A Markovian Queueing System for Modeling a Smart Green Base Station

International audienceWe investigate a model to assess the performance of a base station (BS) fully powered by renewable energy sources. The BS is modeled as a three-queue system where two of them are coupled. One represents accumulated energy, the second is the data queue and the third one serves as a reserve energy queue. This smart BS is able to dynamically adjust its coverage area (thereby controlling the traffic intensity) and to generate signals to the reserve energy queue that trigger the movement of energy units to the main energy buffer. Given the randomness of renewable energy supply and the internal traffic intensity control, our queueing model is operated in a finite state random environment. Using the matrix analytic formalism we construct a five-dimensional Markovian model to study the performance of the BS. The stationary distribution of the system state is obtained and key performance metrics are calculated. A small numerical example illustrates the model and a simplified product-form approximation is proposed

When Backpressure Meets Predictive Scheduling

Motivated by the increasing popularity of learning and predicting human user behavior in communication and computing systems, in this paper, we investigate the fundamental benefit of predictive scheduling, i.e., predicting and pre-serving arrivals, in controlled queueing systems. Based on a lookahead window prediction model, we first establish a novel equivalence between the predictive queueing system with a \emph{fully-efficient} scheduling scheme and an equivalent queueing system without prediction. This connection allows us to analytically demonstrate that predictive scheduling necessarily improves system delay performance and can drive it to zero with increasing prediction power. We then propose the \textsf{Predictive Backpressure (PBP)} algorithm for achieving optimal utility performance in such predictive systems. \textsf{PBP} efficiently incorporates prediction into stochastic system control and avoids the great complication due to the exponential state space growth in the prediction window size. We show that \textsf{PBP} can achieve a utility performance that is within $O(\epsilon)$ of the optimal, for any $\epsilon>0$, while guaranteeing that the system delay distribution is a \emph{shifted-to-the-left} version of that under the original Backpressure algorithm. Hence, the average packet delay under \textsf{PBP} is strictly better than that under Backpressure, and vanishes with increasing prediction window size. This implies that the resulting utility-delay tradeoff with predictive scheduling beats the known optimal $[O(\epsilon), O(\log(1/\epsilon))]$ tradeoff for systems without prediction

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

Optimal data collection in wireless sensor networks with correlated energy harvesting

We study the optimal data collection rate in a hybrid wireless sensor network where sensor data is collected by mobile sinks. In such networks, there is a trade-off between the cost of data collection and the timeliness of the data. We further assume that the sensor node under study harvests its energy from its environment. Such energy harvesting sensors ideally operate energy neutral, meaning that they can harvest the necessary energy to sense and transmit data, and have on-board rechargeable batteries to level out energy harvesting fluctuations. Even with batteries, fluctuations in energy harvesting can considerably affect performance, as it is not at all unlikely that a sensor node runs out of energy, and is neither able to sense nor to transmit data. The energy harvesting process also influences the cost vs. timeliness trade-off as additional data collection requires additional energy as well. To study this trade-off, we propose an analytic model for the value of the information that a sensor node brings to decision-making. We account for the timeliness of the data by discounting the value of the information at the sensor over time, we adopt the energy chunk approach (i.e. discretise the energy level) to track energy harvesting and expenditure over time, and introduce correlation in the energy harvesting process to study its influence on the optimal collection rate

On the Use of Small Solar Panels and Small Batteries to Reduce the RAN Carbon Footprint

The limited power requirements of new generations of base stations make the use of renewable energy sources, solar in particular, extremely attractive for mobile network operators. Exploiting solar energy implies a reduction of the network operation cost as well as of the carbon footprint of radio access networks. However, previous research works indicate that the area of the solar panels that are necessary to power a standard macro base station (BS) is large, making the solar panel deployment problematic, especially within urban areas.In this paper we use a modeling approach based on Markov reward processes to investigate the possibility of combining a connection to the power grid with small area solar panels and small batteries to run a macro base station. By so doing, it is possible to exploit a significant fraction of renewable energy to run a radio access network, while also reducing the cost incurred by the network operator to power its base stations. We assume that energy is drawn from the power grid only when needed to keep the BS operational, or during the night, which corresponds to the period with lowest electricity price. The proposed energy management policies have advantages in terms of both cost and carbon footprint. Our results show that solar panels of the order of 1-2 kW peak, i.e., with a surface of about 5-10 m2, combined with limited capacity energy storage (of the order of 1-5 kWh, corresponding to about 1-2 car batteries) and a smart energy management policy, can lead to an effective exploitation of renewable energy

Performance optimization with energy packets

We investigate how the flow of energy and the flow of jobs in a service system can be used to minimize the average response time to jobs that arrive according to random arrival processes at the servers. An interconnected system of workstations and energy storage units that are fed with randomly arriving harvested energy is analyzed by means of the Energy Packet Network (EPN) model. The system state is discretized, and uses discrete units to represent the backlog of jobs at the workstations, and the amount of energy that is available at the energy storage units. An Energy Packet (EP) which is the unit of energy, can be used to process one or more jobs at a workstation, and an EP can also be expended to move a job from one workstation to another one. The system is modeled as a probabilistic network that has a product-form solution for the equilibrium probability distribution of system state. The EPN model is used to solve two problems related to using the flow of energy and jobs in a multi-server system, so as to minimize the average response time experienced by the jobs that arrive at the system

Analysis of truck delays at container terminal security inspection stations

After September 11, 2001, special attention has been given to the vulnerability at container transportation to terrorist activities. United States Customs and Border Protection (CBP) has set up inspection stations for containers at seaport terminals to screen containers, but this practice affects the truck turnaround time in the seaport by generating additional processing delays. This dissertation analyses the additional truck turnaround time incurred at the inspection stations under various levels of security. Queuing models were used to estimate truck delay as containers are inspected at two successive security inspection stages. Each stage may utilize one or more inspection equipment. The objective is to determine the number of equipment needed to keep the total delay at an acceptable level. Homeland security, CBP, seaport terminal officers, truck and marine carriers may use this research to develop an effective and efficient plan for handling marine freight and containers

Applying Mean-field Approximation to Continuous Time Markov Chains

The mean-field analysis technique is used to perform analysis of a systems with a large number of components to determine the emergent deterministic behaviour and how this behaviour modifies when its parameters are perturbed. The computer science performance modelling and analysis community has found the mean-field method useful for modelling large-scale computer and communication networks. Applying mean-field analysis from the computer science perspective requires the following major steps: (1) describing how the agents populations evolve by means of a system of differential equations, (2) finding the emergent deterministic behaviour of the system by solving such differential equations, and (3) analysing properties of this behaviour either by relying on simulation or by using logics. Depending on the system under analysis, performing these steps may become challenging. Often, modifications of the general idea are needed. In this tutorial we consider illustrating examples to discuss how the mean-field method is used in different application areas. Starting from the application of the classical technique, moving to cases where additional steps have to be used, such as systems with local communication. Finally we illustrate the application of the simulation and uid model checking analysis techniques