process. We also analyse the inverse problem of finding the arrival and service rates from the given spectral data. Numerical illustrations are presented.