Abstract-Our purpose in this paper is to obtain the exact distribution of the number of buffer starvations within a sequence of N consecutive packet arrivals. The buffer is modeled as an M/M/1 queue.When the buffer is empty, the service restarts after a certain amount of packets are prefetched. With this goal, we propose two approaches, one of which is based on Ballot theorem, and the other uses recursive equations. The Ballot theorem approach gives an explicit solution, but at the cost of the high complexity order in certain circumstances. The recursive approach, though not offering an explicit result, needs fewer computations. We further propose a fluid analysis of starvation probability on the file level, given the distribution of file size and the traffic intensity. The starvation probabilities of this paper have many potential applications. We apply them to optimize the quality of experience (QoE) of media streaming service, by exploiting the tradeoff between the start-up delay and the starvation. The starvation probability of a buffer is an important performance measure for protocol design of telecommunication networks, as well as in storage systems and ecological systems (e.g. dams). Starvation is said to occur when the buffer is empty. Various applications use buffering in order to control the rate at which packets are served at the destination. As long as there are packets in the buffer, packets arrive at the destination regularly, i.e. they are spaced by the service time of the buffer. Once the buffer empties packets may arrive at the destination separated by larger times, as the spacing between packets now depends also on the inter-arrival times at the queue. Starvation is in particular undesirable in real time voice as well as in video streaming applications. The time till starvation of a queue is related to the busy period which has been well studied under the assumption of a stationary arrival process (see [2] , [3] and their references). In contrast to this assumption, we consider a finite number of arrivals as we are interested in statistics of starvation when a file of fixed size is transferred. The main goal of this paper is to find the distribution of the number of starvations within a file of N packets. We first model the buffer as an M/M/1 queue, and then extend it to incorporate the bursty packet arrival that is modeled by an interrupted Poisson process (IPP). In this system, a fixed amount of packets are prefetched (also called "prefetching threshold") before the service begins or resumes after a starvation event. In this paper, we propose two approaches (that give the same result) to compute the starvation probabilities and the distribution of the number of starvations for a single file. The first
Xu et al. REF modeled the starvation probability for a file of finite size in M/M/1 and M/D/1 queues.
Probabilistic analysis of buffer starvation in Markovian queues
2012 Proceedings IEEE INFOCOM
2012 Proceedings IEEE INFOCOM
Computer Science