On generalized processor sharing and objective functions: analytical framework

Today, telecommunication networks host a wide range of heterogeneous services. Some demand strict delay minima, while others only need a best-effort kind of service. To achieve service differentiation, network traffic is partitioned in several classes which is then transmitted according to a flexible and fair scheduling mechanism. Telecommunication networks can, for instance, use an implementation of Generalized Processor Sharing (GPS) in its internal nodes to supply an adequate Quality of Service to each class. GPS is flexible and fair, but also notoriously hard to study analytically. As a result, one has to resort to simulation or approximation techniques to optimize GPS for some given objective function. In this paper, we set up an analytical framework for two-class discrete-time probabilistic GPS which allows to optimize the scheduling for a generic objective function in terms of the mean unfinished work of both classes without the need for exact results or estimations/approximations for these performance characteristics. This framework is based on results of strict priority scheduling, which can be regarded as a special case of GPS, and some specific unfinished-work properties in two-class GPS. We also apply our framework on a popular type of objective functions, i.e., convex combinations of functions of the mean unfinished work. Lastly, we incorporate the framework in an algorithm to yield a faster and less computation-intensive result for the optimum of an objective function

On two generalisations of the final value theorem : scientific relevance, first applications, and physical foundations

The present work considers two published generalisations of the Laplace-transform final value theorem (FVT) and some recently appeared applications of one of these generalisations to the fields of physical stochastic processes and Internet queueing. Physical sense of the irrational time functions, involved in the other generalisation, is one of the points of concern. The work strongly extends the conceptual frame of the references and outlines some new research directions for applications of the generalised theorem

Groundwater overexploitation and seawater intrusion in coastal areas of arid and semi-arid regions

The exploitation of groundwater resources is of high importance and has become very crucial in the last decades, especially in coastal areas of arid and semi-arid regions. The coastal aquifers in these regions are particularly at risk due to intrusion of salty marine water. One example is the case of Tripoli city at the Mediterranean coast of Jifarah Plain, North West Libya. Libya has experienced progressive seawater intrusion in the coastal aquifers since the 1930s because of its ever increasing water demand from underground water resources. Tripoli city is a typical area where the contamination of the aquifer in the form of saltwater intrusion is very developed. Sixty-four groundwater samples were collected from the study area and analyzed for certain parameters that indicate salinization and pollution of the aquifer. The results demonstrate high values of the parameters Electrical Conductivity, Na+, K+, Mg2+, Cl- and SO42-, which can be attributed to seawater intrusion, where Cl is the major pollutant of the aquifer. The water types according to the Stuyfzand groundwater classification are mostly CaCl, NaCl and Ca/MgMix. These water types indicate that groundwater chemistry is changed by cation exchange reactions during the mixing process between freshwater and seawater. The intensive extraction of groundwater from the aquifer reduces freshwater outflow to the sea, creates drawdown cones and lowering of the water table to as much as 25 m below mean sea level. Irrigation with nitrogen fertilizers and domestic sewage and movement of contaminants in areas of high hydraulic gradients within the drawdown cones probably are responsible for the high NO3- concentration in the region

Mobility and removal of nitrate in heterogeneous Eocene aquifers

n a study of the principles of lateral and vertical nitrate mobility and removal in unconfined heterogeneous fine sandy Eocene aquifers by long-term observation, no significant nitrate reduction could be observed over short distances (90 m) in the lateral flow direction. Decreasing oxygen contents and limited flow velocity in a downward direction (caused by clay lenses and layers) resulted in a more efficient but incomplete nitrate removal with increasing depth. Chemo-organotrophic and chemo-lithotrophic denitrification coexist in the aquifers. Recharge input of organic matter and the reactivity of sedimentary organic sources, as well as the amounts of pyrite and Fe2+-bearing minerals, control which microbiologically catalysed process finally occurs. Sharp boundaries between different redox zones do not exist due to locally changing availability of organic and inorganic electron donors used for nitrate reduction. Furthermore, preferential flow paths result in a wide spread occurrence of low concentrations of nitrate below the main denitrification zone

Analysis of priority queues with session-based arrival streams

In this paper, we analyze a discrete-time priority queue with session-based arrivals. We consider a user population, where each user can start and end sessions. Sessions belong to one of two classes and generate a variable number of fixed-length packets which arrive to the queue at the rate of one packet per slot. The lengths of the sessions are generally distributed. Packets of the first class have transmission priority over the packets of the other class. The model is motivated by a web server handling delay-sensitive and delay-insensitive content. By using probability generating functions, some performance measures of the queue such as the moments of the packet delays of both classes are calculated. The impact of the priority scheduling discipline and of the session nature of the arrival process is shown by some numerical examples

Queues with Galton-Watson-type arrivals

This paper presents the analysis of a discrete-time single server queueing system with a multi-type Galton-Watson arrival process with migration. It is shown that such a process allows to capture intricate correlation in the arrival process while the corcesponding queueing analysis yields closed-form expressions for various moments of queue content and packet delay

Performance comparison of several priority schemes with priority jumps

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Combined analysis of transient delay characteristics and delay autocorrelation function in the Geo(X)/G/1 queue

We perform a discrete-time analysis of customer delay in a buffer with batch arrivals. The delay of the kth customer that enters the FIFO buffer is characterized under the assumption that the numbers of arrivals per slot are independent and identically distributed. By using supplementary variables and generating functions, z-transforms of the transient delays are calculated. Numerical inversion of these transforms lead to results for the moments of the delay of the kth customer. For computational reasons k cannot be too large. Therefore, these numerical inversion results are complemented by explicit analytic expressions for the asymptotics for large k. We further show how the results allow us to characterize jitter-related variables, such as the autocorrelation of the delay in steady state