Queueing models for mobile ad hoc networks

This thesis presents models for the performance analysis of a recent communication paradigm: mobile ad hoc networking. The objective of mobile ad hoc networking is to provide wireless connectivity between stations in a highly dynamic environment. These dynamics are driven by the mobility of stations and by breakdowns of stations, and may lead to temporary disconnectivity of parts \ud of the network. Applications of this novel paradigm can be found in telecommunication services, but also in manufacturing systems, road-traffic control, animal monitoring and emergency networking. The performance of mobile ad hoc networks in terms of buffer occupancy and delay is quantified in this thesis by employing specific queueing models, viz., time-limited polling models. These polling models capture the uncontrollable characteristic of link availability in mobile ad hoc networks. Particularly, a novel, so-called pure exponential time-limited, service discipline is introduced in the context of polling systems. The highlighted performance characteristics for these polling systems include the stability, the queue lengths and the sojourn times of the customers. Stability conditions prescribe limits on the amount of tra±c that can be sustained by the system, so that the establishment of these conditions is a fundamental keystone in the analysis of polling models. Moreover, both exact and approximate analysis is presented for the queue length and sojourn time in time-limited polling systems with a single server. These exact analytical techniques are extended to multi-server polling systems operating under the pure time-limited service discipline. Such polling systems with multiple servers effectively may reflect large communication networks with multiple simultaneously active links, while the systems with a single server represent performance models for small networks in which a single communication link can be active at a time

Large deviations for polling systems

Related INRIA Research report available at : http://hal.inria.fr/docs/00/07/27/62/PDF/RR-3892.pdfInternational audienceWe aim at presenting in short the technical report, which states a sample path large deviation principle for a resealed process n-1 Qnt, where Qt represents the joint number of clients at time t in a single server 1-limited polling system with Markovian routing. The main goal is to identify the rate function. A so-called empirical generator is introduced, which consists of Q t and of two empirical measures associated with S t the position of the server at time t. The analysis relies on a suitable change of measure and on a representation of fluid limits for polling systems. Finally, the rate function is solution of a meaningful convex program

Mathematical Modeling of Public Opinion using Traditional and Social Media

With the growth of the internet, data from text sources has become increasingly available to researchers in the form of online newspapers, journals, and blogs. This data presents a unique opportunity to analyze human opinions and behaviors without soliciting the public explicitly. In this research, I utilize newspaper articles and the social media service Twitter to infer self-reported public opinions and awareness of climate change. Climate change is one of the most important and heavily debated issues of our time, and analyzing large-scale text surrounding this issue reveals insights surrounding self-reported public opinion. First, I inquire about public discourse on both climate change and energy system vulnerability following two large hurricanes. I apply topic modeling techniques to a corpus of articles about each hurricane in order to determine how these topics were reported on in the post event news media. Next, I perform sentiment analysis on a large collection of data from Twitter using a previously developed tool called the hedonometer . I use this sentiment scoring technique to investigate how the Twitter community reports feeling about climate change. Finally, I generalize the sentiment analysis technique to many other topics of global importance, and compare to more traditional public opinion polling methods. I determine that since traditional public opinion polls have limited reach and high associated costs, text data from Twitter may be the future of public opinion polling

On the Stability of a Polling System with an Adaptive Service Mechanism

We consider a single-server cyclic polling system with three queues where the server follows an adaptive rule: if it finds one of queues empty in a given cycle, it decides not to visit that queue in the next cycle. In the case of limited service policies, we prove stability and instability results under some conditions which are sufficient but not necessary, in general. Then we discuss open problems with identifying the exact stability region for models with limited service disciplines: we conjecture that a necessary and sufficient condition for the stability may depend on the whole distributions of the primitive sequences, and illustrate that by examples. We conclude the paper with a section on the stability analysis of a polling system with either gated or exhaustive service disciplines.Comment: 16 page

Performance analysis of a two-level polling control system based on LSTM and attention mechanism for wireless sensor networks

A continuous-time exhaustive-limited (K = 2) two-level polling control system is proposed to address the needs of increasing network scale, service volume and network performance prediction in the Internet of Things (IoT) and the Long Short-Term Memory (LSTM) network and an attention mechanism is used for its predictive analysis. First, the central site uses the exhaustive service policy and the common site uses the Limited K = 2 service policy to establish a continuous-time exhaustive-limited (K = 2) two-level polling control system. Second, the exact expressions for the average queue length, average delay and cycle period are derived using probability generating functions and Markov chains and the MATLAB simulation experiment. Finally, the LSTM neural network and an attention mechanism model is constructed for prediction. The experimental results show that the theoretical and simulated values basically match, verifying the rationality of the theoretical analysis. Not only does it differentiate priorities to ensure that the central site receives a quality service and to ensure fairness to the common site, but it also improves performance by 7.3 and 12.2%, respectively, compared with the one-level exhaustive service and the one-level limited K = 2 service; compared with the two-level gated- exhaustive service model, the central site length and delay of this model are smaller than the length and delay of the gated- exhaustive service, indicating a higher priority for this model. Compared with the exhaustive-limited K = 1 two-level model, it increases the number of information packets sent at once and has better latency performance, providing a stable and reliable guarantee for wireless network services with high latency requirements. Following on from this, a fast evaluation method is proposed: Neural network prediction, which can accurately predict system performance as the system size increases and simplify calculations

Heavy-traffic analysis of k-limited polling systems

In this paper we study a two-queue polling model with zero switch-over times and $k$-limited service (serve at most $k_i$ customers during one visit period to queue $i$, $i=1,2$) in each queue. The arrival processes at the two queues are Poisson, and the service times are exponentially distributed. By increasing the arrival intensities until one of the queues becomes critically loaded, we derive exact heavy-traffic limits for the joint queue-length distribution using a singular-perturbation technique. It turns out that the number of customers in the stable queue has the same distribution as the number of customers in a vacation system with Erlang-$k_2$ distributed vacations. The queue-length distribution of the critically loaded queue, after applying an appropriate scaling, is exponentially distributed. Finally, we show that the two queue-length processes are independent in heavy traffic

A polling model with an autonomous server

Polling models are used as an analytical performance tool in several application areas. In these models, the focus often is on controlling the operation of the server as to optimize some performance measure. For several applications, controlling the server is not an issue as the server moves independently in the system. We present the analysis for such a polling model with a so-called autonomous server. In this model, the server remains for an exogenous random time at a queue, which also implies that service is preemptive. Moreover, in contrast to most of the previous research on polling models, the server does not immediately switch to a next queue when the current queue becomes empty, but rather remains for an exponentially distributed time at a queue. The analysis is based on considering imbedded Markov chains at specific instants. A system of equations for the queue-length distributions at these instant is given and solved for. Besides, we study to which extent the queues in the polling model are independent and identify parameter settings for which this is indeed the case. These results may be used to approximate performance measures for complex multi-queue models by analyzing a simple single-queue model

A transient analysis of polling systems operating under exponential time-limited service disciplines

In the present article, we analyze a class of time-limited polling systems. In particular, we will derive a direct relation for the evolution of the joint queue-length during the course of a server visit. This will be done both for the pure and the exhaustive exponential time-limited discipline for general service time requirements and preemptive service. More specifically, service of individual customers is according to the preemptive-repeat-random strategy, i.e., if a service is interrupted, then at the next server visit a new service time will be drawn from the original service-time distribution. Moreover, we incorporate customer routing in our analysis, such that it may be applied to a large variety of queueing networks with a single server operating under one of the before-mentioned time-limited service disciplines. We study the time-limited disciplines by performing a transient analysis for the queue length at the served queue. The analysis of the pure time-limited discipline builds on several known results for the transient analysis of the M/G/1 queue. Besides, for the analysis of the exhaustive discipline, we will derive several new results for the transient analysis of an M/G/1 during a busy period. The final expressions (both for the exhaustive and pure case) that we obtain for the key relations generalize previous results by incorporating customer routing or by relaxing the exponentiality assumption on the service times. Finally, based on the interpretation of these key relations, we formulate a conjecture for the key relation for any branching-type service discipline operating under an exponential time-limit