TB/GI/1 queues with arrival traffic envelopes

Consider a queueing system where the job service times are not known upon arrival; e.g., a transmission server of a wireless channel where packet transmission times are random, or a virtual machine handling a stream of tasks whose execution times are not perfectly predictable. We give bounds on the tail of the workload distribution of a partially regulated, single-server queue whose arrival processes are arbitrarily distributed stationary random point processes on the integers that satisfy token-bucket constraints expressed via an arbitrary concave function f, and whose job service times are independent with a common distribution.