Light traffic approximations in general stationary single-server queues

This paper complements two previous studies (Daley and Rolski, 1984, 1991) by indicating the extent to which characteristics of a general stationary point process taken as the arrival process of a single-server queue influence light traffic limit theorems for the two essentially distinct schemes of dilation and thinning as routes to the limit. Properties of both the work-load and the waiting-time processes are derived, reflecting respectively the stationary time-sampling frame that may be appropriate for monitoring the system as a whole, and the customer-sampling frame (Palm distributions). Substantially different results can come from these two different views, and when compounded with the different approaches to the light traffic limits, no single light traffic scenario emerges.