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

Optimum cost analysis for an Geo/Geo/c/N feedback queue under synchronous working vacations and impatient customers

This paper concerns the cost optimisation analysis of a discrete-time finite-capacity multiserver queueing system with Bernoulli feedback, synchronous multiple and single working vacations, balking, and reneging during both busy and working vacation periods. A reneged customer can be retained in the system by employing certain persuasive mechanism for completion of service. Using recursive method, the explicit expressions for the stationary state probabilities are obtained. Various system performance measures are presented. Further, a cost model is formulated. Then, the optimization of the model is carried out using quadratic fit search method (QFSM). Finally, the impact of various system parameters on the performance measures of the queueing system is shown numerically.</p

Performance and economic evaluation of differentiated multiple vacation queueing system with feedback and balked customers

The present paper deals with a single server feedback queueing system under two differentiated multiple vacations and balked customers. It is assumed that the service times of the two vacation types are exponentially distributed with different means. The steady-state probabilities of the model are obtained. Some important performance measures of the system are derived. Then, a cost model is developed. Further, a numerical study is presented

On the M/M/c/N Call Center Queue Modeling and Analysis

The M/M/c/c model is the most widely applied queueing model in the mathematical analysis of call centers. The M/M/c/c model is also referred to as the Erlang Loss System. The Erlang loss model does not take into consideration system attributes such as blocking and busy signals, balking and reneging, retrials and returns. Although, the Erlang loss model is analytically tractable, it is not easy to obtain insight from its results. The need to develop a more accurate call center model has necessitated the modification of the Erlang loss model. In this research, we model and analyze a call center using M/M/c/N the model. The goal of this paper is to extend existing results and prove new results with regards to the monotonicity and limiting behaviour of the M/M/c/N model with respect to the system capacity N

A single server Markovian queuing system with limited buffer and reverse balking

The phenomena are balking can be said to have been observed when a customer who has arrived into queuing system decides not to join it. Reverse balking is a particular type of balking wherein the probability that a customer will balk goes down as the system size goes up and vice versa. Such behavior can be observed in investment firms (insurance company, Mutual Fund Company, banks etc.). As the number of customers in the firm goes up, it creates trust among potential investors. Fewer customers would like to balk as the number of customers goes up. In this paper, we develop an M/M/1/k queuing system with reverse balking. The steady-state probabilities of the model are obtained and closed forms of expression of a number of performance measures are derived

Preemptive Resume Priority Call Center Model with Two Classes of MAP Arrivals

Generally in call centers, voice calls (say Type 1 calls) are given higher priority over e-mails (say Type 2 calls). An arriving Type 1 call has a preemptive priority over a Type 2 call in service, if any, and the preempted Type 2 call enters into a retrial buffer (of finite capacity). Any arriving call not able to get into service immediately will enter into the pool of repeated calls provided the buffer is not full; otherwise, the call is considered lost. The calls in the retrial pool are treated alike (like Type 1) and compete for service after a random amount of time, and can preempt a Type 2 call in service. We assume that the two types of calls arrive according to a Markovian arrival process (MAP) and the services are offered with preemptive priority rule. Under the assumption that the service times are exponentially distributed with possibly different rates, we analyze the model using matrix-analytic methods. Illustrative numerical examples to bring out the qualitative aspects of the model under study are presented

Shot-noise queueing models

We provide a survey of so-called shot-noise queues: queueing models with the special feature that the server speed is proportional to the amount of work it faces. Several results are derived for the workload in an M/G/1 shot-noise queue and some of its variants. Furthermore, we give some attention to queues with general workload-dependent service speed. We also discuss linear stochastic fluid networks, and queues in which the input process is a shot-noise process