CLASS OF APPROXIMATIONS FOR THE WAITING TIME DISTRIBUTION IN A Gl/G/1 QUEUEING SYSTEM.

Single server queueing models are important in the study of a wide variety of stochastic systems. A particularly important example is the study of task schedules for computer systems with real-time applications. A class of approximations is presented for the waiting time distribution in single server queueing systems with general independent (renewal) input and general (independent) service time distributions. These approximations allow the analyst to use as much (or as little) of the structure of the input and service processes as desired. Moreover, they also allow him to concentrate on specific quantities associated with the delay distribution that may represent the most relevant performance criteria. Examples include probability of delay, mean delay, and tails of the delay distribution. The methods given have been used to analyze the performance of task schedules in a variety of processor-based systems.