On the Influence of AQM on Serialization of Packet Losses.

We study the influence of the active queue management mechanism based on the queue size on the serialization of packet losses, i.e., the occurrences of losses in long, consecutive series. We use a traffic model able to mimic precisely the autocorrelation function of traffic, which is known to be far from zero in packet networks. The main contribution is a theorem on the burst ratio parameter, describing the serialization of losses, proven for an arbitrary function assigning drop probabilities to queue sizes. In numerical examples, we show the impact of the autocorrelation strength, drop probability function, and load of the link, on the serialization of losses.

Non-Stationary Characteristics of AQM Based on the Queue Length.

We performed a non-stationary analysis of a class of buffer management schemes for TCP/IP networks, in which the arriving packets were rejected randomly, with probability depending on the queue length. In particular, we derived formulas for the packet waiting time (queuing delay) and the intensity of packet losses as functions of time. These results allow us to observe how the evolution of the waiting time and losses depend on initial conditions (e.g., the full buffer) and system parameters (e.g., dropping probabilities, load, packet size distribution). As side results, the stationary waiting time and packet loss probability were obtained. Numerical examples demonstrate applicability of the theoretical results.

Impact of the Dropping Function on Clustering of Packet Losses.

The dropping function mechanism is known to improve the performance of TCP/IP networks by reducing queueing delays and desynchronizing flows. In this paper, we study yet another positive effect caused by this mechanism, i.e., the reduction in the clustering of packet losses, measured by the burst ratio. The main contribution consists of two new formulas for the burst ratio in systems with and without the dropping function, respectively. These formulas enable the easy calculation of the burst ratio for a general, non-Poisson traffic, and for an arbitrary form of the dropping function. Having the formulas, we provide several numerical examples that demonstrate their usability. In particular, we test the effect of the dropping function's shape on the burst ratio. Several shapes of the dropping function proposed in the literature are compared in this context. We also demonstrate, how the optimal shape can be found in a parameter-depended class of functions. Finally, we investigate the impact of different system parameters on the burst ratio, including the load of the system and the variance of the service time. The most important conclusion drawn from these examples is that it is not only the dropping function that reduces the burst ratio by far; simultaneously, the more variable the traffic, the more beneficial the application of the dropping function.

Burst ratio for a versatile traffic model.

We deal with a finite-buffer queue, in which arriving jobs are subject to loss due to buffer overflows. The burst ratio parameter, which reflects the tendency of losses to form long series, is studied in detail. Perhaps the most versatile model of the arrival stream is used, i.e. the batch Markovian arrival process (BMAP). Among other things, it enables modeling the interarrival time density function, the interarrival time autocorrelation function and batch arrivals. The main contribution in an exact formula for the burst ratio in a queue with BMAP arrivals and arbitrary service time distribution. The formula is presented in an explicite, ready-to-use form. Additionally, the impact of various system parameters on the burst ratio is demonstrated in numerical examples. The primary application area of the results is computer networking, where the complex nature of traffic has a deep impact on the burst ratio. However, due to the versatile arrival model, the results can be applied in other fields as well.

AQM based on the queue length: A real-network study.

Active Queue Management (AQM) is recommended by Internet Engineering Task Force to mitigate the bufferbloat phenomenon in the Internet. In this paper, we show the results of comprehensive measurements carried out in our university network, in which a device with an AQM algorithm, designed and programmed for this purpose, was running. The implemented AQM algorithm was based on the dropping function, i.e. arriving packets were dropped randomly, with the probability being a function of the queue length. Several different dropping function forms, proposed in the networking literature, were used, in addition to the classic FIFO queue (no AQM). The experiment lasted over a month, during which the state of the network was measured and recorded several thousand times. This made the results independent of the natural fluctuations of the users' behavior and the network load. Conclusions on the general performance improvement offered by the implemented AQM, as well as the differences in the performance between particular forms of the dropping function, were reached. Some of these conclusions differ from those drawn previously from simulations. This underlines the need for carrying measurements of new AQMs in real, operating networks, with complex, natural traffic.

On the stability of queues with the dropping function.

In this paper, the stability of the queueing system with the dropping function is studied. In such system, every incoming job may be dropped randomly, with the probability being a function of the queue length. The main objective of the work is to find an easy to use condition, sufficient for the instability of the system, under assumption of Poisson arrivals and general service time distribution. Such condition is found and proven using a boundary for the dropping function and analysis of the embedded Markov chain. Applicability of the proven condition is demonstrated on several examples of dropping functions. Additionally, its correctness is confirmed using a discrete-event simulator.

On the Transient Queue with the Dropping Function.

We deal with a queueing system, in which arriving packets are being dropped with the probability depending on the queue size. Such a scheme is used in several active queue management schemes proposed for Internet routers. In this paper, we derive and analyze a selected transient characteristic of the model, i.e., the probability that in a given time interval the queue size is kept under a predefined level. As the main purpose of the discussed queueing scheme is to maintain the queue size low, this is a natural characteristic to study. In addition to that, the average time to reach a given level is derived. Theoretical results for both characteristics are accompanied by numerical examples. Among other things, they demonstrate that the transient behavior of the queue may vary significantly with the shape of the dropping function, even if the steady-state performance remains unaltered.

Queues with the dropping function and general service time.

We present an analysis of queueing systems with the dropping function, infinite buffer and general distribution of the service time. Firstly, a stability condition, more general than the well-known ρ < 1, is proven. Secondly, the formulas for the queue size distribution, loss ratio and mean duration of the busy period, are derived. Thirdly, numerical examples are given, including optimizations of the shape of the dropping function with regard to the combined cost of the queue size and loss ratio.

Queues with Dropping Functions and General Arrival Processes.

In a queueing system with the dropping function the arriving customer can be denied service (dropped) with the probability that is a function of the queue length at the time of arrival of this customer. The potential applicability of such mechanism is very wide due to the fact that by choosing the shape of this function one can easily manipulate several performance characteristics of the queueing system. In this paper we carry out analysis of the queueing system with the dropping function and a very general model of arrival process--the model which includes batch arrivals and the interarrival time autocorrelation, and allows for fitting the actual shape of the interarrival time distribution and its moments. For such a system we obtain formulas for the distribution of the queue length and the overall customer loss ratio. The analytical results are accompanied with numerical examples computed for several dropping functions.

Achieving High Resolution Timer Events in Virtualized Environment.

Virtual Machine Monitors (VMM) have become popular in different application areas. Some applications may require to generate the timer events with high resolution and precision. This however may be challenging due to the complexity of VMMs. In this paper we focus on the timer functionality provided by five different VMMs-Xen, KVM, Qemu, VirtualBox and VMWare. Firstly, we evaluate resolutions and precisions of their timer events. Apparently, provided resolutions and precisions are far too low for some applications (e.g. networking applications with the quality of service). Then, using Xen virtualization we demonstrate the improved timer design that greatly enhances both the resolution and precision of achieved timer events.