A model of reservation systems

The author considers the performance evaluation of an advanced capacity reservation system using the CCITT defined reserved call establishment mode. A simple model for the traffic process is introduced: calls are assumed to be offered uniformly to the reservation book. The state of the system can then be described statistically in terms of the population of various types of islands of free time slots. The limit where the length of the reservation book tends to infinity is, in particular, considered. For single-server systems with a deterministic holding time of one or two time slots, a closed-form solution is found. For a general holding time distribution, an asymptotic analytical solution is derived and corrections to this asymptotic solution are calculated numerically. For multiserver systems with geometric holding time distribution, the author presents numerical results obtained by simulations. An interpolation formula valid for all traffic intensities is developed. A procedure is given to extrapolate the results to larger systems than were actually simulated