00529nas a2200181   4500000000100000008004100001260002600042653004100068100002400109700002200133700001600155700001700171700001800188700001700206700001600223700001600239245009200255       2026                            d  bIEEEaAvignon, France10aDiffusion approximation; LPWAN; CSMA1 aTadeusz Czachórski1 aKrzysztof Grochla1 aPiotr Pecka1 aAnna Strzoda1 aJean Fourneau1 aLynda Mokdad1 aMonika Nycz1 aTomasz Nycz00aThe Impact of CSMA on LoRaWAN Communication Efficiency: A Diffusion Approximation Model01166nas a2200205   4500000000100000008004100001260003300042653000900075100002400084700002200108700001600130700001700146700001600163700001700179700001600196700001600212245007200228856005000300520061000350       2026                            d  c02/2026bIEEEaLas Vegas USA10aLoRa1 aTadeusz Czachórski1 aKrzysztof Grochla1 aPiotr Pecka1 aAnna Strzoda1 aJ. Fourneau1 aLynda Mokdad1 aMonika Nycz1 aTomasz Nycz00aThe impact of CSMA on LoRaWAN gateways' performance in IoT networks  uhttps://ieeexplore.ieee.org/document/113665363 aThe CSMA mode of operation was recently added to the LoRaWAN standard. We investigate, using a queueing model, how the introduction of CSMA in the communication between devices and the gate in LoRaWan may increase the probability of successful transmission. In the proposed model, customers (transmissions) are served by a multichannel station (gate), and the number of channels corresponds to the number of transmissions that can be performed in parallel. We introduce a queueing model with multiple attempts to find a free channel and investigate their impact on transmission throughput and reliability.02190nas a2200145   4500000000100000008004100001260003300042100001900075700002400094700001700118700001600135700002000151245011000171520176300281       2025                            d  c12/2025bIEEEaParis, France1 aGodlove Kuaban1 aTadeusz Czachórski1 aErol Gelenbe1 aPiotr Pecka1 aPiotr Czekalski00aEnergy Dynamics of Green IoT Nodes with Time-Varying Energy Harvesting, Leakage, and Consumption Patterns3 aThe growing proliferation of Internet of Things (IoT) devices has intensified the need for sustainable energy solutions, particularly in resource-constrained deployments where non-rechargeable batteries and supercapacitors are the primary energy sources. Green IoT (G-IoT) frameworks address this challenge by combining energy-saving techniques with energy harvesting from ambient sources such as solar power. However, the intermittent nature of renewable energy and the non-ideal behavior of energy storage systems—such as energy leakage and capacity degradation—complicate reliable energy provisioning. This paper presents a novel Markovian framework for modelling the coupled dynamics of time-varying solar energy harvesting, time-dependent energy consumption, and state-dependent energy leakage in G-IoT systems. Unlike traditional steady-state models, our approach uses Discrete-Time Markov Chains (DTMCs) to capture the stochastic variability in both energy harvesting and consumption processes. We also introduce a refined leakage model in which the leakage rate is dynamically dependent on the stored energy level, enabling a more realistic characterization of energy losses due to energy leakage. Through extensive analytical evaluation, we examine how key parameters—such as storage capacity, leakage rate coefficient, and energy harvesting and consumption patterns—affect critical performance metrics, including the mean stored energy and energy-related service outage probability. Furthermore, we propose a parameter tuning strategy to optimize energy reliability and storage efficiency. The proposed model provides valuable insights for the design and optimization of robust, energy-aware IoT systems powered by renewable energy sources.02071nas a2200169   4500000000100000008004100001260004000042100001900082700002400101700001700125700001600142700001900158700002000177245008400197520159800281020002201879       2024                            d  c17/07/2024bIEEEaAyia Napa, Cyprus1 aGodlove Kuaban1 aTadeusz Czachórski1 aErol Gelenbe1 aPiotr Pecka1 aValery Nkemeni1 aPiotr Czekalski00aEnergy performance of Internet of Things (IoT) networks for pipeline monitoring3 aPipelines are the most convenient ways to transport fluids (e.g., water, oil, and gas). However, leakage of fluids into the environment results in resource wastage (especially water, which is becoming a scarce resource) and environmental pollution (in the case of leakage of toxic fluids like oil and gas). Emerging technologies like the Internet of Things (IoT), Wireless Sensor Networks (WSNs), Artificial Intelligence (AI), distributed computing, and cloud computing enable continuous monitoring of pipelines to detect leakages and corrosion on the pipeline. The main challenge with using battery-powered sensor nodes to monitor pipelines is the energy constraint, necessitating frequent battery replacement. Thus, there is a need to develop energy-saving mechanisms to prolong the lifetime of these sensor nodes. In this paper, we use the diffusion approximation modelling framework in which the data from the experimental testbed are used to model the dynamics of the battery's energy content and to estimate the mean and variance of the device's lifetime. The novelty in the proposed diffusion model of the battery of an IoT node is the introduction of multiple energy thresholds that split the energy state-space of the battery into multiple energy-saving regimes. As the battery discharges, the node gradually transitions into energy-saving regimes by reconfiguring some of its parameters to reduce energy consumption (sometimes at the cost of trading off some performance metrics). We investigate the impact of energy-saving regimes or the number of thresholds on the node's lifetime.  a979-8-3503-6126-102238nas a2200193   4500000000100000008004100001260001500042100001900057700002400076700001700100700001600117700001800133700001800151700001900169700002000188245005500208490000700263520177400270       2024                            d  c07/11/20241 aGodlove Kuaban1 aTadeusz Czachórski1 aErol Gelenbe1 aPiotr Pecka1 aSapana Sharma1 aPradeep Singh1 aValery Nkemeni1 aPiotr Czekalski00aEnergy performance of self-powered Green IoT nodes0 v123 aThe widespread adoption of the Internet of Things (IoT) partly depends on the successful design and deployment of IoT nodes that can operate for several years without any service outage and the need to replace their energy storage systems (e.g., battery, capacitor, or supercapacitor) when all the stored energy is depleted or when the cycle life of the Energy Storage Systems (ESS) is reached. Replacing batteries in the case of large-scale IoT networks and nodes located in places that are hard to reach is very challenging and costly, requiring the design of IoT nodes that can operate for several years without the need for human intervention. One such example is the deployment of IoT nodes in large agricultural fields (for soil or crop monitoring) or a long-distance pipeline (for pipeline monitoring). This paper investigates the practical implications of imposing energy-saving thresholds on the energy performance metrics of green IoT nodes. We propose an energy packet-based model for the evaluation of the energy performance of a green IoT node with the possibility of switching the node to energy-saving regimes on the fly when the energy content of the ESS reaches defined thresholds. Configuring single or multiple thresholds improves the energy performance of the node significantly (e.g., increases the lifetime of the node and reduces the probability of service outage and energy wastage), and the value of the threshold(s) should be carefully chosen. The energy performance of the IoT node can also be improved by dimensioning the energy harvesting system to ensure that the node operates for several years without running out of energy (e.g., maximizing the lifetime of the nodes and minimising the probability of service outage and energy wastage).01642nas a2200169   4500000000100000008004100001260002500042100001900067700002400086700001700110700001600127700001900143700002000162245007400182856005100256520116500307       2024                            d  bIEEEaKrakow, Poland1 aGodlove Kuaban1 aTadeusz Czachórski1 aErol Gelenbe1 aPiotr Pecka1 aValery Nkemeni1 aPiotr Czekalski00aImpact of energy leakage on the energy performance of green IoT nodes  uhttps://ieeexplore.ieee.org/document/10786519 3 aIn the present paper, we investigate the impact of imperfections (non-idealities) of the energy storage system (e.g., batteries, capacitors, or supercapacitors) on the energy performance of green IoT nodes. In particular, we investigate the impact of energy leakage from the Energy Storage System (ESS) on important energy performance metrics, such as service outage probability, the density of the lifetime of the node, and the time-dependent mean number of energy packets (EPs) in the ESS. Also, we explore various strategies that can be employed to compensate for the impact of energy losses due to energy leakage on the energy performance metrics. Specifically, we examine two potential strategies for improving the energy performance of the IoT nodes: (i) through increasing the energy generation rate of the energy harvesters (e.g., by adding additional solar panels or replacing the existing solar panels with more efficient ones that can produce more energy), and (ii) through reducing the energy consumption rate of the IoT node (e.g., by configuring ESS energy thresholds below which the nodes are forced to operate in low energy consumption states).00315nas a2200121   4500000000100000008004100001260001200042100001600054700001800070245005300088856004400141490000800185       2022                            d  c12/20211 aPiotr Pecka1 aMateusz Nowak00aRouting Algorithms Simulation for Self-Aware SDN  uhttps://www.mdpi.com/2079-9292/11/1/1040 v 1100320nas a2200121   4500000000100000008004100001260000900042100001600051700001800067700001600085700002000101245007700121       2018                            d  c20181 aPiotr Pecka1 aMateusz Nowak1 aArtur Rataj1 aSławomir Nowak00aSolving large Markov models described with standard programming language01123nas a2200205   4500000000100000008004100001260004400042100002000086700001800106700002200124700001600146700001400162700002200176700002000198245007300218856004800291300001000339520054600349020002200895       2017                            d  bSpringer International PublishingaCham1 aSławomir Nowak1 aMateusz Nowak1 aKrzysztof Grochla1 aPiotr Pecka1 aPiotr Gaj1 aAndrzej Kwiecień1 aMichał Sawicki00aApplication of Fault-Tolerant GQP Algorithm in Multihop AMI Networks  uhttps://doi.org/10.1007/978-3-319-59767-6_6  a70-803 aThe paper presents the evaluation of the GQP algorithm in AMI networks using real map based network topologies (low, medium and high density of buildings). The algorithm was compared to the reference algorithms: CB, SBA and DP. It was shown that the GQP algorithm presents the good scalability, relatively optimal number of selected forwarders and by introducing the redundancy factor, good fault tolerance. An improvement to GQP algorithm to add a redundancy factor is proposed, what allows to execute fault tolerant broadcast transmission.  a978-3-319-59767-600654nas a2200205   4500000000100000008004100001260001300042100002200055700001800077700001600095700002000111700001400131700001400145700001700159245010900176856006900285300001200354490006000366020002200426       2017                            d  bSpringer1 aKrzysztof Grochla1 aMateusz Nowak1 aPiotr Pecka1 aSławomir Nowak1 aA Zgrzywa1 aK Choroś1 aA Siemiński00aInfluence of message-oriented middleware on performance of network management system: a modelling study.  uhttps://link.springer.com/chapter/10.1007%2F978-3-319-43982-2_33  a379-3930 vAdvances in Intelligent Systems and Computing, Vol. 506  a978-3-319-43981-501395nas a2200133   4500000000100000008004100001100002000042700001800062700002200080700001600102245011500118300001200233520101600245       2016                            d1 aSławomir Nowak1 aMateusz Nowak1 aKrzysztof Grochla1 aPiotr Pecka00aEfektywne rozgłaszanie w wielohopowej sieci bezprzewodowej. Effective Broadcasts in Multihop Wireless Network  a887-8913 aZnanych jest wiele rozwiązań problemu rozgłaszania wiadomości w sieciach bezprzewodowych typu ad-hoc. Rozwiązania te różnią się w zależności od wielkości sieci, dostępności informacji o topologii, modelu komunikacji, wymagań gwarancji dostarczenia wiadomości itp. Sieci dedykowane są do różnych zastosowań i różnią się specyfiką występujących w nich problemów związanych z komunikacją. W artykule przedstawiono kilka znanych rozwiązań problemu rozgłaszania oraz przedstawiono autorskie rozwiązanie, dedykowane do specyficznego problemu sieci typu AMI (Advanced Metering Infrastructure - zaawansowana infrastruktura pomiarowa). Sieć ta zakładała model komunikacji jeden-do-wielu, stosunkowo niewielką dynamikę zmian w sieci, możliwość istnienia długich ścieżek na drodze transmisji oraz szereg innych wymagań. Analizowane algorytmy nie spełniały postawionych wymagań. Artykuł opisuje opracowaną motodę i porównuje ją do wybranych rozwiązań referencyjncych.00621nas a2200205   4500000000100000008004100001260004400042100002000086700001800106700002200124700001600146700002400162700001700186700002200203700001700225245008600242856005100328300001400379020002200393       2016                            d  bSpringer International PublishingaCham1 aSławomir Nowak1 aMateusz Nowak1 aKrzysztof Grochla1 aPiotr Pecka1 aTadeusz Czachórski1 aErol Gelenbe1 aKrzysztof Grochla1 aRicardo Lent00aGlobal Queue Pruning Method for Efficient Broadcast in Multihop Wireless Networks  uhttp://dx.doi.org/10.1007/978-3-319-47217-1_23  a214–224  a978-3-319-47217-101538nas a2200157   4500000000100000008004100001260005000042100001700092700001700109700001600126700001700142700002500159245012000184300001400304520106200318       2014                            d  bSpringer International Publishing Switzerland1 aB. Wieczorek1 aM. Połomski1 aPiotr Pecka1 aS. Deorowicz1 aStanisław Kozielski00aAn Effective Way of Storing and Accessing Very Large Transition Matrices Using Multi-core CPU and GPU Architectures  a323–3343 aThe topic of probabilistic model checking algoritms of Markov processes makes the problem of storing and processing of very large transition matrices crucial. While the symbolic approach utilises very effective storage and access methods, like Multi-terminal Binary Decision Diagrams, the traditional explicit method of representing and solving the model using sparse matrices has many advantages, especially when we concired the flexibility of computing of different properties. We show and examine a compact representation of a very large transition matrix in the sparse form. The technique employs an effective method of compression, storage, and accessing of the matrix and is suitable for use in mutli-core CPU and GPU environments. Such large transition matrices consume a lot of space and cannot be considered as typical types of data for storage in database systems. Nevertheless, their storage and efficient access to them could be beneficial for solving of Markov models, so constructing specialised compression methods is obviously the way to go.00940nas a2200121   4500000000100000008004100001260001600042100002000058700001600078700001800094245009500112520061100207       2012                            d  bIEEE Xplore1 aSławomir Nowak1 aPiotr Pecka1 aMateusz Nowak00aContent Registry - the distributed database of content localization for the PI CAN network3 aContent addressing and localization are basic issues in the structure of content-centric networks. This paper presents the implementation and performance evaluation of the Content Registry (CR), developed within the framework of the FIE (Future Internet Engineering) project to meet the requirements of the PI CAN network. The CR allows to find the desired Content Record (containing basic transmission parameters and localization of a content) in the network-distributed content database. The results confirm the CR is highly efficient in various configurations of the logical topology of connected nodes.00597nas a2200241   4500000000100000008004100001260003800042100001400080700001900094700001500113700001600128700001800144700001400162700001700176700002000193700001600213700001700229700001300246700001700259700002400276700001500300245004000315       2012                            d  bPolitechnika WarszawskaaWarszawa1 aA. Bęben1 aJ. Śliwiński1 aP. Krawiec1 aPiotr Pecka1 aMateusz Nowak1 aB. Belter1 aJ. Gutkowski1 aŁ. Łopatowski1 aP. Białoń1 aJ.M. Batalla1 aM. Drwal1 aP. Rygielski1 aWojciech Burakowski1 aP. Krawiec00aInżynieria Internetu Przyszłości01135nas a2200133   4500000000100000008004100001100002000042700001600062700001800078245006700096300001600163520080800179022001400987       2012                            d1 aSławomir Nowak1 aPiotr Pecka1 aMateusz Nowak00aRozproszona baza danych dla lokalizacji treści w sieci PI CAN  a1481–14903 aIdentyfikacja i lokalizacja treści stanowią podstawowe zagadnienia przy opracowywaniu sieci ukierunkowanych na treść (content-centric networks). W artykule przedstawiono implementację oraz badania wydajności mechanizmu Content Registry (CR), który został opracowany na potrzeby projektu Inżynieria Internetu Przyszłości, w części dotyczącej mechanizmów i wymagań dla sieci PI CAN (Paralel Internet Content Aware Network). CR umożliwia wydajne wyszukiwanie, w rozproszonej sieciowej bazie danych rekordów opisu treści, które zawierają podstawowe informacje o lokalizacji treści I wymaganiach w zakresie transmisji sieciowej. Rezultaty badań przedstawione w artykule potwierdzają wysoką efektywność proponowanego rozwiązania w różnych konfiguracjach i topologiach sieciowych.  a1230-349600324nas a2200133   4500000000100000008004100001260001300042100001800055700002000073700001600093700002200109245004500131300001400176       2011                            d  bSpringer1 aMateusz Nowak1 aSławomir Nowak1 aPiotr Pecka1 aKrzysztof Grochla00aContent Identification in PI CAN Network  a164–17200917nas a2200181   4500000000100000008004100001260003300042100001600075700002400091700001800115700002400133700002500157700002200182245003000204490000800234520047100242020002200713       2011                            d  bSpringer Berlin / Heidelberg1 aPiotr Pecka1 aSebastian Deorowicz1 aMateusz Nowak1 aTadeusz Czachórski1 aStanisław Kozielski1 aUrszula Stańczyk00aMan-Machine Interaction 20 v1033 aMarkov chains are used in analysis in many fields. One of them is performance evaluation of computer systems, especially computer networks. For the analysis we use OLYMP object library that provides features to describe complex systems and find their statistical parameters. We present two compressed data structures for the most space-consuming parts of data processed by OLYMP. Then, we show how these improvements move the barrier of applicability of the utility.  a978-3-642-23168-100364nas a2200133   4500000000100000008004100001100001600042700001800058700001600076245010300092300001400195490000700209022001400216       2011                            d1 aArtur Rataj1 aMateusz Nowak1 aPiotr Pecka00aModelling CTMC with a standard programming language and using conventions from computer networking  a229–2430 v23  a1896-533400847nas a2200181   4500000000100000008004100001260003400042100001600076700001800092700002000110700002000130700002400150700001500174245006300189490000900252520038200261020002200643       2011                            d  bSpringeraBerlin / Heidelberg1 aPiotr Pecka1 aMateusz Nowak1 aSławomir Nowak1 aSergey Balandin1 aKoucheryavy Yevgeni1 aHu Honglin00aSmart Spaces and Next Generation Wired/Wireless Networking0 v68693 aContent addressing and localization are the basic issues in design of content-aware networks (CAN). The paper summarizes assumptions for content-aware networks and presents content localization algorithm for PI-CAN, developed within FIE (Future Internet Engineering) project. The algorithm allows to find location of desired content in distributed content database in time O(1)  a978-3-642-22874-200875nas a2200133   4500000000100000008004100001260011200042100001800154700001600172700002400188245008300212300001400295520043200309       2010                            d  c1bInstitute of Theoretical and Applied Informatics of the Polish Academy of SciencesaGliwice, Bałtycka 51 aMateusz Nowak1 aPiotr Pecka1 aTadeusz Czachórski00aQoS management for multimedia traffic in synchronous slotted-ring OPS networks  a143–1523 aThe paper presents synchronous slotted-ring network with optical packet switching. The network is equipped with quality of service management, particularly considering multimedia transfers. Thanks to proposed mechanism of guarantees, multimedia data are delivered with guaranteed delay time, not greater than assumed, and in the case the delivery on time is impossible – they are removed, freeing place for remaining packets.01152nas a2200169   4500000000100000008004100001260003600042100001800078700001600096700001600112700001700128700001900145245015900164490000900323520062800332020002200960       2010                            d  c8bSpringer Berlin / Heidelberg1 aMateusz Nowak1 aPiotr Pecka1 aS. Balandin1 aR. Dunaytsev1 aY. Koucheryavy00aSmart Spaces and Next Generation Wired/Wireless Networking. Third Conference on Smart Spaces, ruSMART 2010, and 10th International Conference, NEW2AN 20100 v62943 aModelling with use of Markov chains is difficult from computational point of view, because of a rapid increase in the number of states occurring even when there is only a slight increase in the model’s scale. However, thanks to the appropriate description of the model the number of states can be significantly reduced. This paper discusses a synchronous slotted-ring network with optical packet switching modelled by means of markovian chains with continuous time. Simplifying the description has made it possible to significantly reduce the model’s dimension without significantly diminishing the results’ accuracy.  a978-3-642-14890-301005nas a2200133   4500000000100000008004100001100001800042700001600060245007400076300001400150490000700164520068400171022001600855       2009                            d1 aMateusz Nowak1 aPiotr Pecka00aPriority Registers Mechanism for fair access to ring-type OPS network  a181–1910 v213 aThe paper discusses the architecture of ring-type OPS (Optical Packet Switching) networks with QoS management. The electronic-optical nodes of the network enable optical packet switching within the ring and electronic buffered interface for a client. The differentiation of the quality of service was achieved by means of the system of priorities, and thanks to proposed mechanism of priority registers fair access to the link was achieved. This enables the network to be used for transporting various classes of data with varying requirements as to the quality of service. Simulation trials have been conducted and an analytical model for this type of network has been proposed.  a1896–533401183nas a2200121   4500000000100000008004100001260003300042100001800075700001600093245009200109490000700201520085300208       2009                            d  bSpringer Berlin / Heidelberg1 aMateusz Nowak1 aPiotr Pecka00aSimulation and Analytical Evaluation of a Slotted Ring Optical Packet Switching Network0 v643 aOptical Packet Switching (OPS) is a technology which thanks to its speed of operation may become popular in next-generation networks. Because optical packets are not buffered it is necessary to develop new mechanisms which would allow quality of service management in OPS networks. The paper discusses the architecture of OPS networks of the ring type with nodes enabling optical packet switching, equipped with the mechanism of Quality of Service (QoS) management. The differentiation of the quality of service was achieved by means of the proposed mechanism of priority registers with the timeout mechanism. This enables the network to be used for transporting various classes of data with varying requirements as to the quality of service. Simulation trials have been conducted and an analytical model for this type of network has been proposed.00256nas a2200085   4500000000100000008004100001100002200042700001600064245009000080       2006                            d1 aKrzysztof Grochla1 aPiotr Pecka00aAnaliza wydajności mechanizmu RED za pomocą łańcuchów Markowa z czasem ciągłym00267nas a2200097   4500000000100000008004100001260001200042100001600054245006600070490003300136       2006                            d  c06/20061 aPiotr Pecka00aSymulacja kolejki z negatywnymi klientami i wieloma serwerami0 v Vol. 27, No. 4 = No. 69 [5]00236nas a2200085   4500000000100000008004100001100002200042700001600064245007000080       2006                            d1 aKrzysztof Grochla1 aPiotr Pecka00aThe Markov chain model of RED active queuing management algorithm00222nas a2200085   4500000000100000008004100001260000700042100001600049245007100065       2005                            d  c111 aPiotr Pecka00aSoftware library for the Markov analysis of complex queuing models00227nas a2200085   4500000000100000008004100001100002400042700001600066245005900082       2002                            d1 aTadeusz Czachórski1 aPiotr Pecka00aInternet and real-time performance: a web server model