Sample-path analysis of processes with imbedded point processes
Proceedings of the workshop held at the Mathematical Sciences Institute Cornell University on Mathematical theory of queueing systems
On stability and performance of parallel processing systems
Journal of the ACM (JACM)
A review of L=&lgr;W and extensions
Queueing Systems: Theory and Applications
Rate stability and output rates in queueing networks with shared resources
Performance Evaluation
A note on sample-path stability conditions for input-output processes
Operations Research Letters
A note on the pathwise version of Little's formula
Operations Research Letters
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In this paper we study the sample-path behavior of the workload process in a single server queue without imposing the stationarity hypothesis. In particular we study the stability or worst case growth properties and show that the growth rate is of the form o(t^@a, @a 1, depending on the rate of convergence of the pathwise average of the work brought into the system. We then study the existence of empirical means and in particular show that a pathwise version of the Pollaczek-Khinchine formula plays an important role. Finally we give conditions under which our results hold knowing the rate or intensity of the arrival process. Our results highlight the limitations of pure sample-path techniques.