We study light traffic approximations for queues in series with renewal arrivals and i.i.d. service time vectors. Formulae for limits of functions of the waiting time at different stations based on single customer effect are obtained for two approaches: dilation and thinning of the arrival process. Interdeparture times from a station possess a one-dependence property in light traffic. This paper complements previous studies of Daley and Rolski and also Asmussen's approach to light traffic limits applied to the cases considered.
"Queues in Series in Light Traffic." Ann. Appl. Probab. 3 (3) 881 - 896, August, 1993. https://doi.org/10.1214/aoap/1177005370