Exact transient solution of a discrete time queue with state-dependent rates

Exact expressions are obtained in closed form for the time-dependent system size probabilities of a discrete queue with state-dependent arrival and service rates. The underlying difference equations of system size probabilities is converted into a continued fraction which is then expressed as a power series. As a special case we derive a Geo/Geo/1 queue. Numerical illustrations are presented. © 2006, Taylor & Francis Group, LLC. All rights reserved.