International audience

In the realm of Fifth Generation (5 G) and the upcoming Sixth Generation (6 G) networks, the efficient management of network resources becomes increasingly critical, particularly for applications that have strict Quality of Service (QoS) requirements. This paper addresses the complexities associated with Virtual Network Embedding (VNE), a vital process for establishing multiple virtual networks on shared physical infrastructure within the context of network slicing. We introduce the SetpodNet scheduler, a novel orchestration solution that leverages reinforcement learning to enhance the optimization of latency and bandwidth allocation specifically in Kubernetes environments. The SetpodNet scheduler is designed to dynamically adapt to fluctuating slice arrivals and varying resource demands, ensuring that network performance remains consistent and reliable. Through comprehensive experimental evaluations, we demonstrate improvements in slice acceptance ratios and optimizing QoS.

5G and beyond networks aim to support heterogeneous services with strict QoS and isolation requirements. Network slicing addresses these challenges by creating multiple virtual networks over shared infrastructure, each tailored for specific service types. However, despite its potential, the lack of practical, open, and reproducible testbeds for 5G slicing remains a major barrier to experimentation and adoption. In this demo, we present NexSlice, an open-source, Kubernetes-Native testbed that enables the deployment and orchestration of 5G core network slices using open-source components like OpenAirInterface (OAI) and UERANSIM. Our platform supports SST-based slicing, integrates different Radio Access Networks (RANs), enables auto-scaling of user plane functions, and provides real-time monitoring with Prometheus and Grafana. NexSlice aims to bridge the gap between theoretical slicing frameworks and practical, reproducible experimentation, paving the way toward adaptive and automated slice management in future 6G networks.

The Fifth and Sixth Generation (5G/6G) networks aim to support diverse applications with specific QoS and resource needs. Network Slicing has emerged as a key paradigm to meet these demands by creating multiple Virtual Networks (VNs) over shared physical infrastructure. This process, known as Virtual Network Embedding (VNE), maps virtual nodes and links to physical resources. With Kubernetes becoming the dominant orchestration platform, most infrastructures now rely on Kubernetes clusters, which enforce direct pod-to-pod communication, necessitating a direct-link approach to VNE. However, most existing methods focus on path-based link mapping. In this paper, we present DL-ViNE, a Reinforcement Learning(RL)-based algorithm that improves slice acceptance while addressing the specific constraints of Kubernetes-hosted infrastructures.

We study the placement of virtual functions aimed at minimizing the cost. We propose a novel algorithm, using ideas based on multi-armed bandits. We prove that these algorithms learn the optimal placement policy rapidly, and their regret grows at a rate at most$O(N M \sqrt{T \ln T})$while respecting the feasibility constraints with high probability, where$T$is total time slots,$M$is the number of classes of function and$N$is the number of computation nodes. We show through numerical experiments that the proposed algorithm both has good practical performance and modest computational complexity. We propose an acceleration technique that allows the algorithm to achieve good performance also in large networks where computational power is limited. Our experiments are fully reproducible, and the code is publicly available.

High dimensionality of model-based Reinforcement Learning and Markov Decision Processes can be reduced using abstractions of the state and action spaces. Although hierarchical learning and state abstraction methods have been explored over the past decades, explicit methods to build useful abstractions of models are rarely provided. In this work, we provide a new state abstraction method for solving infinite horizon problems in the discounted and total settings. Our approach is to progressively disaggregate abstract regions by iteratively slicing aggregations of states relatively to a value function. The distinguishing feature of our method, in contrast to previous approximations of the Bellman operator, is the disaggregation of regions during value function iterations (or policy evaluation steps). The objective is to find a more efficient aggregation that reduces the error on each piece of the partition. We provide a proof of convergence for this algorithm without making any assumptions about the structure of the problem. We also show that this process decreases the computational complexity of the Bellman operator iteration and provides useful abstractions. We then plug this state space disaggregation process in classical Dynamic Programming algorithm namely Approximate Value Iteration, Q-Value Iteration and Policy Iteration. Finally, we conduct a numerical comparison on randomly generated MDPs as well as classical MDPs. Those experiments show that our policy-based algorithm is faster than both traditional dynamic programming approach and recent aggregative methods that use a fixed number of adaptive partitions.

In 5G networks, physical resources can be virtualized and allocated to separate virtual networks (or network slices), with distinct requirements. The Virtual Network Embedding (VNE) problem consists in finding the optimal mapping of virtual resources (virtual links and nodes) onto a physical infrastructure. A recent trend consists in virtualizing 5G networks using Kubernates (K8s), a popular virtualization technology.In this paper we perform an experimental study to show the limit of using the standard K8s deployment strategy when dealing with dynamically arriving slices in a heavy loaded setting. By deploying the virtual components of a slice one by one, standard K8s is prone to wasting resources and energy due to partially deploying slices that, at the end, are found to be infeasible, due to lack of available resources. We propose an alternative K8s deployment strategy that first solves VNE via a Genetic Algorithm and then, for each slice, deploys either all its components or none. Our experimental results show a notable improvement in slice acceptance, energy efficiency and deployment time. Our work shows that it is necessary to adapt cloud native technologies to the specific requirements of telecommunication scenarios, as they are different from the cloud ones for which such technologies were originally developed.

Communication and computation services supporting Connected and Automated Vehicles (CAVs) are characterized by stringent requirements, in terms of response time and relia-bility. Fulfilling these requirements is crucial for ensuring road safety and traffic optimization. The conceptually simple solution of hosting these services in the vehicles increases their cost (mainly due to the installation and maintenance of computation infrastructure) and may drain their battery excessively. Such disadvantages can be tackled via Multi-Access Edge Computing (MEC), consisting in deploying computation capability in network nodes deployed close to the devices (vehicles in this case), such as to satisfy the stringent CAV requirements. However, it is not yet clear under which conditions MEC can support CAV requirements and for which services. To shed light on this question, we conduct a simulation campaign using well-known open-source simulation tools, namely OMNeT++, Simu5G, Veins, INET, and SUMO. We are thus able to provide a reality check on MEC for CAV, pinpointing what are the computation capacities that must be installed in the MEC, to support the different services, and the amount of vehicles that a single MEC node can support. We find that such parameters must vary a lot, depending on the service considered. This study can serve as a preliminary basis for network operators to plan future deployment of MEC to support CAV.

The paper addresses the problem of performance-energy trade-off in DVFS (Dynamic Voltage Frequency Scaling) systems. We propose a stochastic hybrid model between hysteresis models and server block models. We provide a closed form for the steady-state distribution probability and we establish a "st" type order to compare the performance measures. The fast computation of power and performance measures leads to a multi-objective optimization analysis in two forms: a scalarization method and a Pareto based method. For the two approaches, we propose fast and efficient approximate algorithms that construct progressively an optimal solution. To discuss results, the model is used to simulate a physical server hosting several VMs (Virtual Machines) where we investigate optimal thresholds for the performance-energy trade-off.

Thanks to resource virtualization, Physical Network Operators (PNOs) can share their 5G network to multiple Mobile Virtual Network Operators (MVNOs) which can leverage the shared physical infrastructure to deploy their services up to the edge. This allows much more flexibility with respect to the previous generation of cellular networks: MVNO software components can be placed at different locations, can be allocated a certain amount of virtual resources (e.g., bandwidth, CPU cycles), and be reachable via different paths. To the best of our knowledge, strategies to minimize energy consumption while satisfying Service Level Agreements (SLAs) between the PNO and the MVNOs are still largely missing, particularly if it is required to take the nonlinearity of delays into account. To fill this gap, we formulate the problem of joint placement of software components, routing of user requests and resource dimensioning. SLAs are represented in terms of latency and reliability constraints. Via Column Generation, we obtain exact solutions in real-sized networks. Our numerical results show that we can save up to 50% energy in networks with up to 30 nodes compared to the state-of-the-art algorithms, which are focused on placement or resource minimization.

Energy consumption represents a major part of the operating expenses of mobile network operators. With the densification foreseen with 5G and beyond, energy optimization has become a problem of crucial importance. While energy optimization is widely studied in the literature, there are limited insights and algorithms for energy-saving techniques for Integrated Access and Backhaul (IAB), a self-backhauling architecture that ease deployment of dense cellular networks reducing the number of fiber drops. This paper proposes a novel optimization model for dynamic joint routing and energy optimization in IAB networks. We leverage the closed-loop control framework introduced by the Open Radio Access Network (O-RAN) architecture to minimize the number of active IAB nodes while maintaining a minimum capacity per User Equipment (UE). The proposed approach formulates the problem as a binary nonlinear program, which is transformed into an equivalent binary linear program and solved using the Gurobi solver. The approach is evaluated on a scenario built upon open data of two months of traffic collected by network operators in the city of Milan, Italy. Results show that the proposed optimization model reduces the RAN energy consumption by 47%, while guaranteeing a minimum capacity for each UE.

Within network slicing, Virtual Network Embedding has been vastly studied, i.e., deciding in which physical nodes and links to place virtual functions and links. However, the performance of slices does not only depend on where virtual functions and links are placed, but also on how much resources they can use, which has been mostly neglected in the literature. We thus propose a method for optimal resource dimensioning, via dimensioning capacities of multiple Jackson networks (one per slice) co-existing in the same resource-constrained network. Despite the long history of Jackson networks, we are the first, to the best of our knowledge, to model such a problem. The objective is to minimize energy consumption while satisfying the latency requirements of heterogeneous service providers. We show numerically that our solution is able to achieve both goals, differently from classic approaches, which assume that the amount of resources assigned to slices is fixed a-priori.

Network slicing in the upcoming Telecom generation is a fundamental feature which is deployed to satisfy the various demands in term of data rate and latency. On the other hand, it is seen as a topic that imposes other questions such as the coexistence of physical and virtual functions. In this context, we consider the resource management problem for 5G networks slicing since the solution searches to optimally allocate multiple Virtual Network Requests (VNRs) on a substrate virtualized physical network. In this demo, we present an integrated framework that uses an agile service platform (Kube5G) to deploy one of the VNE proposed solutions with zero-touch configuration. The aim of this integration is to validate the proposed solution and to practically study the performance differences among multiple algorithms that will be conducted later as well. The overview of the process is shown in steps as exposing the resources’ availability of the Physical Nodes (PN), which will be the input of the orchestration algorithm. Successively, the last takes the suitable decision to deploy VNRs on a substrate network, based on the VNRs’ demands such as CPU and radio resources and PNs’ availability. Afterwards, the decision will be sent to the platform to host the virtual nodes on the chosen physical machines. Bearing in mind that the essential objective of this algorithm is to achieve a better resource usage and increase the VNR acceptance ratio on the physical nodes with respect to the constraints that might affect the performance.

We address the problem of a Network Operator (NO) owning limited resources at the network edge. The NO wishes to enable advanced services, by virtualizing and allocating such resources among multiple tenants, i.e., third-party Service Providers, co-existing at the edge, with different Quality of Service (QoS) constraints. The NO applies a resource allocation policy with the objective of minimizing energy consumption via switching off non-used resources while guaranteeing tenants QoS requirements. We propose a resource allocation policy based on Markov Decision Processes (MDP). In simulation we show that our policy is able to reduce energy consumption, by turning off unused resources, while meeting heterogeneous SP requirements. Our code is available as open source.

As today’s networking systems utilise more virtual-isation, efficient auto-scaling of resources becomes increasingly critical for controlling both the performance and energy consumption. In this paper, we study the techniques to learn the optimal auto-scaling policies in a distributed network when parts of the system dynamics are unknown. Reinforcement Learning methods have been applied to solve auto-scaling problems. However they can run into computational and convergence issues as the problem scale grows. On the other hand, distributed networks have relational structures with local dependencies between physical and virtual resources. We can exploit these structures to overcome the convergence issues by using a factored representation of the system.We consider a distributed network in the form of a tandem queue composed of two nodes. The objective of the auto-scaling problem is to find policies that have a good trade-off between quality of service (QoS) and operating costs. We develop a factored Reinforcement Learning algorithm, named FMDP online, to find the optimal auto-scaling policies. We evaluate our algorithm with a simulated environment. We compare it with existing Reinforcement Learning methods and show its relevance in terms of policy efficiency and convergence speed.

The 5G telecommunication ecosystem is expected to dynamically support new and various applications from the industrial and the service sectors that are very heterogeneous in terms of QoS and resources’ requirements. In this context, a promising important concept for network resource management is emerging, denoted by Network Slicing. It involves decisions on embedding and managing several virtual networks on the same physical resources. This problem in its simplified form can be modeled by the Virtual Network Embedding (VNE) problem. In this paper, we propose a new resolution method, in which we first reduce the set of admitted routes and then solve an integer program. Our proposed approach is then compared to the optimal solution and to a method from the state of the art. Obtained results show that our approach provides good result in terms of slice acceptance ratio and resource consumption while reducing the overall complexity and runtime.

In this paper, we consider the Virtual Network Embedding (VNE) problem for 5G networks slicing. This consists in optimally allocating multiple Virtual Networks (VN) on a substrate virtualized physical network while maximizing among others, resource utilization, maximum number of placed VNs and network operator's benefit. We solve the online version of the problem where slices arrive over time. We propose the use of the Nested Rollout Policy Adaptation (NRPA) algorithm, a variant of the well known Monte Carlo Tree Search (MCTS). Both algorithms learn by randomly simulating the embedding, but NRPA also learns how to perform better simulations over time. Performance analysis with different scenarios, show that NRPA improves acceptance and reward ratios (by up to 69% and 65%). We also show how a smart initialization of the learning process can help improve the results furthermore (up to a 12.5% increase of acceptance ratio).

The use of Ethernet packet-switched networks for the fronthaul links with a Cloud-based Radio Access Network (C-RAN) architecture are nowadays considered. The high capacity and low latency fronthaul (FH) links requirement in the C- RAN architecture can be reduced by a flexible functional split of baseband processing between remote radio heads (RRHs) and Baseband units (BBUs). These will allow leveraging statistical multiplexing gains, infrastructure reuse and cost reduction. However, in order to satisfy latency requirements, most of the studies advocate the use of lower fronthaul split options like the eCPRI (evolved Common Public Radio Interface) Iu split, requiring huge fronthaul link capacity. In this paper, we propose an alternative uplink physical split, denoted IIU. The objective is to reduce capacity requirements on the fronthaul while meeting latency constraints. As a future work, the proposed split will be evaluted and analyzed for both fast and slow fading channel situations.

Next generation cellular networks are targeting higher bit rates, lower delays and enhanced inter-cell coordination. For that to happen, higher capacity and lower latency fronthaul solutions are required, among others. The use of Ethernet packet-switched networks for the fronthaul links with a Cloud-based Radio Access Network (C-RAN) architecture are nowadays considered. These will allow leveraging statistical multiplexing gains, infrastructure reuse and cost reduction. In the literature, different fronthaul split options are proposed. However, in order to satisfy latency requirements, most of these studies advocate the use of lower fronthaul split options like the eCPRI (evolved Common Public Radio Interface) IUsplit, requiring huge fronthaul link capacity. In this paper, we propose and evaluate an alternative uplink physical split, denoted IIU. The objective is to reduce capacity requirements on the fronthaul while meeting latency constraints. The proposed split is analyzed for both fast and slow fading channel situations. Two variants are proposed for the IIUsplit: a subframe based and slot-based multiplexing. Performance results show that the proposed IIUsplit satisfies the stringent latency requirements of next generation mobile networks while reducing the deployment cost of links and Ethernet switches of the fronthaul.

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.

This paper presents a queuing model to evaluate the performances of cooperation mechanisms in 4G/5G cellular networks. The main contribution is the proposal of an approximation model with a closed form formula allowing fast numerical evaluation of throughput and loss probabilities per service class, while considering traffic load, radio conditions and the available resources in each collaborating cell. The proposed queuing model is successfully applied to the enhanced Inter-Cell Interference Coordination mechanism with service differentiation in the context of Heterogeneous Cloud based Radio Access Networks. Numerical results are compared to Matlab simulations with realistic radio conditions and user distributions. Through it, decisions on resource allocation among the cooperating cells to achieve the optimal capacity of the system become faster and adaptive. In conclusion, the proposed queue-based model can be used in order to tune the front-haul links and the core network resources.

Reducing the energy consumption of a cloud system while guaranteeing a given quality of service level is a crucial problem encountered today by cloud providers. We consider an auto-scaling model where virtual machines are turned on and off depending on the queue's occupation (or thresholds). This model represents the variability of allocated resources (Virtual Machines or VMs) according to user demands. It can be studied using an hysteresis queuing model, which is represented by a multidimensional Markov chain, whose calculation of the stationary distribution becomes complex when the number of VMs grows. We adopt a cost-aware approach and define a mean cost computed as a reward function on the stationary distribution. This cost takes into account both the performance (for Service Level Agreement: SLA) and the use of the resources (for Energy). We propose efficient optimisation methods to find threshold values minimising the global cost. Because this mean cost is a non-convex function, the research of the optimal value is complex. We propose different optimisation methods: the first one, based on heuristics, coupled with aggregation of the Markov Chain to reduce the execution time and the second one which is a meta heuristic: the Simulated Annealing. Finally, we present a real case of a cloud system that we model and set parameter values to test our optimisation algorithms and show their relevance.

In this paper, we propose mathematical models to evaluate the performances of the interference remediation technique eICIC/ABS (enhanced Inter- Cell Interference Coordination / Almost Blank Sub-frame) in the context of Heterogeneous Cloud based Radio Access Networks (H-CRAN) architecture and 5G networks. The objective is to propose a dynamic resource management tool to ease decisions on the activation/deactivation of micro cells as well as for the distributions of sub-frames among macro and micro cells. First, we propose a Markov chain based model that fits the behavior of the considered scheme and allows the analysis of the cell throughput according to traffic load, radio conditions and the distribution of available resources among macro and micro cells. Then, we propose an approximation model with a closed form formula. The two models are validated and evaluated in terms of accuracy and computation time. Numerical results are compared to Matlab simulations reproducing realistic radio conditions. Results show that both models are accurate, while the closed form approximation is less complex and provides faster results.

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.

Current architecture of many computer systems relies on dynamic allocation of a pool of resources according to workload conditions to meet specific performance objectives while minimizing cost (e.g., energy or billing). In such systems, different levels of operation may be defined, and switching between operating levels occurs at certain thresholds of system congestion. To avoid rapid oscillations between levels of service, “hysteresis” is introduced by using different thresholds for increasing and decreasing workload levels, respectively. We propose a model of such systems with general arrivals, arbitrary number of servers and operating levels where each higher operating level may correspond to an arbitrary number of additional servers and soft (i.e., non-deterministic) thresholds to account for “inertia” in switching between operating levels. In our model, request service times are assumed to be memoryless and server processing rates may be a function of the current operating level and of the number of requests (users) in the system. Additionally, we allow for delays in the activation of additional operating levels. We use simple mathematics to obtain a semi-numerical solution of our model. We illustrate the versatility of our model using several case study examples inspired by features of real systems. In particular, we explore optimal thresholds as a tradeoff between performance and energy consumption.

We evaluate the performance of a cloud system using a hysteresis queueing system with phase-type and batch arrivals. To represent the dynamic allocation of the resources, the hysteresis queue activates and deactivates the virtual machines according to the threshold values of the queue length. We suppose by batches, and follow a phase-type process. This system is analyze, especially when the size of the state space increases and the length of batch arrival distribution is large. So, to solve this problem, we propose to use stochastic bounds and the performance measures and compare the proposed bounding models with the exact one. The relevance of our methodology is to offer a trade-off between computational complexity and accuracy of the results and provide very interesting solutions for network dimensioning.

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.

Cloud providers need to size their systems to determine the right amount of resources to allocate as a function of customer's needs so as to meet their SLAs (Service Level Agreement), while at the same time minimizing their costs and energy use. Queueing theory based tools are a natural choice when dealing with performance aspects of the QoS (Quality of Service) part of the SLA and forecasting resource utilization. The characteristics of a cloud center lead to a queueing system with multiple servers (nodes) in which there is potentially a very large number of servers and both the arrival and service process can exhibit high variability. We propose to use a G/G/c-like model to represent a cloud system and assess expected performance indices. Given the potentially high number of servers in a cloud system, we present an efficient, fast and easy-to-implement approximate solution. We have extensively validated our approximation against discrete-event simulation for several QoS performance metrics such as task response time and blocking probability with excellent results. We apply our approach to examples of system sizing and our examples clearly demonstrate the importance of taking into account the variability of the tasks arrivals and thus expose the risk of under- or over-provisioning if one relies on a model with Poisson assumptions.

Considering a cloud system, we propose in this paper to apply bounding aggregations for mathematical analysis of a data center. Modeled as a hysteresis queueing system, a data center is characterized by forward and backward thresholds which allow to represent its dynamic behavior. The client requests (or jobs) are represented by bulk arrivals which arrive into the buffers and are executed by Virtual Machines (VMs). According to the occupation of the queue and the thresholds, the VMs are activated and deactivated. The system is represented by a complex Markov chain which is difficult to analyze when the size of the system is huge. We propose to use in this case bounding aggregations on the batch arrivals, in order to compute performance measure bounds. We present some numerical results for the performance measures in order to compare the bounding values with the exact ones according to the different input parameters. The relevance of this paper is to propose a tradeoff between computational complexity and accuracy of the results, which provides very interesting solutions in networking dimensioning.

We consider large queueing networks for which transient and stationary probability distributions are very difficult or impossible to obtain due to the state space explosion problem. In performance analysis, we need in general to study only a part of the network (a node or a path). Thus, we propose to define bounding systems that lead to compute bounds on performance measures of the considered subsystem. The original large state space is mapped into a smaller space to overcome the state space explosion problem, and bounds both on stationary and on transient performance measures are computed from these reduced-size models. This approach provides an interesting solution for complex networks since we have a trade-off between the quality of the bounds and the state space size, thus the computational complexity. As an application, we study a general multi-server queueing network, with finite capacity queues. We define bounding systems to compute blocking probabilities. The influence of parameters on the precision of the computed bounds are studied through some numerical examples in order to give more insights into the proposed approach.

We use a mathematical method based on stochastic comparison of multidimensional Markov chains in order to compute packet loss rates in IP routers for MPLS networks. The key idea of this methodology is that given a complex system represented by a Markov chain which is too large to be solved, we propose to build smaller Markov chains providing performance measures bounds.

End to end QoS of communication systems is essential for users but their performance evaluation is a complex issue. The abstraction of such systems are usually given by multidimensional Markov processes whose analysis is very difficult and even intractable, if there is no specific solution form. In this study, we propose an algorithm in order to automatically derive aggregated Markov processes providing upper and lower bounds on performance measures. We applied the algorithm to the analysis of an open tandem queueing network with rejection in order to derive performance measure bounds. Parametric aggregation schemes have been proposed in order to compute bounds on loss probabilities and end to end mean delays. Therefore a tradeoff between the accuracy of the bound and the size of considered Markov chains is possible.

International audience

A simple analytical model is presented to evaluate the effective multicast capacity of unidirectional multi-channel slotted ring networks where each node is equipped with one fixed or tuned transmitter and an array of fixed receivers (i.e., FT-FR w and TT-FR w systems). Furthermore, an approximate approach is developed to compare the mean access delay of a multicast packet between these networks and the TT-FR system [1]. The approach is based on the discrete Geom/Geom/1 queue [2] and on the computation of blocking probabilities. Moreover, the analysis is validated by simulations and the impact of self-similar traffic is shown. The presented methodology enables the comparison of performance of future wavelength division multiplexing (WDM) multicast-capable medium access (MAC) protocols, allowing destination stripping, in terms of effective transmission, and multicast throughput capacity in addition to the access delay.

Scheutzow et al. have presented an analytical model to evaluate the capacity of the unidirectional and bidirectional TT-FR packet-switched ring network under multicast traffic (i.e., a ring where each node is equipped with one tuned transmitter, TT, and one fixed receiver, FR). In this paper, we investigate the impact of multicast on the access delay of the bidirectional TT-FR, by means of an analytical model based on the computation of blocking probability and on the discrete Geom/Geom/1 queue. Moreover, the capacity and the delay of the TT-FRW system (i.e., each ring node has as many fixed receivers as wavelength channels W) are calculated and compared to those of TT-FR. The obtained results are validated by using extensive simulations, and the self-similarity influence is also shown. This work offers an important and simple analytical tool to compare the impact of multicast on access delays and multicast capacity in future slotted ring networks

Summary form only given. Due to random access in wireless networks using CSMA/CA like in Wifi networks, the integration of services with a lot of quality of service needs is impossible. In this paper, we propose to study and to evaluate a new MAC protocol that takes into account different types of traffic (e.g.. voice and data) and for each traffic, different priority levels are considered. To improve the QoS of WIFI MAC protocols, we add a selective reject and push-out mechanisms. To model our protocol, using Markov chain is impossible because it provides Markov chain with a large state-space. This is due to the resource management and user mobility. Thus, we propose to build an aggregated Markov chain with a less state-space that allows to compute easily performance measures. We have used stochastic comparisons of Markov chains to prove that the considered access protocol (with selective reject and push-out mechanisms) gives less loss rates of high priority connections (data and voices) than the traditional one (without selective reject and push-out mechanisms). We give numerical results to confirm mathematical proofs.

We present in this paper a mathematical method based on stochastic comparisons of Markov chains in order to compute in a mobile network performance measures that are important Q parameters for users: the dropping handover of voice and the blocking probability of a new voice call. The key idea of this methodology is that given a complex system represented by a multi-dimensional Markov chain which is too large to be solved, we propose to reduce the state space, and so to define a new Markov chain which is a simplified version of the original one. This reduced Markov chain is defined as an aggregated one, which represents a stochastic bound for performance measures written as increasing reward function on the stationary distribution. The main steps of the construction of the aggregated Markov chain applied into mobile networks are presented in this paper. As the number of mobile users with different kinds of applications increases, the associated model is more complex and it can be represented by multi-dimensional continuous time Markov chain with a very large size. Thus, we define an aggregated Markov chain represented by a multi-dimensional birth and death process which is very easy to solve. We have proved that there is a weak ordering between the original Markov chain and the aggregated one using increasing set formalism. We have computed upper bounds of dropping handover and blocking probability for different values of input parameters. Numerical results prove that upper bounds give good results and so the stochastic methodology is an interesting mathematical tool for the performance evaluation of complex systems. Keywords: Mobile Networks, Quality of Service, Stochastic ordering, stochastic comparisons, Continuous Time Markov Chains.