Let be i.i.d. interrenewal times such that , ; let be i.i.d. rewards independent of with and (FVR, finite variance rewards) or , (IVR, infinite variance rewards) (, are slowly varying functions at infinity). The renewal reward process is defined as if belongs to the th interrenewal interval, , where are i.i.d. copies of . The author considers the limit behavior of as , . E.g. in the FVR case it is shown that if is a slowly varying function such that , as and
(in distribution), where is a standard fractional Brownian motion. In other results the limit processes are the symmetric Lévy motion and a symmetric -stable process. The processes are used to describe a centered load of one workstation in the Ethernet local area network at time . Then is the aggregated load.