Mathematical modelling and analysis of communication networks: Transient characteristics of traffic processes and models for end-to-end delay and delay- jitter (original) (raw)

Rejoinder on: Queueing models for the analysis of communication systems

TOP, 2014

Queueing models can be used to model and analyze the performance of various subsystems in telecommunication networks, for instance to estimate the packet loss and packet delay in network routers. Since time is usually synchronized, discretetime models come natural. We start this paper with a review of suitable discretetime queueing models for communication systems. We pay special attention to two important characteristics of communication systems. First, traffic usually arrives in bursts, making the classic modeling of the arrival streams by Poisson processes inadequate and requiring the use of more advanced correlated arrival models. Second, different applications have different quality-of-service requirements (packet loss, packet delay, jitter,. . .). Consequently, the common first-come-first-served (FCFS) scheduling is not satisfactory and more elaborate scheduling disciplines are required. Both properties make common memoryless queueing models (M/M/1-type models) inadequate. After the review, we therefore concentrate on a discrete-time queueing analysis with two traffic classes, heterogeneous train arrivals and a priority scheduling discipline, as an example analysis where both time correlation and heterogeneity in the arrival process as well as non-FCFS scheduling are taken into account. Focus is on delay performance measures, such as the mean delay experienced by both types of packets and probability tails of these delays.

Transient Behaviour of Queueing Systems with Correlated Traffic

Performance Evaluation, 1996

In this paper, we present the time-dependent solutions of various stochastic processes associated with a finite Quasi-Birth-Death queueing system. These include the transient queueing solutions, the transient departure and loss intensity processes and certain transient cumulative measures associated with the queueing system. The focus of our study is the effect of the arrival process correlation on the queueing system before it reaches steady-state. With the aid of numerous examples, we investigate the strong relationship between the time scales of variation of the arrival process and those of the transient queueing, loss and departure processes. These time-dependent solutions require the computation of the exponential of the stochastic generator matrix G which may be of very large order. This precludes the use of known techniques to solve the matrix exponential such as the eigenvalue decomposition of G. We present a numerical technique based on the computation of the Laplace Transform of the matrix exponential which may then be numerically inverted to obtain the time-dependent solutions. In this paper, we also propose new QoS metrics based on transient measures and efficient techniques for their computation.

Queueing models for the analysis of communication systems

Top, 2014

Queueing models can be used to model and analyze the performance of various subsystems in telecommunication networks; for instance, to estimate the packet loss and packet delay in network routers. Since time is usually synchronized, discretetime models come natural. We start this paper with a review of suitable discrete-time queueing models for communication systems. We pay special attention to two important characteristics of communication systems. First, traffic usually arrives in bursts, making the classic modeling of the arrival streams by Poisson processes inadequate and requiring the use of more advanced correlated arrival models. Second, different applications have different quality-of-service requirements (packet loss, packet delay, jitter, etc.). Consequently, the common first-come-first-served (FCFS) scheduling is not satisfactory and more elaborate scheduling disciplines are required. Both properties make common memoryless queueing models (M/M/1-type models) inadequate. After the review, we therefore concentrate on a discrete-time queueing analysis with two traffic classes, heterogeneous train arrivals and a priority scheduling discipline, as an example analysis where both time correlation and heterogeneity in the arrival This invited paper is discussed in the comments available

Analytical Results on the Stochastic Behaviour of an Averaged Queue Length

2000

The joint dynamics of the instantaneous and exponentially averaged queue length in an M/M/1/K queue is studied. A system of ordinary dierential equa- tions is derived for the joint stationary distribution of the instantaneous and the exponentially averaged queue length. The equations are similar to those gov- erning an MMRP driven uid queue. An analytical solution to the equations is

Analysis of a correlated queue in communication systems

In this paper we study a family of queues where the service time B n of customer n depends on the interarrival time I n between customers n ? 1 and n. In particular, we focus on dependencies that arise naturally in the context of communication systems, where the nite speed of the communication links constrains the amount of data that can be received in a given time interval. Speci cally, we study queues where the random variables I n and B n exhibit some form of proportionality relation. Such dependencies can have signi cant impact on system performance and it is, therefore, critical to develop tractable models that account for them.

A generalized Markovian queue and its applications to performance analysis in telecommunications networks

2009

In this paper the MM K k=1 CP P k /GE/c/L G-queue is introduced and proposed as a generalised Markovian node model in telecommunications networks. An exact and computationally efficient solution is obtained for the steady-state probabilities and performance measures. Issues concerning the computational effort are also discussed. The proposed queue is applied to the performance analysis of optical burst switching (OBS) nodes. The numerical results obtained and also the numerical results of a previous model are compared to the simulation results of the OBS obtained using captured traffic traces. We have also introduced negative customers into the model, in an innovative way, in order to account for the loss of packets due to technology limitations of the FDL's (fiber delay loop), which is rather specific to the optical domain. The model is quite promising as a viable performance predictor.

ANALYSIS OF DISCRETE-TIME MULTISERVER QUEUES WITH CONSTANT SERVICE TIMES AND CORRELATED ARRIVALS

We investigate the behavior of a discrete-time multi- server buer system with innite buer size. Packets arrive at the system according to a two-state corre- lated arrival process. The service times of the pack- ets are assumed to be constant, equal to multiple slots. The behavior of the system is analyzed by means of an analytical technique based on proba- bility generating functions (pgf's). Explicit expres- sions are obtained for the pgf's of the system contents and the packet delay. From these, the moments and the tail distributions of the system contents and the packet delay can be calculated. Numerical examples are given to show the inuence of various model pa- rameters on the system behavior.