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

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

Time-Limited and k-Limited Polling Systems: A Matrix Analytic Solution

In this paper, we will develop a tool to analyze polling systems with the autonomous-server, the time-limited, and the k-limited service discipline. It is known that these disciplines do not satisfy the well-known branching property in polling system, therefore, hardly any exact result exists in the literature for them. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-length at the beginning and the end of a server visit to a queue. These kernel relations are derived using the theory of absorbing Markov chains. Finally, we will show that our tool works also in the case of a tandem queueing network with a single server that can serve one queue at a time

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

Consumption-as-usual instead of ceteris paribus assumption for demand: Integration of potential rebound effects into LCA

Background, aims, and scope: Life cycle assessment (LCA) according to ISO 14040 standard (ISO-LCA) is applied to assess the environmental impact per functional unit of new or modified products. However, new or modified products can also induce demand changes—so-called rebound effects. If overall environmental impact is of interest, there is a need to assess the potential magnitude of such rebound effects and to allow recommendations on how to mitigate these effects. To do so, this study proposes to complement the constant demand assumption (implicitly assumed by the ISO-LCA), commonly known as the ceteris paribus assumption, with a consumption-as-usual assumption allowing a systematic stepwise inclusion of rebound effects. Materials and methods: We base our results on a formal description of household consumption. To indicate the relevance of the proposed integration of rebound effects, different comparative LCAs are reviewed and the concept is applied to mobility as illustrative examples. Results: Based on a description of household demand and consumption feedback loops, we propose the consumption-as-usual concept, which in contrast to the constant demand assumption assumes that (1) the use of household resources for consumption does not change and (2) preferences remain the same. Household resources for example are purchasing power (we assume that households do not work less), time, and living space. We outline how this concept allows integrating potential rebound effects into ISO-LCA by considering three different cases of reallocating freed household resources. To illustrate the use of the consumption-as-usual concept, we draw implications for different comparative LCAs from the literature and illustrate cases with income and time rebound for different personal travel modes. Discussion: The consumption-as-usual concept is applicable to a broad range of product modifications and allows an important complementation of the LCA regarding rebound effects. For products with various changes in the need for household resources, the assessment becomes however a challenging task. The limits of the consumption-as-usual concept are mainly given by its two underlying assumptions. Therefore, new or modified products with the potential to change consumer preferences or even the amount of household resources used for consumption go beyond this concept. Conclusions: The integration of rebound effects is feasible for many comparative LCAs. It helps in increasing the reliability of the assessment of overall environmental impact reduction through new or modified products. In addition, a basis is provided with which to mitigate rebound effects and give appropriate recommendations to product users. Recommendations and perspectives: Potential rebound effects should be included in LCA in order to guide consumers and policy towards sustainable consumption. We recommend the consumption-as-usual concept for this purpose. To predict rebound effects under consumption as usual instead of outlining potential amplitudes, further research on household preferences is needed and an optimisation model should be applied for household consumption. However, even if data are available for such a prediction, the assessment of potential rebound effects is still recommended in order to recognise dangers and opportunities in consumption change

Traffic noise in LCA: Part 1: state-of-science and requirement profile for consistent context-sensitive integration of traffic noise in LCA

Background, aim, and scope: According to some recent studies, noise from road transport is estimated to cause human health effects of the same order of magnitude as the sum of all other emissions from the transport life cycle. Thus, ISO 14′040 implies that traffic noise effects should be considered in life cycle assessment (LCA) studies where transports might play an important role. So far, five methods for the inclusion of noise in LCA have been proposed. However, at present, none of them is implemented in any of the major life cycle inventory (LCI) databases and commonly used in LCA studies. The goal of the present paper is to define a requirement profile for a method to include traffic noise in LCA and to assess the compliance of the five existing methods with this profile. It concludes by identifying necessary cornerstones for a model for noise effects of generic road transports that meets all requirements. Materials and methods: Requirements for a methodological framework for inclusion of traffic noise effects in LCA are derived from an analysis of how transports are included in 66 case studies published in International Journal of Life Cycle Assessment in 2006 and 2007, in the sustainability reports of ten Swiss companies, as well as on the basis of theoretical considerations. Then, the general compliance of the five existing methods for inclusion of noise in LCA with the postulated requirement profile is assessed. Results: Six general requirements for a methodological framework for inclusion of traffic noise effects in LCA were identified. A method needs to be applicable for (1) both generic and specific transports, (2) different modes of transport, (3) different vehicles within one mode of transport, (4) transports in different geographic contexts, (5) different temporal contexts, and (6) last but not least, the method needs to be compatible with the ISO standards on LCA. One of the reviewed methods is not specific for transports at all and two are only applicable for specific transports. The other two allow generic and specific road transports to be assessed. The methods either deal with road traffic noise only or they compare noise from different sources, ignoring the fact that not only physical sound levels but also the source of sound determines the effect. Three methods only differentiate between vehicle classes (lorries and passenger cars) while one method differentiates between specific vehicles of the same class. Four of the methods consider the geographic context and three of them differentiate between day- and nighttime traffic. Discussion: None of the existing methods for traffic noise integration in LCA complies with the proposed requirement profile. They either lack the genericness for a wide application or they lack the specificity needed for differentiations in LCA studies. There is no method available that allows for appropriate inter- or intramodal comparison of traffic noise effects. Thus, the benefit of the existing methods is limited. They can, in the better cases, only demonstrate the relative importance of road or rail traffic noise effects compared to the nonnoise-related effects of transportation. Conclusions: Currently, none of the major LCI databases includes traffic noise indicators. Thus, noise effects are usually not considered in LCA studies. We introduce a requirement profile for methods that allow the inclusion of noise in LCI. Due to the estimated significance of noise in transport LCA, this inclusion will change the overall results of many LCA studies. None of the existing methods fully complies with the requirement profile. Two of the methods can be modified and extended for inclusion in generic LCI databases. A third model allows for intermodal comparison. From an LCA perspective, all methods include weaknesses and need to be amended in order to make them widely usable. Recommendations and perspectives: In part 2 of this paper, an in-depth analysis of the promising methods is provided, improvement potential is evaluated, and a new context-sensitive framework for the consistent LCI modeling of noise emissions from road transportation is presented. Appropriate methods for modeling rail and air traffic noise will have to be developed in the future in order to arrive at a methodological framework fully compliant with the requirement profile. Furthermore, future research is needed to identify appropriate methods for impact assessmen

Traffic noise in LCA: Part 2: Analysis of existing methods and proposition of a new framework for consistent, context-sensitive LCI modeling of road transport noise emission

Background, aim, and scope: An inclusion of traffic noise effects could change considerably the overall results of many life cycle assessment (LCA) studies. However, at present, noise effects are usually not considered in LCA studies, mainly because the existing methods for their inclusion do not fulfill the requirement profile. Two methods proposed so far seem suitable for inclusion in generic life cycle inventory (LCI) databases, and a third allows for inter-modal comparison. The aim of this investigation is an in-depth analysis of the existing methods and the proposition of a framework for modeling road transport noise emissions in LCI in accordance to the requirement profile postulated in part 1. Materials and methods: This paper analyzes three methods for inclusion of traffic noise in LCA (Danish LCA guide method, Swiss EPA method, and Swiss FEDRO method) in detail. The additional basis for the analysis are the Swiss road traffic emission model "SonRoad,” traffic volume measurements at 444 sites in the Swiss road network, vehicle-type-specific noise measurements in free floating traffic situations in Germany, and noise emission measurements from different tires. Results: The Danish LCA guide method includes a major flaw that cannot be corrected within the methodological concept. It applies a dose-response function valid for average noise levels of a traffic situation to maximum noise levels of single vehicles. The Swiss FEDRO method is based on an inappropriate assumption since it bases distinctions of specific vehicles on data that do not allow for such a distinction. Noise emissions cannot be distinguished by the make and type of a vehicle since other factors, especially the tires, are dominant for noise emissions. Several problems are also identified in the Swiss EPA method, but they are not of a fundamental nature. Thus, we are able to base a new framework for vehicle and context-sensitive inclusion of road traffic noise emissions in LCI on the Swiss EPA method. We show how specific vehicle classes can be distinguished, how the influence of different tires can be dealt with, and what temporal and spatial aspects of traffic need to be distinguished. Discussion: While the Danish LCA guide method and the Swiss FEDRO method are not suitable for our purpose, the Swiss EPA method can be used as a basis to better meet the requirement profile identified in Part 1 of this paper. The proposed method for consistent, context-sensitive modeling of noise emissions from road transports in LCI meets all the requirements except that it is restricted to road transport. Conclusions: We show limitations of the existing methods and approaches for improving them. Our proposed model allows for a more specific consideration of the various vehicles and contexts in terms of space and time and thus in terms of speed and traffic volume. This can be used on one hand for a consistent, context sensitive assessment of different vehicles in different traffic situations. On the other hand, it also allows for an inclusion of noise in LCA of transports on which only very little is known. This new LCI model meets five of the six requirements postulated in Part 1. Recommendations and perspectives: In a next step, additional noise emissions due to additional traffic needs to be calculated based on the proposed framework and national or regional traffic models. Furthermore, the consideration of noise from different traffic modes should be addressed. The approach presented needs to be extended in order to make it also applicable for rail and air traffic noise, and the methods need to be implemented in LCI databases to make them easily available to practitioners. Furthermore, suitable impact assessment methods need to be identified or developed. They could base on the proposals made in the Swiss EPA and in the Swiss FEDRO method

Scenario Modelling in Prospective LCA of Transport Systems. Application of Formative Scenario Analysis (11 pp)

Background: Tools and methods able to cope with uncertainties are essential for improving the credibility of Life Cycle Assessment (LCA) as a decision support tool. Previous approaches have focussed predominately upon data quality. Objective: and Scope. An epistemological approach is presented conceptualising uncertainties in a comparative, prospective, attributional LCA. This is achieved by considering a set of cornerstone scenarios representing future developments of an entire Life Cycle Inventory (LCI) product system. We illustrate the method using a comparison of future transport systems. Method: Scenario modelling is organized by means of Formative Scenario Analysis (FSA), which provides a set of possible and consistent scenarios of those unit processes of an LCI product system which are time dependent and of environmental importance. Scenarios are combinations of levels of socio-economic or technological impact variables. Two core elements of FSA are applied in LCI scenario modelling. So-called impact matrix analysis is applied to determine the relationship between unit process specific socio-economic variables and technology variables. Consistency Analysis is employed to integrate unit process scenarios, based on pair-wise ratings of the consistency of the levels of socio-economic impact variables of all unit processes. Two software applications are employed which are available from the authors. Results and Discussion: The study reveals that each possible level or development of a technology variable is best conceived of as the impact of a specific socio-economic (sub-) scenario. This allows for linking possible future technology options within the socio-economic context of the future development of various background processes. In an illustrative case study, the climate change scores and nitrogen dioxide scores per seat kilometre for six technology options of regional rail transport are compared. Similar scores are calculated for a future bus alternative and an average Swiss car. The scenarios are deliberately chosen to maximise diversity. That is, they represent the entire range of future possible developments. Reference data and the unit process structure are taken from the Swiss LCA database 'ecoinvent 2000'. The results reveal that rail transport remains the best option for future regional transport in Switzerland. In all four assessed scenarios, four technology options of future rail transport perform considerably better than regional bus transport and car transport. Conclusions: and Recommendations. The case study demonstrates the general feasibility of the developed approach for attributional prospective LCA. It allows for a focussed and in-depth analysis of the future development of each single unit process, while still accounting for the requirements of the final scenario integration. Due to its high transparency, the procedure supports the validation of LCI results. Furthermore, it is well-suited for incorporation into participatory methods so as to increase their credibility. Outlook: and Future Work. Thus far, the proposed approach is only applied on a vehicle level not taking into account alterations in demand and use of different transport modes. Future projects will enhance the approach by tackling uncertainties in technology assessment of future transport systems. For instance, environmental interventions involving future maglev technology will be assessed so as to account for induced traffic generated by the introduction of a new transport syste

Stability of two exponential time-limited polling models

In this article, we consider the stability of two single-server polling models. More specifically, we will state and prove the stability conditions of single-server polling systems operating under the pure and exhaustive exponential time-limited service discipline. These conditions will be proven for the polling system operating under the periodic polling strategy and preemptive service. The stability proof of the pure time-limited discipline is straightforward as stability may be considered for each queue in isolation. The proof for the exhaustive time-limited discipline is more laborious. We follow the line of proof as introduced by Fricker and Ja\"{i}bi for a large class of service disciplines. Unfortunately, the preemptive nature of the exhaustive time-limited discipline excludes it from this class and as a result substantial efforts are required to modify the proof as to allow for preemptive disciplines. Finally, the extension of the proofs to the Markovian polling strategy is discussed

Time-limited polling systems with batch arrivals and phase-type service times

In this paper, we develop a general framework to analyze polling systems with either the autonomous-server or the time-limited service discipline. According to the autonomous-server discipline, the server continues servicing a queue for a certain period of time. According to the time-limited service discipline, the server continues servicing a queue for a certain period of time or until the queue becomes empty, whichever occurs first. We consider Poisson batch arrivals and phase-type service times. It is known that these disciplines do not satisfy the well-known branching property in polling systems. Therefore, hardly any exact results exist in the literature. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-lengths at the beginning and the end of a server visit to a queue. These kernel relations are derived using the theory of absorbing Markov chains