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

Performance Analysis of Two Priority Queuing Systems in Tandem

In this paper, we consider a tandem of two head-of-line (HOL) non-preemptive priority queuing systems, each with a single server and a deterministic service-time. Two classes of traffic are considered, namely high priority and low priority traffic. By means of a generating function approach, we present a technique to derive closed-form expressions for the mean buffer occupancy at each node and mean delay. Finally, we illustrate our solution technique with some numerical examples, whereby we illustrate the starvation impact of the HOL priority scheduling discipline on the performance of the low-priority traffic stream. Our research highlights the important fact that the unfairness of the HOL priority scheduling becomes even more noticeable at the network level. Thus this priority mechanism should be used with caution

Performance analysis of buffers with train arrivals and correlated output interruptions

In this paper, we study a discrete-time buffer system with a timecorrelated packet arrival process and one unreliable output line. In particular, packets arrive to the buffer in the form of variable-length packet trains at a fixed rate of exactly one packet per slot. The packet trains are assumed to have a geometric length, such that each packet has a fixed probability of being the last of its corresponding train. The output line is governed by a Markovian process, such that the probability that the line is available during a slot depends on the state of the underlying J-state Markov process during that slot. First, we provide a general analysis of the state of the buffer system based on a matrix generating functions approach. This also leads to an expression for the mean buffer content. Additionally, we take a closer look at the distributions of the packet delay and the train delay. In order to make matters more concrete, we next present a detailed and explicit analysis of the buffer system in case the output line is governed by a 2-state Markov process. Some numerical examples help to visualise the influence of the various model parameters

Analysis of a discrete-time single-server queue with an occasional extra server

We consider a discrete-time queueing system having two distinct servers: one server, the "regular" server, is permanently available, while the second server, referred to as the "extra" server, is only allocated to the system intermittently. Apart from their availability, the two servers are identical, in the sense that the customers have deterministic service times equal to 1 fixed-length time slot each, regardless of the server that processes them. In this paper, we assume that the extra server is available during random "up-periods", whereas it is unavailable during random "down-periods". Up-periods and down-periods occur alternately on the time axis. The up-periods have geometrically distributed lengths (expressed in time slots), whereas the distribution of the lengths of the down-periods is general, at least in the first instance. Customers enter the system according to a general independent arrival process, i.e., the numbers of arrivals during consecutive time slots are i.i.d. random variables with arbitrary distribution. For this queueing model, we are able to derive closed-form expressions for the steady-state probability generating functions (pgfs) and the expected values of the numbers of customers in the system at various observation epochs, such as the start of an up-period, the start of a down-period and the beginning of an arbitrary time slot. At first sight, these formulas, however, appear to contain an infinite number of unknown constants. One major issue of the mathematical analysis turns out to be the determination of these constants. In the paper, we show that restricting the pgf of the down-periods to be a rational function of its argument, brings about the crucial simplification that the original infinite number of unknown constants appearing in the formulas can be expressed in terms of a finite number of independent unknowns. The latter can then be adequately determined based on the bounded nature of pgfs inside the complex unit disk, and an extensive use of properties of polynomials. Various special cases, both from the perspective of the arrival distribution and the down-period distribution, are discussed. The results are also illustrated by means of relevant numerical examples. Possible applications of this type of queueing model are numerous: the extra server could be the regular server of another similar queue, helping whenever an idle period occurs in its own queue; a geometric distribution for these idle times is then a very natural modeling assumption. A typical example would be the situation at the check-in counter at a gate in an airport: the regular server serves customers with a low-fare ticket, while the extra server gives priority to the business-class and first-class customers, but helps checking regular customers, whenever the priority line is empty. (C) 2017 Elsevier B.V. All rights reserved

نماذج التأخير والضياع الماركوفية في شبكات البيانات

تستخدم نظرية الترتيل بشكل واسع لتحليل شبكات اتصالات البيانات المؤلفة من عقد تبديلية مرتبطة فيما بينها بواسطة وصلات النقل ويتم تحليل شبكات البيانات بفصلها إلى نظم جزئية وتحليل كل نظام جزئي بشكل منفرد باستخدام أحد نماذج الترتيل المعروفة. يقدم هذا البحث دليلاً عملياً لتحليل التأخير والضياع وفق منهجية جديدة ومتكاملة لشرح وعرض وتحليل أسس نظرية الترتيل ونماذج الترتيل الماركوفية في شبكات البيانات. يقوم البحث بدراسة وتحليل ومقارنة نماذج الترتيل الماركوفية الأساسية مع التركيز على التأخير والضياع كمقياسين هامين من مقاييس جودة الخدمة والأداء في شبكات البيانات. يوضح البحث كيفية استخدام سلاسل ماركوف لاستنتاج الحالة المستقرة لنماذج الترتيل الماركوفية الأساسية واستنتاج الصيغ الرياضية لمقاييس الأداء المختلفة لهذه النماذج. كما يتضمن البحث استنتاجات وتوصيات مناسبة تساعد في تطوير وإنشاء نماذج أخرى بوجود فرضيات معينة. The Queuing Theory is widely used for the analysis of data communication networks consisted of switched nodes. The analysis of data networks is based on method of decomposition where the total network is broken up into subsystem and the subsystems are analyzed individually by using one of the well known queuing models.   This paper provides a practical guide to analysis the delay and loss according to a new integrated method to explain, show, and analyze the queuing theory basics and Markovian queuing models in the data networks.   The paper investigates, analyzes, and compares the basic Markovian queuing models, and also focuses on analyzing the delay and loss as two important measures of the quality of service and performance in the data networks. The paper has conclusions and recommendations which help in the development and establishment other queuing models with specific assumptions

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

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