On two generalisations of the final value theorem : scientific relevance, first applications, and physical foundations

The present work considers two published generalisations of the Laplace-transform final value theorem (FVT) and some recently appeared applications of one of these generalisations to the fields of physical stochastic processes and Internet queueing. Physical sense of the irrational time functions, involved in the other generalisation, is one of the points of concern. The work strongly extends the conceptual frame of the references and outlines some new research directions for applications of the generalised theorem

Discrete-time queueing models with priorities

This PhD-dissertation contains analyses of several discrete-time two-class priority queueing systems. We analyze non-preemptive, preemptive resume as well as preemptive repeat priority queues. The analyses are heavily based on probability generating functions that allow us to calculate moments and tail probabilities of the system contents and packet delays of both classes. The results are applicable in heterogeneous telecommunication networks, when delay-sensitive traffic gets transmission priority over best-effort traffic. Our results predict the influence of priority scheduling on the QoS (Quality-of-Service) of the different types of traffic

Analysis of priority queues with session-based arrival streams

In this paper, we analyze a discrete-time priority queue with session-based arrivals. We consider a user population, where each user can start and end sessions. Sessions belong to one of two classes and generate a variable number of fixed-length packets which arrive to the queue at the rate of one packet per slot. The lengths of the sessions are generally distributed. Packets of the first class have transmission priority over the packets of the other class. The model is motivated by a web server handling delay-sensitive and delay-insensitive content. By using probability generating functions, some performance measures of the queue such as the moments of the packet delays of both classes are calculated. The impact of the priority scheduling discipline and of the session nature of the arrival process is shown by some numerical examples

Queues with Galton-Watson-type arrivals

This paper presents the analysis of a discrete-time single server queueing system with a multi-type Galton-Watson arrival process with migration. It is shown that such a process allows to capture intricate correlation in the arrival process while the corcesponding queueing analysis yields closed-form expressions for various moments of queue content and packet delay

Performance comparison of several priority schemes with priority jumps

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Combined analysis of transient delay characteristics and delay autocorrelation function in the Geo(X)/G/1 queue

We perform a discrete-time analysis of customer delay in a buffer with batch arrivals. The delay of the kth customer that enters the FIFO buffer is characterized under the assumption that the numbers of arrivals per slot are independent and identically distributed. By using supplementary variables and generating functions, z-transforms of the transient delays are calculated. Numerical inversion of these transforms lead to results for the moments of the delay of the kth customer. For computational reasons k cannot be too large. Therefore, these numerical inversion results are complemented by explicit analytic expressions for the asymptotics for large k. We further show how the results allow us to characterize jitter-related variables, such as the autocorrelation of the delay in steady state

Analysis of the transient delay in a discrete-time buffer with batch arrivals

We perform a discrete-time analysis of the delay of customers in a FIFO buffer with batch arrivals. The numbers of arrivals per slot are independent and identically distributed variables. Since the arrivals come in batches, the delays of the subsequent customers do not constitute a Markov chain, which complicates the analysis. By using generating functions and the supplementary variable technique, moments of the delay of the k-th customer are calculated