Performance analysis of networks on chips

Modules on a chip (such as processors and memories) are traditionally connected through a single link, called a bus. As chips become more complex and the number of modules on a chip increases, this connection method becomes inefficient because the bus can only be used by one module at a time. Networks on chips are an emerging technology for the connection of on-chip modules. In networks on chips, switches are used to transmit data from one module to another, which entails that multiple links can be used simultaneously so that communication is more efficient. Switches consist of a number of input ports to which data arrives and output ports from which data leaves. If data at multiple input ports has to be transmitted to the same output port, only one input port may actually transmit its data, which may lead to congestion. Queueing theory deals with the analysis of congestion phenomena caused by competition for service facilities with scarce resources. Such phenomena occur, for example, in traffic intersections, manufacturing systems, and communication networks like networks on chips. These congestion phenomena are typically analysed using stochastic models, which capture the uncertain and unpredictable nature of processes leading to congestion (such as irregular car arrivals to a traffic intersection). Stochastic models are useful tools for the analysis of networks on chips as well, due to the complexity of data traffic on these networks. In this thesis, we therefore study queueing models aimed at networks on chips. The thesis is centred around two key models: A model of a switch in isolation, the so-called single-switch model, and a model of a network of switches where all traffic has the same destination, the so-called network of polling stations. For both models we are interested in the throughput (the amount of data transmitted per time unit) and the mean delay (the time it takes data to travel across the network). Single-switch models are often studied under the assumption that the number of ports tends to infinity and that traffic is uniform (i.e., on average equally many packets arrive to all buffers, and all possible destinations are equally likely). In networks on chips, however, the number of buffers is typically small. We introduce a new approximation specifically aimed at small switches with (memoryless) Bernoulli arrivals. We show that, for such switches, this approximation is more accurate than currently known approximations. As traffic in networks on chips is usually non-uniform, we also extend our approximation to non-uniform switches. The key difference between uniform and nonuniform switches is that in non-uniform switches, all queues have a different maximum throughput. We obtain a very accurate approximation of this throughput, which allows us to extend the mean delay approximation. The extended approximation is derived for Bernoulli arrivals and correlated arrival processes. Its accuracy is verified through a comparison with simulation results. The second key model is that of concentrating tree networks of polling stations (polling stations are essentially switches where all traffic has the same output port as destination). Single polling stations have been studied extensively in literature, but only few attempts have been made to analyse networks of polling stations. We establish a reduction theorem that states that networks of polling stations can be reduced to single polling stations while preserving some information on mean waiting times. This reduction theorem holds under the assumption that the last node of the network uses a so-called HoL-based service discipline, which means that the choice to transmit data from a certain buffer may only depend on which buffers are empty, but not on the amount of data in the buffers. The reduction theorem is a key tool for the analysis of networks of polling stations. In addition to this, mean waiting times in single polling stations have to be calculated, either exactly or approximately. To this end, known results can be used, but we also devise a new single-station approximation that can be used for a large subclass of HoL-based service disciplines. Finally, networks on chips typically implement flow control, which is a mechanism that limits the amount of data in the network from one source. We analyse the division of throughput over several sources in a network of polling stations with flow control. Our results indicate that the throughput in such a network is determined by an interaction between buffer sizes, flow control limits, and service disciplines. This interaction is studied in more detail by means of a numerical analysis

A Low-Delay MAC for IoT Applications: Decentralized Optimal Scheduling of Queues without Explicit State Information Sharing

We consider a system of several collocated nodes sharing a time slotted wireless channel, and seek a MAC (medium access control) that (i) provides low mean delay, (ii) has distributed control (i.e., there is no central scheduler), and (iii) does not require explicit exchange of state information or control signals. The design of such MAC protocols must keep in mind the need for contention access at light traffic, and scheduled access in heavy traffic, leading to the long-standing interest in hybrid, adaptive MACs. Working in the discrete time setting, for the distributed MAC design, we consider a practical information structure where each node has local information and some common information obtained from overhearing. In this setting, "ZMAC" is an existing protocol that is hybrid and adaptive. We approach the problem via two steps (1) We show that it is sufficient for the policy to be "greedy" and "exhaustive". Limiting the policy to this class reduces the problem to obtaining a queue switching policy at queue emptiness instants. (2) Formulating the delay optimal scheduling as a POMDP (partially observed Markov decision process), we show that the optimal switching rule is Stochastic Largest Queue (SLQ). Using this theory as the basis, we then develop a practical distributed scheduler, QZMAC, which is also tunable. We implement QZMAC on standard off-the-shelf TelosB motes and also use simulations to compare QZMAC with the full-knowledge centralized scheduler, and with ZMAC. We use our implementation to study the impact of false detection while overhearing the common information, and the efficiency of QZMAC. Our simulation results show that the mean delay with QZMAC is close that of the full-knowledge centralized scheduler.Comment: 28 pages, 19 figure

Mathematical Analysis of Queue with Phase Service: An Overview

We discuss various aspects of phase service queueing models. A large number of models have been developed in the area of queueing theory incorporating the concept of phase service. These phase service queueing models have been investigated for resolving the congestion problems of many day-to-day as well as industrial scenarios. In this survey paper, an attempt has been made to review the work done by the prominent researchers on the phase service queues and their applications in several realistic queueing situations. The methodology used by several researchers for solving various phase service queueing models has also been described. We have classified the related literature based on modeling and methodological concepts. The main objective of present paper is to provide relevant information to the system analysts, managers, and industry people who are interested in using queueing theory to model congestion problems wherein the phase type services are prevalent

Discrete Time Analysis of Consolidated Transport Processes

Diese Arbeit beschäftigt sich mit der Entwicklung zeitdiskreter Modelle zur Analyse von Transportbündelungen. Mit den entwickelten Modellen für Bestands- und Fahrzeugbündelungen, insbesondere Milkrun-Systeme, kann eine detaillierte Leistungsbewertung in kurzer Zeit durchgeführt werden. Darüber hinaus erlauben die Modelle die Analyse der Umschlagslagerbündelungen, beispielweise Hub-und-Spoke-Netzwerke, indem sie im Rahmen einer Netzwerkanalyse mit einander verknüpft werden

Discrete Time Analysis of Multi-Queue Systems with Multiple Departure Streams in Material Handling and Production under Different Service Rules

In this work, we present a modelling approach in order to depict service rules holistically. The developed model is called multi-queue system with multiple departure streams (MQSMDS). The MQSMDS is modelled as a discrete time Markov chain. On the basis of a numerical study, the system characteristics are evaluated. The results of this work enable a rapid and low-cost analysis of material handling and production systems as well as a fast and easy identification of suitable service rules

Queueing systems with periodic service

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On some queueing systems with server vacations, extended vacations, breakdowns, delayed repairs and stand-bys

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This research investigates a batch arrival queueing system with a Bernoulli scheduled vacation and random system breakdowns. It is assumed that the repair process does not start immediately after the breakdown. Consequently there maybe a delay in starting repairs. After every service completion the server may go on an optional vacation. When the original vacation is completed the server has the option to go on an extended vacation. It is assumed that the system is equipped with a stand-by server to serve the customers during the vacation period of the main server as well as during the repair process. The service times, vacation times, repair times, delay times and extended vacation times are assumed to follow different general distributions while the breakdown times and the service times of the stand-by server follow an exponential distribution. By introducing a supplementary variable we are able to obtain steady state results in an explicit closed form in terms of the probability generating functions. Some important performance measures including; the average length of the queue, the average number of customers in the system, the mean response time, and the value of the traffic intensity are presented. The professional MathCad 2001 software has been used to illustrate the numerical results in this study

Analysis of some batch arrival queueing systems with balking, reneging, random breakdowns, fluctuating modes of service and Bernoulli schedulled server vacations.

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonThe purpose of this research is to investigate and analyse some batch arrival queueing systems with Bernoulli scheduled vacation process and single server providing service. The study aims to explore and extend the work done on vacation and unreliable queues with a combination of assumptions like balking and re-service, reneging during vacations, time homogeneous random breakdowns and fluctuating modes of service. We study the steady state properties, and also transient behaviour of such queueing systems. Due to vacations the arriving units already in the system may abandon the system without receiving any service (reneging). Customers may decide not to join the queue when the server is in either working or vacation state (balking). We study this phenomenon in the framework of two models; a single server with two types of parallel services and two stages of service. The model is further extended with re-service offered instantaneously. Units which join the queue but leave without service upon the absence of the server; especially due to vacation is quite a natural phenomenon. We study this reneging behaviour in a queueing process with a single server in the context of Markovian and non-Markovian service time distribution. Arrivals are in batches while each customer can take the decision to renege independently. The non-Markovian model is further extended considering service time to follow a Gamma distribution and arrivals are due to Geometric distribution. The closed-form solutions are derived in all the cases. Among other causes of service interruptions, one prime cause is breakdowns. We consider breakdowns to occur both in idle and working state of the server. In this queueing system the transient and steady state analysis are both investigated. Applying the supplementary variable technique, we obtain the probability generating function of queue size at random epoch for the different states of the system and also derive some performance measures like probability of server‟s idle time, utilization factor, mean queue length and mean waiting time. The effect of the parameters on some of the main performance measures is illustrated by numerical examples to validate the analytical results obtained in the study. The Mathematica 10 software has been used to provide the numerical results and presentation of the effects of some performance measures through plots and graphs