Level-Crossing Characteristics of an Actively Managed Buffer

In this paper, we examine a buffer with active management that rejects packets basing on the buffer occupancy. Specifically, we derive several metrics characterizing how effectively the algorithm can prevent the queue of packets from becoming too long and how well it assists in flushing the buffer quickly when necessary. First, we compute the probability that the size of the queue is kept below a predefined level L. Second, we calculate the distribution of the amount of time needed to cross level L, the buffer overflow probability, and the average time to buffer overflow. Third, we derive the distribution of the amount of time required to flush the buffer and its average value. A general modeling framework is used in derivations, with a general service time distribution, general rejection function, and a powerful model of the arrival process. The obtained formulas enable, among other things, the solving of many design problems, e.g., those connected with the design of wireless sensor nodes using the N-policy. Several numerical results are provided, including examples of design problems and other calculations.