The NxD-BMAP/G/1 queueing model : queue contents and delay analysis

We consider a single-server discrete-time queueing system with N sources, where each source is modelled as a correlated Markovian customer arrival process, and the customer service times are generally distributed. We focus on the analysis of the number of customers in the queue, the amount of work in the queue, and the customer delay. For each of these quantities, we will derive an expression for their steady-state probability generating function, and from these results, we derive closed-form expressions for key performance measures such as their mean value, variance, and tail distribution. A lot of emphasis is put on finding closed-form expressions for these quantities that reduce all numerical calculations to an absolute minimum

On the Queue Length Distribution in BMAP Systems

Batch Markovian Arrival Process – BMAP – is a teletraffic model which combines high ability to imitate complex statistical behaviour of network traces with relative simplicity in analysis and simulation. It is also a generalization of a wide class of Markovian processes, a class which in particular include the Poisson process, the compound Poisson process, the Markovmodulated Poisson process, the phase-type renewal process and others. In this paper we study the main queueing performance characteristic of a finite-buffer queue fed by the BMAP, namely the queue length distribution. In particular, we show a formula for the Laplace transform of the queue length distribution. The main benefit of this formula is that it may be used to obtain both transient and stationary characteristics. To demonstrate this, several numerical results are presented

Analysis of generic discrete-time buffer models with irregular packet arrival patterns

De kwaliteit van de multimediadiensten die worden aangeboden over de huidige breedband-communicatienetwerken, wordt in hoge mate bepaald door de performantie van de buffers die zich in de diverse netwerkele-menten (zoals schakelknooppunten, routers, modems, toegangsmultiplexers, netwerkinter- faces, ...) bevinden. In dit proefschrift bestuderen we de performantie van een dergelijke buffer met behulp van een geschikt stochastisch discrete-tijd wachtlijnmodel, waarbij we het geval van meerdere uitgangskanalen en (niet noodzakelijk identieke) pakketbronnen beschouwen, en de pakkettransmissietijden in eerste instantie één slot bedragen. De grillige, of gecorreleerde, aard van een pakketstroom die door een bron wordt gegenereerd, wordt gekarakteriseerd aan de hand van een algemeen D-BMAP (discrete-batch Markovian arrival process), wat een generiek kader creëert voor het beschrijven van een superpositie van dergelijke informatiestromen. In een later stadium breiden we onze studie uit tot het geval van transmissietijden met een algemene verdeling, waarbij we ons beperken tot een buffer met één enkel uitgangskanaal. De analyse van deze wachtlijnmodellen gebeurt hoofdzakelijk aan de hand van een particuliere wiskundig-analytische aanpak waarbij uitvoerig gebruik gemaakt wordt van probabiliteitsgenererende functies, die er toe leidt dat de diverse performantiematen (min of meer expliciet) kunnen worden uitgedrukt als functie van de systeemparameters. Dit resul-teert op zijn beurt in efficiënte en accurate berekeningsalgoritmen voor deze grootheden, die op relatief eenvoudige wijze geïmplementeerd kunnen worden

A discrete-time Markov modulated queuing system with batched arrivals

This paper examines a discrete-time queuing system with applications to telecommunications traffic. The arrival process is a particular Markov modulated process which belongs to the class of discrete batched Markovian arrival processes. The server process is a single server deterministic queue. A closed form exact solution is given for the expected queue length and delay. A simple system of equations is given for the probability of the queue exceeding a given length.Comment: to appear Performance Evaluatio

Traffic modeling in mobile internet protocol : version 6.

Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2005.Mobile Internet Protocol Version 6 (lPv6) is the new version of the Internet Protocol (IP) born out of the great success of Internet Protocol version 4 (IPv4). The motivation behind the development of Mobile IPv6 standard stems from user's demand for mobile devices which can connect and move seamlessly across a growing number of connectivity options. It is both suitable for mobility between subnets across homogenous and inhomogeneous media. The protocol allows a mobile node to communicate with other hosts after changing its point of attachment from one subnet to another. The huge address space available meets the requirements for rapid development of internet as the number of mobile nodes increases tremendously with the rapid expansion of the internet. Mobility, security and quality of service (QoS) being integrated in Mobile TPv6 makes it the important foundation stone for building the mobile information society and the future internet. Convergence between current network technologies: the intern et and mobile telephony is taking place, but the internet's IP routing was designed to work with conventional static nodes. Mobile IPv6 is therefore considered to be one of the key technologies for realizing convergence which enables seamless communication between fixed and mobile access networks. For this reason, there is numerous works in location registrations and mobility management, traffic modeling, QoS, routing procedures etc. To meet the increased demand for mobile telecommunications, traffic modeling is an important step towards understanding and solving performance problems in the future wireless IP networks. Understanding the nature of this traffic, identifying its characteristics and developing appropriate traffic models coupled with appropriate mobility management architectures are of great importance to the traffic engineering and performance evaluation of these networks. It is imperative that the mobility management used keeps providing good performance to mobile users and maintain network load due to signaling and packet delivery as low as possible. To reduce this load, Intemet Engineering Task Force (IETF) proposed a regional mobility management. The load is reduced by allowing local migrations to be handled locally transparent from the Home Agent and the Correspondent Node as the mobile nodes roams freely around the network. This dissertation tackles two major aspects. Firstly, we propose the dynamic regional mobility management (DRMM) architecture with the aim to minimize network load while keeping an optimal number of access routers in the region. The mobility management is dynamic based on the movement and population of the mobile nodes around the network. Most traffic models in telecommunication networks have been based on the exponential Poisson processes. This model unfortunately has been proved to be unsuitable for modeling busty IP traffic. Several approaches to model IP traffic using Markovian processes have been developed using the Batch Markovian Alrival Process (BMAP) by characterizing arrivals as batches of sizes of different distributions. The BMAP is constructed by generalizing batch Poisson processes to allow for non-exponential times between arrivals of batches while maintaining an underlying Markovian structure. The second aspect of this dissertation covers the traffic characterization. We give the analysis of an access router as a single server queue with unlimited waiting space under a non pre-emptive priority queuing discipline. We model the arrival process as a superposition of BMAP processes. We characterize the superimposed arrival processes using the BMAP presentation. We derive the queue length and waiting time for this type of queuing system. Performance of this traffic model is evaluated by obtaining numerical results in terms of queue length and waiting time and its distribution for the high and low priority traffic. We finally present a call admission control scheme that supports QoS

Cross-layer performance control of wireless channels using active local profiles

To optimize performance of applications running over wireless channels state-of-the-art wireless access technologies incorporate a number of channel adaptation mechanisms. While these mechanisms are expected to operate jointly providing the best possible performance for current wireless channel and traffic conditions, their joint effect is often difficult to predict. To control functionality of various channel adaptation mechanisms a new cross-layer performance optimization system is sought. This system should be responsible for exchange of control information between different layers and further optimization of wireless channel performance. In this paper design of the cross-layer performance control system for wireless access technologies with dynamic adaptation of protocol parameters at different layers of the protocol stack is proposed. Functionalities of components of the system are isolated and described in detail. To determine the range of protocol parameters providing the best possible performance for a wide range of channel and arrival statistics the proposed system is analytically analyzed. Particularly, probability distribution functions of the number of lost frames and delay of a frame as functions of first- and second-order wireless channel and arrival statistics, automatic repeat request, forward error correction functionality, protocol data unit size at different layers are derived. Numerical examples illustrating performance of the whole system and its elements are provided. Obtained results demonstrate that the proposed system provide significant performance gains compared to static configuration of protocols

Findings about the two-state BMMPP for modeling point processes in reliability and queueing systems

The Batch Markov Modulated Poisson Process (BMMPP) is a subclass of the versatile Batch Markovian Arrival process (BMAP) which have been widely used for the modeling of dependent and correlated simultaneous events (as arrivals, failures or risk events, real-time multimedia communications). Both theoretical and applied aspects are examined in this paper. On one hand, the identifiability of the stationary BMMPP2(K) is proven, where K is the maximum batch size. This is a powerful result when inferential tasks related to real data sets are carried out. On the other hand, some findings concerning the correlation and autocorrelation structures are provided.The first and second authors acknowledge financial support from the Spanish Ministry of Economy and Competitiveness, research project ECO2015-66593-P. The Third author acknowledge financial support from the Spanish Ministry of Economy and Competitiveness, research project MTM2015-65915-R; and also from Junta de Andalucía, and BBVA Fundation, research project P11- FQM-7603 and FQM-32