Joint Routing and Energy Optimization for Integrated Access and Backhaul with Open RAN

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.Comment: 6 pages, Accepted at IEEE GLOBECOM 202

Reducing the complexity of the performance analysis of a multi- server facilities

Systems with multiple servers are common in many areas and their correct dimensioning is in general a difficult problem under realistic assumptions on the pattern of user arrivals and service time distribution. We present an approximate solution for the underlying Ph/Ph/c/N queueing model. Our approximation decomposes the solution of the Ph/Ph/c/N queue into solutions of simpler M/Ph/c/N and Ph/M/c/N queues. It is conceptually simple, easy to implement and produces generally accurate results for the mean number in the system, as well as the loss probability. A significant speed advantage compared to the numerical solution of the full Ph/Ph/c/N queue can be gained as the number of phases representing the arrival process and/or the number of servers increases

On the choice of the stochastic comparison method for multidimensional Markov chains analysis

International audienceThe stochastic comparison of multidimensional Continuous Time Markov Chains (CTMC)s is an efficient but a complex method for the performability evaluation of computer systems. Different techniques can be applied for the stochastic comparison of Markov chains. The coupling is an intuitive method, and may be applied by comparing the evolution of sample paths due to events to establish the strong ordering. The increasing set method is based on the comparison of transition rates for a family of increasing sets. It is a more general formalism as it can be applied for all stochastic orderings (strong and weak). The goal of this paper is to identify the relationships between these orderings, in order to determine the method to apply for establishing comparisons between models. Although the strong ordering between random variables implies weak orderings, this result could not be generalized to the comparison of stochastic processes. However even the strong ordering does not exist between processes, the weak constraints could be satisfied. In this paper, we aim to give the intuition to choose the most suitable method with respect to the underlying performability stud

Stochastic monotonicity in queueing networks

International audienceStochastic monotonicity is one of the sufficient conditions for stochastic comparisons of Markov chains. On a partially ordered state space, several stochastic orderings can be defined by means of increasing sets. The most known is the strong stochastic (sample-path) ordering, but weaker orderings (weak and weak*) could be defined by restricting the considered increasing sets. When the strong ordering could not be defined, weaker orderings represent an alternative as they generate less constraints. Also, they may provide more accurate bounds. The main goal of this paper is to provide an intuitive event formalism added to stochastic comparisons methods in order to prove the stochastic monotonicity for multidimensional Continuous Time Markov Chains (CTMC). We use the coupling by events for the strong monotonicity. For weaker monotonicity, we give a theorem based on generator inequalities using increasing sets. We prove this theorem, and we present the event formalism for the definition of the increasing sets. We apply our formalism on queueing networks, in order to establish monotonicity propertie

Weak stochastic comparisons for performability verification

International audienceThe probabilistic model checking provides a precise formalism for the performance and reliability verification of telecommunication systems modeled by Markov chains. We study a queueing system similar to a Jackson network except that queues have a finite capacity. We propose to study in this paper (state and path) formulas from the Continuous Stochastic Logic (CSL), in order to verify performability properties. Unfortunately, transient and stationary analysis is very complex for multidimensional Markov processes. So we propose to use the stochastic comparisons in the sense of weak orderings to define bounding processes. Bounding processes are represented by independent M/M/1 queues for which transient and stationary distributions can be computed as the product of probability distributions of each queue. We use the increasing set method, and we develop an intuitive formalism based on events to establish weak stochastic comparison

Strong and weak orderings for an accurate resource dimensioning

International audienceEnd to end QoS (Quality of Service) is crucial in computer networks, but very hard to study as the systems are in general very complex. We suppose that systems can be modeled by multidimensional Markov processes, which could be very hard to analyse if there is no specific solution form. We propose to apply stochastic comparisons of Markov processes in order to solve this problem. We provide new processes, easier to analyze and representing stochastic bounds (upper or lower) for the original model. In this paper, we propose strong and weak bounding processes for a general queueing network model, and discuss their accuracy for QoS constraint

Stochastic comparisons: a methodology for the performance evaluation of fixed and mobile

We propose to use a mathematical method based on stochastic comparisons of Markov chains in order to derive performance indices bounds. The main objective is to find Markovian bounding models with reduced state spaces, which are easier to solve. We apply the methodology to performance evaluation of complex telecommunication systems modelled by large size Markov chains which cannot be solved by exact methods. This methodology can be applied for continuous- or discrete-time Markov chains. In the first study, we consider an MPLS switch represented by two stages of buffers. Various kinds of traffic with different QoS levels enter the first stage, and transit in the second stage. The goal is to compute packet loss rates in the second stage. In the other study, we define a CAC scheme in a mobile network which gives the priority to the handover over the new calls. Performance evaluation of the CAC scheme consists in the computation of the dropping handover and call blocking probabilities. For the two studies, systems are represented by large state Markov chains whose resolution is difficult. We propose to define intuitively bounding systems in order to compute performance measures bounds. Using stochastic comparisons methods, we prove that the new systems represent bounds for the exact ones. Different methods can be used. For the MPLS switch, we use the coupling equivalent to the sample-path ordering, allowing the comparison of the loss rates. In the case of the CAC scheme, we apply the increasing sets formalism used to define weaker orderings, enabling the comparison of the dropping handovers and blocking probabilities. We validate stochastic comparison method by presenting some numerical results illustrating the interest of the approach.ou

Accuracy of strong and weak comparisons for network of queues

International audienceQuality of performance measure bounds is crucial for an accurate dimensioning of computer network resources. We study stochastic comparisons of multidimensional Markov processes for which quantitative analysis could be intractable if there is no specific solution form. On partially ordered state space, different stochastic orderings can be defined as the strong or the less constrained weak ordering. The goal of the present paper is to compare these two orderings with respect the quality of derived bounds. We propose to study a system similar to a Jackson network except that queues have finite capacity. Different bounding systems are built either in the sense of the strong ordering with hard constraints, or in the sense of the weak ordering with less ones. The proofs of the stochastic comparisons are done using the coupling and the increasing set methods, with an intuitive event based formalism. The qualities of bounding systems are compared regarding to blocking probabilities

Strong and weak stochastic bounds for multidimensional Markov chains

International audienceWe study queueing networks similar to Jackson networks, modelled by a multidimensional Markov chain. The performance analysis may be very difficult or intractable, if there is no specific solution form. We explain how stochastic comparisons of Markov chains can be used to overcome this problem. We build new queueing which are easier to analyse and providing stochastic bounds (upper or lower) for the original model. In this paper, we propose different queueing systems in the sense of the strong and weak stochastic ordering for a general queueing network model in order to compute performance measure bounds as blocking probabilities. We discuss the accuracy of the bounds under different input parameter value

Performance Evaluation of Cloud Computing Centers with General Arrivals and Service

International audienceCloud 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