Queues with Lévy input and hysteretic control

We consider a (doubly) reflected Lévy process where the Lévy exponent is controlled by a hysteretic policy consisting of two stages. In each stage there is typically a different service speed, drift parameter, or arrival rate. We determine the steady-state performance, both for systems with finite and infinite capacity. Thereby, we unify and extend many existing results in the literature, focusing on the special cases of M/G/1 queues and Brownian motion. © The Author(s) 2009

Shot-noise queueing models

We provide a survey of so-called shot-noise queues: queueing models with the special feature that the server speed is proportional to the amount of work it faces. Several results are derived for the workload in an M/G/1 shot-noise queue and some of its variants. Furthermore, we give some attention to queues with general workload-dependent service speed. We also discuss linear stochastic fluid networks, and queues in which the input process is a shot-noise process

First Passage Time of Filtered Poisson Process with Exponential Shape Function

Solving some integro-differential equation we find the Laplace transformation of the first passage time for Filtered Poisson Process generated by pulses with uniform or exponential distributions. Also, the martingale technique is applied for approximations of expectations accuracy is veryfying with the help of Monte-Carlo simulations.first passage times; laplace transformation; martingales; integro-differential equations; filtered poisson process; ornstein-uhlenbeck process

On a make-to-stock production/mountain model with hysteretic control

We consider a make-to-stock production-inventory model with one machine that produces stock in a buffer. The machine is subject to breakdowns. During up periods, the machine fils the buffer at a level-dependent rate a(x) > 0. During down periods, the production rate is zero, and the demand rate is either ß(x) > 0 or ¿(x) > 0 when the inventory level is x; which of the two demand rates applies depends on a hysteretic control policy. We determine the conditions under which the steady-state distribution of the inventory level exists, and we derive that distribution. Other performance measures under consideration are the number of switches from ß(.) to ¿(.) per busy period, the busy period distribution, and the overshoot above a particular hysteretic level

Aspects of the conservation biology of an exploited population of migratory European river lamprey (Lampetra fluviatilis)

Populations of anadromous lampreys across the globe have declined in recent years as a result of anthropogenic impacts. One such species is the European river lamprey, Lampetra fluviatilis, which has declined due to the consequences of factors such as pollution, over-exploitation and anthropogenic barriers. The Humber River Basin contains one of Western Europe’s most important populations of L. fluviatilis but this population may be threatened by the impacts of anthropogenic barriers and commercial exploitation for angling bait. This thesis’s objectives were two-fold. Firstly, to evaluate the efficiency of a semi-formalised nature like bypass specifically designed, but previously untested, to allow upstream passage of migrating river lamprey past a weir at the tidal limit. Secondly, to determine the proportion of UK coarse predator anglers who use lamprey as bait and to gauge their opinions and knowledge regarding the use of lamprey as bait. Passive Integrated Transponder and acoustic telemetry indicated that although attraction efficiency into the bypass was high, up to 70.8 % (calculated as the number of acoustically tagged lamprey that entered the bypass as a percentage of those detected downstream of the weir), the bypass was very inefficient with an estimated passage efficiency of 5.4 % (calculated as the number of PIT tagged lamprey which successfully used the bypass to travel upstream of Naburn weir as a percentage of those that were detected within the bypass during the period of time that the most upstream PIT antennas was operational). Most lamprey that passed the weir directly when the weir was drowned rather than using the bypass. It appears that periods of high river stage increased attraction into the bypass but also created conditions unsuitable for passage through the bypass due to high velocities, especially at an undershot control sluice at the upstream end. Telephone questionnaires of freshwater predator (principally pike, Esox lucius) anglers revealed that 67.8 % of participants used lamprey as bait to some degree and 39.1 % of participants would prefer lamprey to be sourced from the UK. Although participants knew little about the source of their lamprey, they generally agreed that bait companies should source their baits sustainably, that lamprey should be conserved and if lampreys were threatened by exploitation, a ban on their use as angling bait should be implemented. However, the results indicate the existence of a subset of anglers who highly value lamprey as bait and so may oppose conservation efforts or restrictions on use. Overall, this thesis indicates that upstream passage solutions for weaker swimming fish should be focused on removing redundant barriers in waterways rather than creating novel designs for fishways. Additionally, the lack of knowledge surrounding the origin of angling baits combined with the widespread use of threatened species highlights the lack of transparency within the angling bait industry, an issue that deserves further investigation

Adaptive Power Control for Energy Harvesting Communication Systems

Sustaining energy requirement for wireless devices is the main barrier in building autonomous communication systems and service-free networks. Specifically, in large-scale networks where normally wired energy infrastructures are unavailable, regular battery maintenance for each individual node is inefficient or unfeasible. To resolve this problem, current and future state of the art technologies are focused on development of perpetual energy resources by harvesting free energy in the environment such as kinetic, thermal, solar, or wind energies. However, the integration of energy harvesting architectures with communication systems requires innovating adaptive transmission power policies. In this thesis, we investigate the structure of efficient transmission power policies for a multiple access communication system with energy harvesting nodes where the utility function is taken to be the long-term average sum-throughput. We assume a causal structure for energy arrivals and study the problem in the continuous time regime. For this setting, we first characterize a \textit{storage dam} model that captures the dynamics of a battery with energy harvesting and variable transmission power. Using this model, we next establish an upper bound on the throughput problem as a function of battery capacity. We also formulate a non-linear optimization problem to determine optimal achievable power policies for transmitters. Applying the calculus of variation technique, we derive Euler-Lagrange equations as necessary conditions for optimum power policies in terms of a system of coupled partial integro-differential equations (PIDEs). Based on a Gauss-Seidel algorithm, we then devise an iterative algorithm to solve these equations. Finally, we propose a fixed-point algorithm for the symmetric multiple access setting in which the statistical descriptions of energy harvesters are identical. To support our iterative algorithms, comprehensive numerical results are also obtained