Packet loss characteristics for M/G/1/N queueing systems

In this contribution we investigate higher-order loss characteristics for M/G/1/N queueing systems. We focus on the lengths of the loss and non-loss periods as well as on the number of arrivals during these periods. For the analysis, we extend the Markovian state of the queueing system with the time and number of admitted arrivals since the instant where the last loss occurred. By combining transform and matrix techniques, expressions for the various moments of these loss characteristics are found. The approach also yields expressions for the loss probability and the conditional loss probability. Some numerical examples then illustrate our results

Analysis of Buffer Starvation with Application to Objective QoE Optimization of Streaming Services

Our purpose in this paper is to characterize buffer starvations for streaming services. The buffer is modeled as an M/M/1 queue, plus the consideration of bursty arrivals. When the buffer is empty, the service restarts after a certain amount of packets are \emph{prefetched}. With this goal, we propose two approaches to obtain the \emph{exact distribution} of the number of buffer starvations, one of which is based on \emph{Ballot theorem}, and the other uses recursive equations. The Ballot theorem approach gives an explicit result. We extend this approach to the scenario with a constant playback rate using T\`{a}kacs Ballot theorem. The recursive approach, though not offering an explicit result, can obtain the distribution of starvations with non-independent and identically distributed (i.i.d.) arrival process in which an ON/OFF bursty arrival process is considered in this work. We further compute the starvation probability as a function of the amount of prefetched packets for a large number of files via a fluid analysis. Among many potential applications of starvation analysis, we show how to apply it to optimize the objective quality of experience (QoE) of media streaming, by exploiting the tradeoff between startup/rebuffering delay and starvations.Comment: 9 pages, 7 figures; IEEE Infocom 201

Probabilistic Analysis of Buffer Starvation in Markovian Queues

International audienceOur purpose in this paper is to obtain the \emph{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 \emph{prefetched}. With this goal, we propose two approaches, one of which is based on \emph{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

On Loss Probabilities in Presence of Redundant Packets with Random Drop

The purpose of this paper is to study the loss probabilities of messages in an M/M/1/K queueing system where in addition to losses due to buffer overflow there are also random losses in the incoming and outgoing links. We focus on the influence of adding redundant packets to the messages (as in error correction coding, e.g. Reed--Solomon code, etc.). In the first part we use multi-dimensional probability generating functions for solving the recursions which generalize those introduced by Cidon et al. [IEEE Trans. Inform. Theory 39 (1) (1993) 98] for computing the loss probabilities and derive analytical formulae for a special case. In the second part of the paper we use combinatorial arguments and Ballot theorem results to alternatively obtain the loss probabilities. The analytical results allow us to investigate when does adding redundancy decrease the loss probabilities. 2003 Elsevier Science B.V. All rights reserved