The overflow process from a state-dependent queue

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 r th 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. © 2005 Taylor & Francis Group Ltd.