Performance Bounds for Synchronized Queueing Networks

Las redes de Petri estocásticas constituyen un modelo unificado de las diferentes extensiones de redes de colas con sincronizaciones existentes en la literatura, válido para el diseño y análisis de prestaciones de sistemas informáticos distribuidos. En este trabajo se proponen técnicas de cálculo de cotas superiores e inferiores de las prestaciones de redes de Petri estocásticas en estado estacionario. Las cotas obtenidas son calculables en tiempo polinómico en el tamaño del modelo, por medio de la resolución de ciertos problemas de programación lineal definidos a partir de la matriz de incidencia de la red (en este sentido, las técnicas desarrolladas pueden considerarse estructurales). Las cotas calculadas dependen sólamente de los valores medios de las variables aleatorias que describen la temporización del sistema, y son independientes de los momentos de mayor orden. Esta independencia de la forma de las distribuciones de probabilidad asociadas puede considerarse como una útil generalización de otros resultados existentes para distribuciones particulares, puesto que los momentos de orden superior son, habitualmente, desconocidos en la realidad y difíciles de estimar. Finalmente, las técnicas desarrolladas se aplican al análisis de diferentes ejemplos tomados de la literatura sobre sistemas informáticos distribuidos y sistemas de fabricación. ******* Product form queueing networks have long been used for the performance evaluation of computer systems. Their success has been due to their capability of naturally expressing sharing of resources and queueing, that are typical situations of traditional computer systems, as well as to their efficient solution algorithms, of polynomial complexity on the size of the model. Unfortunately, the introduction of synchronization constraints usually destroys the product form solution, so that general concurrent and distributed systems are not easily studied with this class of models. Petri nets have been proved specially adequate to model parallel and distributed systems. Moreover, they have a well-founded theory of analysis that allows to investigate a great number of qualitative properties of the system. In the original definition, Petri nets did not include the notion of time, and tried to model only the logical behaviour of systems by describing the causal relations existing among events. This approach showed its power in the specification and analysis of concurrent systems in a way independent of the concept of time. Nevertheless the introduction of a timing specification is essential if we want to use this class of models for the performance evaluation of distributed systems. One of the main problems in the actual use of timed and stochastic Petri net models for the quantitative evaluation of large systems is the explosion of the computational complexity of the analysis algorithms. In general, exact performance results are obtained from the numerical solution of a continuous time Markov chain, whose dimension is given by the size of the state space of the model. Structural computation of exact performance measures has been possible for some subclasses of nets such as those with state machine topology. These nets, under certain assumptions on the stochastic interpretation are isomorphic to Gordon and Newell's networks, in queueing theory terminology. In the general case, efficient methods for the derivation of performance measures are still needed. Two complementary approaches to the derivation of exact measures for the analysis of distributed systems are the utilization of approximation techniques and the computation of bounds. Approximate values for the performance parameters are in general more efficiently derived than the exact ones. On the other hand, "exactness" only exists in theory! In other words, numerical algorithms must be applied in practice for the computation of exact values, therefore making errors is inevitable. Performance bounds are useful in the preliminary phases of the design of a system, in which many parameters are not known accurately. Several alternatives for those parameters should be quickly evaluated, and rejected those that are clearly bad. Exact (and even approximate) solutions would be computationally very expensive. Bounds become useful in these instances since they usually require much less computation effort. The computation of upper and lower bounds for the steady-state performance of timed and stochastic Petri nets is considered in this work. In particular, we study the throughput of transitions, defined as the average number of firings per time unit. For this measure we try to compute upper and lower bounds in polynomial time on the size of the net model, by means of proper linear programming problems defined from the incidence matrix of the net (in this sense, we develop structural techniques). These bounds depend only on the mean values and not on the higher moments of the probability distribution functions of the random variables that describe the timing of the system. The independence of the probability distributions can be viewed as a useful generalization of the performance results, since higher moments of the delays are usually unknown for real cases, and difficult to estimate and assess. From a different perspective, the obtained results can be applied to the analysis of queueing networks extended with some synchronization schemes. Monoclass queueing networks can be mapped on stochastic Petri nets. On the other hand, stochastic Petri nets can be interpreted as monoclass queueing networks augmented with synchronization primitives. Concerning the presentation of this manuscript, it should be mentioned that chapter 1 has been written with the object of giving the reader an outline of the stochastic Petri net model: its definition, terminology, basic properties, and related concepts, together with its deep relation with other classic stochastic network models. Chapter 2 is devoted to the presentation of the net subclasses considered in the rest of the work. The classification presented here is quite different from the one which is usual in the framework of Petri nets. The reason lies on the fact that our classification criterion, the computability of visit ratios for transitions, is introduced for the first time in the field of stochastic Petri nets in this work. The significance of that criterion is based on the important role that the visit ratios play in the computation of upper and lower bounds for the performance of the models. Nevertheless, classical important net subclasses are identified here in terms of the computability of their visit ratios from different parameters of the model. Chapter 3 is concerned with the computation of reachable upper and lower bounds for the most restrictive subclass of those presented in chapter 2: marked graphs. The explanation of this fact is easy to understand. The more simple is the model the more accessible will be the techniques an ideas for the development of good results. Chapter 4 provides a generalization for live and bounded free choice nets of the results presented in the previous chapter. Quality of obtained bounds is similar to that for strongly connected marked graphs: throughput lower bounds are reachable for bounded nets while upper bounds are reachable for 1-bounded nets. Chapter 5 considers the extension to other net subclasses, like mono-T-semiflow nets, FRT-nets, totally open deterministic systems of sequential processes, and persistent nets. The results are of diverse colours. For mono-T-semiflow nets and, therefore, for general FRT-nets, it is not possible (so far) to obtain reachable throughput bounds. On the other hand, for bounded ordinary persistent nets, tight throughput upper bounds are derived. Moreover, in the case of totally open deterministic systems of sequential processes the exact steady-state performance measures can be computed in polynomial time on the net size. In chapter 6 bounds for other interesting performance measures are derived from throughput bounds and from classical queueing theory laws. After that, we explore the introduction of more information from the probability distribution functions of service times in order to improve the bounds. In particular, for Coxian service delay of transitions it is possible to improve the throughput upper bounds of previous chapters which held for more general forms of distribution functions. This improvement shows to be specially fruitful for live and bounded free choice nets. Chapter 7 is devoted to case studies. Several examples taken from literature in the fields of distributed computing systems and manufacturing systems are modelled by means of stochastic Petri nets and evaluated using the techniques developed in previous chapters. Finally, some concluding remarks and considerations on possible extensions of the work are presented

Stability and partial instability of multi-class retrial queues

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Dynamic Time Windows and Generalized Virtual Clocks-Combined Closed-Loop/Open-Loop Mechanisms for Congestion Control of Data Traffic in High Speed Wide Area Networks

This paper presents a set of mechanisms for congestion control of data traffic in high speed wide area networks (HSWANs) along with preliminary performance results. The model of the network assumes reservation of resources based on average requirements. The mechanisms address (a) the different network time constants (short term and medium-term), (b) admission control that allows controlled variance of traffic as a function of medium-term congestion, and (c) prioritized scheduling which is based on a new fairness criterion. This latter criterion is perceived as the appropriate fairness measure for HSWANs. Preliminary performance studies show that the queue length statistics at switching nodes (mean, variance and max) are approximately proportional to the end-point \u27time window\u27 size. Further, * when network utilization approaches unity, the time window mechanism can protect the network from buffer overruns and excessive queueing delays, and * when network utilization level is smaller, the time window may be increased to allow a controlled amount of variance that attempts to simultaneously meet the performance goals of the end-user and that of the network. The prioritized scheduling algorithms proposed and studied in this paper are a generalization of the Virtual Clock algorithm [Zhang 1989]. The study here investigates * necessary and sufficient conditions for accomplishing desired fairness, * simulation and (limited analytical results for expected waiting times, * ability to protect against misbehaving users, and * relationship between end-point admission control (Time-Window) and internal scheduling (\u27Pulse\u27 and Virtual Clock) at the switch

Random Access in DVB-RCS2: Design and Dynamic Control for Congestion Avoidance

In the current DVB generation, satellite terminals are expected to be interactive and capable of transmission in the return channel with satisfying quality. Considering the bursty nature of their traffic and the long propagation delay, the use of a random access technique is a viable solution for such a Medium Access Control (MAC) scenario. In this paper, random access communication design in DVB-RCS2 is considered with particular regard to the recently introduced Contention Resolution Diversity Slotted Aloha (CRDSA) technique. This paper presents a model for design and tackles some issues on performance evaluation of the system by giving intuitive and effective tools. Moreover, dynamic control procedures that are able to avoid congestion at the gateway are introduced. Results show the advantages brought by CRDSA to DVB-RCS2 with regard to the previous state of the art.Comment: Accepted for publication: IEEE Transactions on Broadcasting; IEEE Transactions on Broadcasting, 201

Saturation routing for asynchronous transfer mode (ATM) networks

The main objective of this thesis is to show that saturation routing, often in the past considered inefficient, can in fact be a viable approach to use in many important applications and services over an Asynchronous Transfer Mode (ATM) network. For other applications and services, a hybrid approach (one that partially uses saturation routing) is presented. First, the minimum effects of saturation routing are demonstrated by showing that the ratio, defined as f, of routing overhead cells over information cells is small even for large networks. Second, modeling and simulation and M/D/l queuing analysis techniques are used to show that the overall effect on performance when using saturation routing is not significant over ATM networks. Then saturation routing ATM implementation is also provided, with important extensions to services such as multicast routing. After an analytical comparison, in terms of routing overhead, is made between Saturation Routing and the currently proposed Private Network-Network Interface (PNNI) procedure for ATM routing made by the ATM forum. This comparison is made for networks of different sizes (343node and 2401 -node networks) and different number of hierarchical levels (3 and 4 levels of hierarchy). The results show that the higher the number of levels of hierarchy and the farthest (in terms of hierarchical levels) the source and the destination nodes are from each other, the more advantageous saturation routing becomes. Finally, a set of measures of performance for use by saturation routing (or any routing algorithm), as metrics for routing path selection, is proposed. Among these measures, an innovative new measure of performance derived for measuring quality of service provided to Constant Bit Rate (CBR) users (e.g., such as voice and video users) called the Burst Voice Arrival Lag (BVAL) is described and derived

A study of topologies and protocols for fiber optic local area network

The emergence of new applications requiring high data traffic necessitates the development of high speed local area networks. Optical fiber is selected as the transmission medium due to its inherent advantages over other possible media and the dual optical bus architecture is shown to be the most suitable topology. Asynchronous access protocols, including token, random, hybrid random/token, and virtual token schemes, are developed and analyzed. Exact expressions for insertion delay and utilization at light and heavy load are derived, and intermediate load behavior is investigated by simulation. A new tokenless adaptive scheme whose control depends only on the detection of activity on the channel is shown to outperform round-robin schemes under uneven loads and multipacket traffic and to perform optimally at light load. An approximate solution to the queueing delay for an oscillating polling scheme under chaining is obtained and results are compared with simulation. Solutions to the problem of building systems with a large number of stations are presented, including maximization of the number of optical couplers, and the use of passive star/bus topologies, bridges and gateways

Capacity analysis of reservation-based random access for broadband wireless access networks

Abstract—In this paper we propose a novel model for the capacity analysis on the reservation-based random multiple access system, which can be applied to the medium access control protocol of the emerging WiMAX technology. In such a wireless broadband access system, in order to support QoS, the channel time is divided into consecutive frames, where each frame consists of some consequent mini-slots for the transmission of requests, used for the bandwidth reservation, and consequent slots for the actual data packet transmission. Three main outcomes are obtained: first, the upper and lower bounds of the capacity are derived for the considered system. Second, we found through the mathematical analysis that the transmission rate of reservationbased multiple access protocol is maximized, when the ratio between the number of mini-slots and that of the slots per frame is equal to the reciprocal of the random multiple access algorithm’s transmission rate. Third, in the case of WiMAX networks with a large number of subscribers, our analysis takes into account both the capacity and the mean packet delay criteria and suggests to keep such a ratio constant and independent of application-level data traffic arrival rate