The 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.

We analyze a networking system powered by solar panels, where the harvested energy is stored in a battery that can also be sold when fully charged. Then the networking operator faces dual objectives: maintaining the functionality of its infrastructure and selling (or supplying to other networks) the filled batteries. These two goals are contradictory as selling the battery's energy may result in operational disruptions (e.g., packet delays) during certain periods. To address these challenges, we have developed a Markovian Decision Process (MDP) model that integrates positive rewards for battery release as well as penalties for energy packet loss and battery depletion. From this modeling, we present the optimal policy that balances these conflicting objectives and maximizes an average reward function. We advocate that integrating the particular structure of the MDP will enhance efficiency and precision of the numerical analysis. We provide numerical comparisons from small-scale to large-scale models and present a detailed analysis of agent behavior under the optimal policy.

Energy Packet Networks (EPNs) model the interaction between renewable sources generating energy following a random process and communication devices that consume energy. This network is formed by cells and, in each cell, there is a queue that handles energy packets and another queue that handles data packets. We assume Poisson arrivals of energy packets and of data packets to all the cells and exponential service times. We consider an EPN model with a dynamic load balancing where a cell without data packets can poll other cells to migrate jobs. This migration can only take place when there is enough energy in both interacting cells, in which case a batch of data packets is transferred and the required energy is consumed (i.e. it disappears). We consider that data packet also consume energy to be routed to the next station. Our main result shows that the steady-state distribution of jobs in the queues admits a product form solution provided that a stable solution of a fixed point equation exists. We prove sufficient conditions for irreducibility. Under these conditions and when the fixed point equation has a solution, the Markov chain is ergodic. We also provide sufficient conditions for the existence of a solution of the fixed point equation. We then focus on layered networks and we study the polling rates that must be set to achieve a fair load balancing, i.e., such that, in the same layer, the load of the queues handling data packets is the same. Our numerical experiments illustrate that dynamic load balancing satisfies several interesting properties such as performance improvement or fair load balancing.

LoRaWAN is a network technology that provides a long-range wireless network at low energy consumption. In order to save energy, it takes the pure Aloha MAC protocol and the duty-cycle limitation at both uplink and downlink on the MAC layer. Moreover, LoRaWAN also adapts the orthogonal parameters to avoid the collision. However, the star-topology synchronization and the complicated collision mechanism make quantitative model analysis difficult in LoRaWAN. This study modeled the Class-A device in the LoRaWAN protocol using Probabilistic Timed Automata (PTA). It is a mathematical model that presents the nondeterministic and probabilistic choice with time passing. Using the time representation in PTA, the transmission schedule of LoRaWAN's MAC layer of is modeled. Moreover, the full collision model is built in the PTA. Several properties are verified with the probabilistic model checker PRISM, and the quantitative properties are calculated under different cases.

LoRaWAN attracted lots of attention with its capacity for large device numbers, long-range, and low-power consumption. In order to simplify the transmission procedure, a pure Aloha protocol is implemented into its MAC layer. However, as the number of connected devices to the base station increases, the devices’ transmission parameters allocation becomes a vital issue related to network performance. This research contributes to the decentralized dynamic spreading factor (SF) allocation strategies during transmission by proposing a score table-based evaluation and parameters surfing (STEPS) approach. STEPS is a reinforcement learning-based method that evaluates and changes the parameters based on probability and score tables. It provides a nondeterministic parameter selection method by updating the table while transmitting. Some variants of STEPS with different algorithms are proposed. Moreover, an estimation-based initialization is proposed to improve learning performance. Simulations and statistical tests are carried out with MULANE, a lightweight LoRaWAN Simulator developed in our previous work. The results show that the estimation has a high confidence level. Compared with the baseline methods, the proposed methods reduce energy consumption by 24%–27% in different numbers of nodes. For bi-directional transmission, the proposed methods increase the 18% network throughput in a small number of nodes and 33% in a large number of nodes. Moreover, the proposed methods provide a framework of decentralized parameter allocation, which gives the extendability of this work.

LoRaWAN is one of the network technologies that provide a long-range wireless network at low energy consumption. However, the pure Aloha MAC protocol and the duty-cycle limitation at both end devices and gateway make LoRaWAN very sensitive to malicious behaviors in the MAC layer. Moreover, this kind of sensitivity makes the false-positives problem challenging for malicious behavior detection with simple threshold methods. This study investigates two malicious behaviors - greedy and attack on the MAC layer. Furthermore, by combining the threshold method with a Local Outlier Factor (LOF) model in machine learning, LoRaLOFT is proposed. It is a centralized malicious node detection method. Analytical results show that the proposed method gives high detection accuracy while significantly reducing the false-positive rate in both behaviors.

As one of the technologies in the wide-area network category, LoRaWAN provides a wireless network with a large capacity of end devices (ED) in long-range. With a pure Aloha protocol implemented into its MAC layer, LoRaWAN can reduce its power consumption. Besides, some orthogonal transmission parameters give LoRaWAN capability to avoid collision and packet loss. Thus, allocating transmission parameters to increase the network performance becomes a challenging issue for LoRaWAN. Some dynamic Spreading Factor (SF) allocation strategies are studied in this paper. A distributed Markov Decision Process (MDP) model is constructed for the uplink transmission of the class-A device in LoRaWAN. The model is also solved and implemented to the algorithms for the initial strategy prediction. Analytical results show that the MDP model increases the performance of the studied algorithms on the transmission of the packet.

LoRaWAN (LOng RAnge radio Wide Area Network) belongs to the LPWAN (Low Power Wide Area Network) category, it aims to provide a wide area, long range and low power consumption communication network solution. However, with the large number of connected devices to the base-station and a pure Aloha MAC protocol, the packet lost and collisions become an important issue in the network related to the transmission parameters of the devices. For this issue, STEPS is proposed in this study. The goal of the proposed method is to establish a score table based evaluation and parameters surfing approach. STEPS provides an approach of evaluating and changing the parameters based on probability and score table when transmission failure appears. It can also update the table while transmitting. STEPS is compatible with pure Aloha, and doesn't need any change on the MAC protocol and is easy to be implemented. In this study, the spreading factor is chosen as the parameter to establish the table, that will be evaluated and to be surfed. Simulation results show that STEPS provides a remarkable improvement on bi-directional transmission of the packet and a capability of decreasing the packet lost and collisions even with higher data rate than classical LoRaWAN scenario.

As one of the LPWAN categories, LoRaWAN attracts great attention on IoT and M2M communication. It offers a comprehensive area communication network solution with a low data rate and low power consumption. Many research works on medium scheduling or resource allocation have been proposed to improve network performance. However, with many devices in the network, it is sometimes too difficult to deploy a test-bed to evaluate the network performance in the industry. However, different studies often use different simulators. Thus, it is also challenging to study the impact of different algorithms on the network by simulation. Thus, an extendable simulator becomes necessary for both industrial networks deploying and academic study. In this paper, we developed a lightweight, extendable simulator exclusive to LoRaWAN named MULANE. We also offered a GUI is to simplify the simulation process. Moreover, the simulator is agent-oriented, making the research works implementation easier by creating new agents,

We present a model of a sensor networks with energy harvesting. We assume that the network is associated with solar panels or wind turbines. Therefore the energy harvesting is random and is strongly correlated to the day and night succession (for solar panels) or the strength of the wind (for turbines). We generalize the model of Energy Packet Networks (EPNs), recently introduced by Gelenbe to accommodate a ON-OFF arrival process for energy packets. We assume that during the night period, when the networks do not receive energy, the evolution of the network is stopped. We prove that such a network has a product form distribution for its a steady-state distribution of number of packets (under some technical assumptions) leading to the performance analysis for such systems.

Energy Packet Network (EPN) consists of a queueing network formed by N blocks, where each of them is formed by one data queue, that handles the workload, and one energy queue, that handles packets of energy. We study an EPN model where the energy packets start the transfer. In this model, energy packets are sent to the data queue of the same block. An energy packet routes one workload packet to the next block if the data queue is not empty, and it is lost otherwise. We assume that the energy queues have a finite buffer size and if an energy packet arrives to the system when the buffer is full, jump-over blocking (JOB) is performed, and therefore with some probability it is sent to the data queue and it is lost otherwise. We first provide a value of the jump-over blocking probability such that the steady-state probability distribution of packets in the queues admits a product form solution. The product form is established for multiserver and multiclass data packet queues under FCFS, preemptive LCFS and PS discipline. Moreover, in the case of a directed tree queueing network, we show that the number of data packets in each subtree decreases as the JOB probability increases for each block.

We consider an Energy Packet Network (EPN) model where the service times of the packets follow a Coxian distribution. EPNs are a recent type of models proposed by Gelenbe and his colleagues to study the interactions between energy consumption and the processing or the transmission of data. We prove that such a network has a product form solution for its steady-state distribution. We also state some sufficient conditions for the existence of the flow equations. Finally we study the performances and the energy consumption and we show how to optimize the assignemenl of Δ solar panels over a sensor network.

In recent years, more and more functionally similar Web Services are offered to users. Quality of Service (QoS) parameters are used to characterize their performances and thus to facilitate their selection. Nowadays, clients are demanding more sophisticated services rather than those offered by single web services. Therefore, selecting a composition plan of web services among numerous choreographies by re-using existing services satisfying user's requirements has become a very challenging issue. QoS aware service composition aims to satisfy user's QoS needs during service composition. Traditional methods simply attempt to maximize user satisfaction by provisioning the composite service instance with the best QoS. These approaches do not consider in general that there are many consumers that are competing to acquire the same services. This could impact negatively the overall QoS and the decisions to take in the selection process. To respond to this particular problem, we propose a formal methodology based on Discrete Markov Chain to evaluate the performances of the QoS aware Web service composition system with multiple communities of consumers. The goal of this methodology is to help the designer to predict some useful performance parameters as the average time to reach a given QoS for a community of consumers in a competitive environment. The theoretical modelling of the problem is provided together with analytical results obtained by simulations using the Xborne tool.

We model the end to end delay and energy efficiency in the optical network architecture NGREEN. As the architecture is based on an optical ring, the random part of the delay comes from the random times needed to build an optical container from arriving Data Units and the insertion of the optical container on the ring. We first build a DTMC (Discrete Time Markov Chain) to model the filling of the optical container with Data Units. We take into account a deadline (to have a small latency) and a constraint on a minimal filling of the container (to be energy efficient). We obtain through a numerical analysis using an ad-hoc algorithm we proved, the distribution of the container filling and the distribution of the time needed to build a container. Then, we use this distribution to model the inter arrival of optical containers at a station on the ring. Through simulations and numerical analysis of Markov chains, we obtain the insertion delays and the occupancy of the queue before insertion. The relevance of the paper is to propose a trade-off between energy efficiency and latency for both opportunistic and reservation insertion modes into the ring.

With the diversity of services and the need of different traffic classes in wireless networks, WIMAX technology (Worldwide Interoperability for Microwave Access), has been developed as a broadband wireless access technology based on IEEE standard 802.16. Indeed, this technology is able to mix real time and non real time services with the definition of service classes. To improve the admission rate of the different classes when implementing the admission control component, we propose in this paper a traffic scheduling based on WRR policy and a new mechanism to handle the rejected requests. Finally, we provide the Markov Chain based modelling of our solution and compute thereof primary performance evaluation results.

The wireless shared medium used by Wireless Sensor Networks applications causes a problem related to interference, specially with dense deployment that characterizes the WSNs. This requires the use of congestion control scheme to avoid interferences and buffer overflow that degrade the application reliability. REFIACC (Reliable, Efficient, fair and Interference aware Congestion control) schedule scheme is a cross layer congestion control protocol that avoids the aforementioned problems while maximizing throughput and fairness. In our previously studies, we have validated REFIACC using extensive simulations. In this study, REFIACC is modeled using Stochastic Automata Networks (SAN). In fact, SAN presents a good tool to avoid state-space explosion of Markov chains.

We model networks of Energy Packets which have been previously introduced by Gelenbe and his colleagues to represent the interactions between communication units and energy units in data processing networks with energy harvesting. We consider failures of batteries and the network structure models the connectivity. The model explicitly represents the amount of Energy Packets needed to transfer a Data Packet. We consider both Data Packets and Jumbo Data Packets which require distinct amounts of energy to be transmitted. Unlike previous models, our approach is based on the assumption that the transmission time of a Data Packet can be neglected when we model Energy Packets harvesting and Leakage which are operating on a larger time scale. We prove that the network of queues associated with the batteries has a product form steady-state distribution under usual Markovian assumptions. An important feature of our model is the ability to study Data Packet losses due to the lack of energy at certain nodes or to the failure of the components which cannot be obtained in previous models with closed form solutions.

We present an approach to derive performance bounds of a queue under histogram-based input traffics. The results are obtained through strong stochastic bounds on the queue length and on the output traffic. The bounds provide probability inequalities on transient behaviors and on steady-state when it exists. We consider both stationary and non-stationary traffics and provide some numerical techniques in both cases. Unlike approximate methods, these bounds can be used to check if the Quality of Service constraints are satisfied or not. Our approach provides a trade-off between the accuracy of results and the computational complexity and it is much faster than the histogram-based simulation.

We study the steady-state distribution of networks of order independent queues with negative signals which delete customers. An Order Independent queue is defined by a service rate which is independent on the order of the customers in the queue. Such an abstract discipline may be used to model complex blocking mechanism (for instance the Multiserver Station with Concurrent Classes of Customers). Order independent queues are in general neither symmetric nor reversible. We prove that, under usual assumptions on the arrivals, the services and the routing of customers, such a network of queues with signals has a steady-state distribution with product form solution. The proof is based on the quasi-reversibility of the queues. We also present some examples of application for this new analytical result.

Restart is a common technique for improving response-times in complex systems where the causes of delays can either not be discerned, or not be addressed by the user. With restart, the user aborts a running job that exceeds a deadline, and resubmits it to the system immediately. In many common scenarios, this approach can reduce the response-times that the user experiences. Restart has been well-studied for scenarios where only one user applies restart, and typically in cases where queueing effects can be neglected. In this paper we approach the question of restart in a scenario where restart is applied by many users in a system that can be modelled as an open queueing network. We apply the G-Networks formalism to this problem. We use negative customers to model the abortion and retry of a request. The open G-network uses multiple classes with phase-type distributed service times. This allows the approximation of a preemptive repeat different behaviour as it is natural for multiple restarts of a request. We compute the response time of a request and show that an optimal restart interval can be found. The results are compared with simulation.

doi: 10.1093/comjnl/bxq067 Comp J 2011;54(2): 274–284 This paper was intended to be published as part of the Probability Models in Performance Engineering special issue but was published separately in issue 54(2) of The Computer Journal in error. We would like to apologise to the authors for this oversight.

We consider a queueing network of symmetric G-queues with customers and signals. Since the seminal papers by Gelenbe in the early 1990s (Gelenbe, E. (1991) Product-form queueing networks with negative and positive customers. J. Appl. Probab., 28, 656–663; Gelenbe, E. (1993); G-networks with instantaneous customer movement. J. Appl. Probab., 30, 742–748; Gelenbe, E. (1993) G-Networks with signals and batch removal. Probab. Eng. Inform. Sci., 7, 335–342), generalized networks of queues have received considerable attention. But most papers assume to obtain a product form such that the service times follow exponential distributions. Here, we propose a new generalization of this model with phase-type service times. We also assume a new type of signal. When a signal enters a queue, it changes the phase of the customer in service if there is any. As usual, after completion of its service, a customer moves to another queue and may become a signal. We prove that the steady-state distribution for such a network of queues has a product form solution.

We show how we can perform the time parallel simulation of Web servers to solve some performance issues. Both the classical version and the monotone version we have recently introduced may be used. We present the monotone improvement of time parallel simulation and we state that the model of a web server satisfy the assumption: monotonicity and predictability.

Abstract We propose new techniques to simplify the computation of the end‐to‐end delay for an evaluation of a Web services model. The simplification processes are associated with stochastic comparisons of random variables. Thus, the simplified models are stochastic bounds for the original ones. In this study, we consider that the Web service model can be represented by an acyclic directed graph. Thus, we propose upper and lower bounds on the response times by considering in one case special random variables for service times and in the other case we substitute the precedence graph by another one. We prove that the response times computed on the bounding models are really upper and lower bounds on the considered models. We also propose to generalize the model by considering the contention time when several executions of composite Web services are invocated. We propose in this case upper and lower bounds on response times by proposing bounding models. The response times are easier to compute on these new models. We give the corresponding proofs based on stochastic comparisons. We present several numerical results in order to show the accuracy of our bounds. Copyright © 2010 John Wiley & Sons, Ltd.

We improve the efficiency of time parallel simulation using some concepts of monotonicity of simulation models. The time parallel simulation technique partitions the simulation timespan into simulation periods which are independently executed. Such a technique relies on strong stochastic assumptions: regeneration or short influence of the initial point a on sample path. If these assumptions are not satisfied, we only obtain an approximation. We prove that if the model is monotone we can increase the parallelization of the simulations and we can prove some bounds on the result.

We propose new techniques to simplify the computation of the end to end delay for an evaluation of a Web services. These techniques allow us to simplify the model description to reduce the number of states of the underlying Markov chain. The simplification processes are associated with stochastic comparisons of random variables. Thus the simplified models are stochastic bounds for the original ones.

By extending the pulsed recurrent random neural network (RNN) discussed in Gelenbe (1989, 1990, 1991), we propose a recurrent random neural network model in which each neuron processes several distinctly characterized streams of "signals" or data. The idea that neurons may be able to distinguish between the pulses they receive and use them in a distinct manner is biologically plausible. In engineering applications, the need to process different streams of information simultaneously is commonplace (e.g., in image processing, sensor fusion, or parallel processing systems). In the model we propose, each distinct stream is a class of signals in the form of spikes. Signals may arrive to a neuron from either the outside world (exogenous signals) or other neurons (endogenous signals). As a function of the signals it has received, a neuron can fire and then send signals of some class to another neuron or to the outside world. We show that the multiple signal class random model with exponential interfiring times, Poisson external signal arrivals, and Markovian signal movements between neurons has product form; this implies that the distribution of its state (i.e., the probability that each neuron of the network is excited) can be computed simply from the solution of a system of 2Cn simultaneous nonlinear equations where C is the number of signal classes and n is the number of neurons. Here we derive the stationary solution for the multiple class model and establish necessary and sufficient conditions for the existence of the stationary solution. The recurrent random neural network model with multiple classes has already been successfully applied to image texture generation (Atalay & Gelenbe, 1992), where multiple signal classes are used to model different colors in the image.

This Hot-Topics Session on G-Networks aims at bringing these relatively new models which we introduced for the first time in 1989 and 1990, to the attention of the performance evaluation and modeling community. The session includes presentations by Peter Harrison, Onno Boxma, Jean-Michel Fourneau and myself. We will cover the basic concepts, some examples of potential applications, as well as recent research efforts in this area.

A method for modeling a spatial priority mechanism called the push-out buffer management policy is proposed. It is a known mechanism which takes into account two kinds of cells: vital and ordinary ones. It also ensures a high degree of flexibility for asynchronous transfer mode (ATM) services. The use of the diffusion approximation allows modeling general interarrival and service time distributions. The developed transient solution helps describe the burstiness of the flow of cells arriving at a node. The model may be useful for dimensioning network buffers within ATM networks.>