Loss bounds for a single-server finite-capacity queue based on partial information about an input process

摘要

We consider a single-server finite-capacity queue under the circumstances that, along the time axis divided into fixed-length slots, the amount of work brought into the queue during each slot is sequentially observed. Since the interarrival time of customers might be shorter than the length of slot, the sequence of the amounts of work per slot, which is referred to as slot-wise input process in this paper, gives us only partial information about the input process. We present, in this paper, how the performance of the queue can be evaluated based on observations of (less informative) slot-wise input process. In particular, we establish the upper bounds of work-loss probability for two kinds of queues that respectively have deterministic and stochastic inputs. Our results would give useful tools to evaluate the performance of queueing systems even when the information about input processes in fine time scale is not available.