A tandem queue with Lévy input: a new representation of the downstream queue length.

In this paper we present a new representation for the steady state distribution of the workload of the second queue in a two-node tandem network. It involves the difference of two suprema over two adjacent intervals. In case of spectrally-positive

Markovian arrivals in stochastic modelling: a survey and some new results

This paper aims to provide a comprehensive review on Markovian arrival processes (MAPs), which constitute a rich class of point processes used extensively in stochastic modelling. Our starting point is the versatile process introduced by Neuts (1979) which, under some simplified notation, was coined as the batch Markovian arrival process (BMAP). On the one hand, a general point process can be approximated by appropriate MAPs and, on the other hand, the MAPs provide a versatile, yet tractable option for modelling a bursty flow by preserving the Markovian formalism. While a number of well-known arrival processes are subsumed under a BMAP as special cases, the literature also shows generalizations to model arrival streams with marks, nonhomogeneous settings or even spatial arrivals. We survey on the main aspects of the BMAP, discuss on some of its variants and generalizations, and give a few new results in the context of a recent state-dependent extension.Peer Reviewe

Performance analysis of priority queueing systems in discrete time

The integration of different types of traffic in packet-based networks spawns the need for traffic differentiation. In this tutorial paper, we present some analytical techniques to tackle discrete-time queueing systems with priority scheduling. We investigate both preemptive (resume and repeat) and non-preemptive priority scheduling disciplines. Two classes of traffic are considered, high-priority and low-priority traffic, which both generate variable-length packets. A probability generating functions approach leads to performance measures such as moments of system contents and packet delays of both classes

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

Performance Analyses and Improvements for the IEEE 802.15.4 CSMA/CA Scheme with Heterogeneous Buffered Conditions

Studies of the IEEE 802.15.4 Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) scheme have been received considerable attention recently, with most of these studies focusing on homogeneous or saturated traffic. Two novel transmission schemes—OSTS/BSTS (One Service a Time Scheme/Bulk Service a Time Scheme)—are proposed in this paper to improve the behaviors of time-critical buffered networks with heterogeneous unsaturated traffic. First, we propose a model which contains two modified semi-Markov chains and a macro-Markov chain combined with the theory of M/G/1/K queues to evaluate the characteristics of these two improved CSMA/CA schemes, in which traffic arrivals and accessing packets are bestowed with non-preemptive priority over each other, instead of prioritization. Then, throughput, packet delay and energy consumption of unsaturated, unacknowledged IEEE 802.15.4 beacon-enabled networks are predicted based on the overall point of view which takes the dependent interactions of different types of nodes into account. Moreover, performance comparisons of these two schemes with other non-priority schemes are also proposed. Analysis and simulation results show that delay and fairness of our schemes are superior to those of other schemes, while throughput and energy efficiency are superior to others in more heterogeneous situations. Comprehensive simulations demonstrate that the analysis results of these models match well with the simulation results

Markovian arrivals in stochastic modelling : a survey and some new results

This paper aims to provide a comprehensive review on Markovian arrival processes (MAPs), which constitute a rich class of point processes used extensively in stochastic modelling. Our starting point is the versatile process introduced by Neuts (1979) which, under some simplified notation, was coined as the batch Markovian arrival process (BMAP). On the one hand, a general point process can be approximated by appropriate MAPs and, on the other hand, the MAPs provide a versatile, yet tractable option for modelling a bursty flow by preserving the Markovian formalism. While a number of well-known arrival processes are subsumed under a BMAP as special cases, the literature also shows generalizations to model arrival streams with marks, nonhomogeneous settings or even spatial arrivals. We survey on the main aspects of the BMAP, discuss on some of its variants and generalizations, and give a few new results in the context of a recent state-dependent extension