The overflow process from a state-dependent queue

Abstract

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.

Keywords:

• Overflow process
• Continued fractions
• Continuants
• State-dependent queues

Acknowledgements

P.R.P. is grateful to Professor Helmut Neunzert for his invitation to visit the University of Kaiserslautern, Germany, where this work was completed.