Goodput analysis of a fluid queue with selective discarding and a responsive bursty source

In this paper we analyse a feedback system consisting of a finite buffer fluid queue and a responsive source. The source alternates between silence periods and active periods. At random epochs of times the source becomes ready to send a burst of fluid. The length of the bursts (length of the active periods) are independent and identically distributed with some general distribution. The queue employs a threshold discarding policy in the sense that only those bursts at whose commencement epoch (the instant at which the source is ready to send), the workload (i.e., the amount of fluid in the buffer) is less than some preset threshold are accepted. If the burst is rejected then the source backs off from sending. Using techniques from Volterra integral equations we obtain an explicit characterization of the queue length distribution at commencement epochs of bursts from which we obtain an explicit characterization of the goodput ratio associated with such a feedback system. For the particular case of exponential distribution of on-periods we are able to obtain explicit closed form expression for the goodput ratio. Our explicit characterizations shall be quite helpful in studying the sensitivity of goodput ratio to different parameters, in selecting optimal discarding threshold etc. which will further provide useful "engineering" guidelines for better network designing.