Queue normalization methods in systems GI/GI/1/m with infinite variance of service time

Queuing systems with an infinite variance of service time are considered. The average waiting time in such systems is equal to infinity at a stationary regime. We analyze the efficiency of introducing of absolute priorities with infinite number of priority classes determined by the special axis marking on intervals for possible values of service time. It is stated that queues in systems become normalized, i.e. the average queue length become finite, when using regular marking. Furthermore, request loss probabilities radically decrease when buffer size is finite. More efficient marking - exponential marking - is proposed for practical purposes in networks with fractal traffic. The optimization problems of regular and exponential markings are solved

Single and dual queueing schemes with prioritised traffic scheduling and finite waiting room

Analysis of new schemes aimed at improving congestion in communications systems is vital for todays service providers. Many techniques are used to evaluate such schemes be it precisely via mathematics or approximately using simulation. This thesis introduces a new scheme, the multi priority dual queue (MPDQ). The MPDQ is the combination of two concepts, the dual queue introduced by [Hayes et. al., 1999] and prioritised traffic. The MPDQ is a system with finite waiting room with two queues where traffic upon arrival if finding the first queue full wait in the second queue if there is room. When a space becomes vacant in the first queue, a customer at the front of the second queue enters the back of the first, which is the queue that has the service centre at the front of it. The traffic can be of two or more classes. The analysis of such a system is complex, both analytically using queueing theory and approximately using simulation analysis. Both approaches are taken in this thesis. To begin, the new algorithmic approach used for the MPDQ is applied for the single buffer model. The steady state and waiting time distributions are obtained and later compared to the MPDQ. Next the performance characteristics are obtained by solving the steady state and waiting time distributions of a two class MPDQ. Preemptive and non-preemptive service disciplines are investigated. Maple is also used to solve the algorithm. To broaden the application of the MPDQ scheme, computer simulations using Arena are undertaken to extend the application of the scheme (and existing finite queueing models) to situations with more than two priorities, something that is extremely difficult to solve analytically. Using simulation, comparisons are undertaken for the single and dual queue schemes for more than two priorities with a variety of queueing disciplines used including First In First Out (FIFO), Last In First Out (LIFO), High Class First (HCF), and Low Class First (LCF). Network scenarios are also modelled to determine the performance of the MPDQ in this environment

Численный метод анализа моделей систем массового обслуживания со скачкообразными приоритетами

Розроблено алгоритмічний підхід до дослідження моделей систем масового обслуговування із загальною обмеженою та необмеженою чергами за наявності стрибкоподібних пріоритетів. Припускається, що в момент надходження нового низькопріоритетного виклику один виклик такого типу з деякою ймовірністю може перейти у кінець черги високопріоритетних викликів. Ймовірність переходу залежить від стану черги різнотипних викликів. Наведено алгоритми розрахунку характеристик таких моделей обслуговування.An algorithmic approach to study the queuing models with common finite and infinite buffer and jump priorities is developed. It is assumed that upon arrival of a low-priority call, one call of such kind might be transferred to the end of the queue of high-priority calls. The transfer probability depends on the state of the queue of heterogeneous calls. The algorithms are proposed to calculate the quality of service metrics of such queuing models

The effective bandwidth problem revisited

The paper studies a single-server queueing system with autonomous service and $\ell$ priority classes. Arrival and departure processes are governed by marked point processes. There are $\ell$ buffers corresponding to priority classes, and upon arrival a unit of the $k$th priority class occupies a place in the $k$th buffer. Let $N^{(k)}$, $k=1,2,...,\ell$ denote the quota for the total $k$th buffer content. The values $N^{(k)}$ are assumed to be large, and queueing systems both with finite and infinite buffers are studied. In the case of a system with finite buffers, the values $N^{(k)}$ characterize buffer capacities. The paper discusses a circle of problems related to optimization of performance measures associated with overflowing the quota of buffer contents in particular buffers models. Our approach to this problem is new, and the presentation of our results is simple and clear for real applications.Comment: 29 pages, 11pt, Final version, that will be published as is in Stochastic Model

A discrete-time performance model for congestion control mechanism using queue thresholds with QOS constraints

This paper presents a new analytical framework for the congestion control of Internet traffic using a queue threshold scheme. This framework includes two discrete-time analytical models for the performance evaluation of a threshold based congestion control mechanism and compares performance measurements through typical numerical results. To satisfy the low delay along with high throughput, model-I incorporates one threshold to make the arrival process step reduce from arrival rate ¿1 directly to ¿2 once the number of packets in the system has reached the threshold value L1. The source operates normally, otherwise. Model-II incorporates two thresholds to make the arrival rate linearly reduce from ¿1 to ¿2 with system contents when the number of packets in the system is between two thresholds L1 and L2. The source operates normally with arrival rate ¿1 before threshold L1, and with arrival rate ¿2 after the threshold L2. In both performance models, the mean packet delay W, probability of packet loss PL and throughput S have been found as functions of the thresholds and maximum drop probability. The performance comparison results for the two models have also been made through typical numerical results. The results clearly demonstrate how different load settings can provide different tradeoffs between throughput, loss probability and delay to suit different service requirements

Partially shared buffers with full or mixed priority

This paper studies a finite-sized discrete-time two-class priority queue. Packets of both classes arrive according to a two-class discrete batch Markovian arrival process (2-DBMAP), taking into account the correlated nature of arrivals in heterogeneous telecommunication networks. The model incorporates time and space priority to provide different types of service to each class. One of both classes receives absolute time priority in order to minimize its delay. Space priority is implemented by the partial buffer sharing acceptance policy and can be provided to the class receiving time priority or to the other class. This choice gives rise to two different queueing models and this paper analyses both these models in a unified manner. Furthermore, the buffer finiteness and the use of space priority raise some issues on the order of arrivals in a slot. This paper does not assume that all arrivals from one class enter the queue before those of the other class. Instead, a string representation for sequences of arriving packets and a probability measure on the set of such strings are introduced. This naturally gives rise to the notion of intra-slot space priority. Performance of these queueing systems is then determined using matrix-analytic techniques. The numerical examples explore the range of service differentiation covered by both models

Modeling the fraud-like investment founds by Petri nets

In this paper we model the fraud-like investment founds using place-transition Petri nets. We will also classify the business using regression line in order to find the possible fraud-like investment founds. In these regression lines we compute analytical the mark of a place in function of some other elements of the Petri net, and next we express this value in function of the same elements using regression. From the identity of the coefficients we find a ratio between two weights of arcs. We make also a program where the marks and transitions are implemented as classes for Petri nets, and, using the heritage mechanism we extend the Petri net to Petri net with priorities.Petri nets, fraud-like investment founds, objects programming.