Sabine Wittevrongel

Discrete-time multiserver queues with geometric service times

In this paper, a discrete-time multiserver queueing system with infinite buffer size and general independent arrivals is considered. The service times of packets are assumed to be independent and identically distributed according to a geometric distribution. Each packet gets service from only one server. In the paper, the behavior of the queueing system is studied analytically by means of a generating-functions approach. This results in closed-form expressions for the mean values, the variances and the tail distributions of the system contents and the packet delay. Some numerical examples are given to illustrate the analysis.

Analysis and Modeling of Video Popularity Evolution in Various Online Video Content Systems: Power-Law versus Exponential Decay

Internet evolved from a world communication network with restricted information transmission capabilities into an entertainment and information network with many broadband clients and more multimedia-rich applications. In particular, video (streaming) applications are gaining in popularity and usage, but those are also notorious for their high resources demand. A study of the popularity evolution of videos in different online video content systems can give insight and have implications for adequate network dimensioning. In this paper we study and model the popularity evolution of some video traces from YouTube, one Dutch catch-up TV online portal, and historical data on DVD rentals in the US. The model we put forward can degenerate into either a power-law distribution or an exponential distribution depending on its form-determining parameter. We find out that not all traces have a power-law decay as suggested in other works, but also a significant part of those expose an exponential popularity evolution.

Correlation effects in ATM queues due to data format conversions

Abstract We study the performance of a statistical multiplexer to which messages composed of a variable number of fixed-length packets arrive at the rate of one packet per slot (“train arrivals”), resulting in a correlated packet arrival stream. In this paper, unlike in previous related studies, the distribution of the message lengths is general. We introduce a technique for the exact analysis of the system, which is essentially a generating-functions approach that uses an infinite-dimensional state description. Explicit expressions are obtained for the probability generating functions of the queue length and the packet delay. Also, closed-form results are found for the mean, variance and tail distribution of the queue length and the packet delay. The mean message waiting time and the mean message delay are derived as well. A comparison is made between the buffer behavior with train arrivals and that with batch arrivals, where all the packets of a message enter the buffer during the same slot, and also it is shown that the correlation has a strong effect on the performance of the system. By means of some numerical examples, we also show that the exact nature of the message-length distribution has a significant impact on the multiplexer performance.

A Discrete-Time Priority Queue with Train Arrivals

We analyze a discrete-time priority queue with train arrivals. Messages of a variable number of fixed-length packets belonging to two classes arrive to the queue at the rate of one packet per slot. We assume geometrically distributed message lengths. Packets of the first class have transmission priority over the packets of the other class. By using probability generating functions, some performance measures such as the moments of the packet delay are calculated. The impact of the priority scheduling discipline and the correlation in the arrival process is shown by some numerical examples.

Performance analysis of the IEEE 802.16e sleep mode for correlated downlink traffic

In this paper, we evaluate the performance of the IEEE 802.16e sleep mode mechanism in wireless access networks. This mechanism reduces the energy consumption of a mobile station (MS) by allowing it to turn off its radio interface (sleep mode) when there is no traffic present at its serving base station (BS). After a sleep period expires, the MS briefly checks the BS for data packets and switches off for the duration of another sleep period if none are available. Specifically for IEEE 802.16e, each additional sleep period doubles in length, up to a certain maximum. Clearly, the sleep mode mechanism can extend the battery life of the MS considerably, but also increases the delay at the BS buffer. For the performance analysis, we use a discrete-time queueing model with general service times and multiple server vacations. The vacations represent the sleep periods and have a length depending on the number of preceding vacations. Unlike previous studies, we take the (short-range) traffic correlation into account by assuming a D-BMAP arrival process, i.e. the distribution of the number of packet arrivals per slot is modulated by the transitions in a Markov chain with N background states. As results, we obtain the distribution of the number of packets in the queue at various sets of time epochs, the distribution of the packet delay and the antenna activity rate. We apply these results to the IEEE 802.16e sleep mode mechanism with correlated downlink traffic. By means of some examples, we show the influence of both the configuration parameters and the traffic correlation on the delay and the energy consumption.

Discrete-time queues with correlated arrivals and constant service times

Abstract A discrete-time single-server finite-capacity queue with correlated arrivals and constant service times of arbitrary length is investigated in this paper. Cells are generated by a bursty on/off source, with geometrically distributed lengths of the on-periods and the off-periods. The performance of the system is evaluated by means of an analytical technique, based on generating functions, whose comutational complexity does not depend on the buffer space. As a result of the analysis, closed-form expressions are obtained for the cell loss ratio, the steady-state probability generating functions of the queue length, the unfinished work and the cell delay and the joint probability generating function of two consecutive interdeparture times at the output of the queue. Some numerical examples illustrate the results. Scope and purpose Discrete-time queueing models are suitable for the performance evaluation of Asynchronous Transfer Mode (ATM) multiplexers and switches. In these models, the time axis is divided into fixed-length slots and the service of a customer must start and end at slot boundaries. Most analytical studies of discrete-time queues assume constant service times equal to one slot, an infinite buffer capacity and/or uncorrelated arrival process. The present paper is an attempt to explore whether analytical techniques are still applicable in absence of these restricting assumptions. Specifically, we focus on a discrete-time single-server queueing system with constant service times of arbitrary length, a finite storage capacity and a simple non-independent arrival model. The analysis method is based on an extensive use of generating functions, an approach which has traditionally been reserved for infinite-capacity queues. We show in this paper that generating functions can also be very useful in the finite-capacity case.

Delay versus energy consumption of the IEEE 802.16e sleep-mode mechanism

We propose a discrete-time queueing model for the evaluation of the IEEE 802.16e sleep-mode mechanism of power saving class (PSC) I in wireless access networks. Contrary to previous studies, we model the downlink traffic by means of a discrete batch Markov arrival process (D-BMAP) with N phases, which allows to take traffic correlation into account. The tradeoff between energy saving and increased packet delay is discussed. In many situations, the sleep-mode performance improves for heavily correlated traffic. Also, when compared to other strategies, the exponential sleep-period update strategy of PSC I may not always be the best.

Comparison of simulcast and scalable video coding in terms of the required capacity in an IPTV network

The diversity of multimedia-enabled devices supporting streamed multimedia is ever growing. Multicast delivery of TV channels in IP networks to a heterogeneous set of clients can be organised in many different ways, which brings up the discussion which one is optimal. Scalable video streaming has been believed to be more efficient in terms of network capacity utilisation than simulcast video delivery because one flow can serve all terminals, while with simulcast all resolutions are offered in parallel. At the same time, it is also largely recognised that in order to provide the same video quality compared to non-layered video coding, scalable video coding (SVC) incurs a bit rate penalty. In this paper we compare simulcast and SVC in terms of their required capacity in an IPTV network scenario where a bouquet of TV channels is offered to the subscribers. We develop methods to calculate and approximate the capacity demand for two different subscriber behaviour models. These methods are then used to explore the influence of various parameters: the SVC bit rate penalty, the number of offered channels, the channel popularity and the number of subscribers. The main contribution of this paper is that we derive an analytical formula to calculate the SVC limit bit rate penalty beyond which SVC is less efficient than simulcast. In the realistic IPTV examples considered here, the limit is found to lie between 16% and 20%, while the reported values for this coding penalty range from 10% up to 30% for current H.264 SVC codecs, indicating that SVC in IPTV is not always more efficient than simulcast.

Modelling H.264/AVC VBR video traffic: comparison of a Markov and a self-similar source model

We compare the adequacy of two models for realistic video sources, namely the fractional Brownian motion (fBm) and Markov modulated fluid flow (Mmff) models. We use the effective bandwidth approach to get the probability that the buffer content exceeds a certain threshold. We use a formula in which the variance function, i.e., the variance of the traffic arriving in an interval of length τ, plays a central role and we model it as variance associated either with the Mmff or fBm model.We measure the variance function for an artificial source we construct, using Variable Bit Rate (VBR) H.264/AVC (Advanced Video Codec) video traces of real movies. There is a good correspondence between the buffer threshold exceeding probability obtained via trace-based simulations and the one predicted theoretically, based on the measured variance function. These we take as benchmark results against which we check both models—fBm and Mmff.First, we try to tune the model parameters such that their variance function matches the measured one over a large range of τ values, but this proves to be difficult. When matching the variance function over a short range of the τ of interest, we conclude that the Mmff model is better suited to model VBR video sources. We conduct an error sensitivity analysis with non-optimal model parameters and conclude that they do not influence considerably the buffer exceeding probability.Most reliable results are achieved with the measured variance function; if by some reason it needs to be modelled, the Mmff is preferred over the fBm model.

Performance of the IEEE 802.16e Sleep Mode Mechanism in the Presence of Bidirectional Traffic

We refine existing performance studies of the WiMAX sleep mode operation to take into account uplink as well as downlink traffic. This as opposed to previous studies which neglected the influence of uplink traffic. We obtain numerically efficient procedures to compute both delay and energy efficiency characteristics. A test scenario with an Individual Subscriber Internet traffic model in both directions shows that even a small amount of uplink traffic has a profound effect on the system performance.