Loss bounds for a finite-capacity queue based on interval-wise traffic observation

We study a single–server finite–capacity queue with batch fluid inputs. We assume that the input traffic is observed in an interval–wise basis; that is, along the time axis divided into fixed–length intervals, with the amount of work brought into the queue during each interval sequentially observed. Since the sequence of the amounts of work during respective intervals, which is referred to as the interval–wise input process in this paper, does not reveal complete information about an input process, we cannot be precisely aware of the performance of the queue. Thus, in this paper, we focus on knowing the performance limit of the queue based on the interval–wise input process. In particular, we establish an upper limit of the long–run loss ratio of the workload in the queue. Our results would reveal useful tools to evaluate the performance of queuing systems when information about input processes in a fine timescale is not available.