Branching processes, the max-plus algebra and network calculus

Branching processes can describe the dynamics of various queueing systems, peer-to-peer systems, delay tolerant networks, etc. In this paper we study the basic stochastic recursion of multitype branching processes, but in two non-standard contexts. First, we consider this recursion in the max-plus algebra where branching corresponds to finding the maximal offspring of the current generation. Secondly, we consider network-calculus-type deterministic bounds as introduced by Cruz, which we extend to handle branching-type processes. The paper provides both qualitative and quantitative results and introduces various applications of (max-plus) branching processes in queueing theory

An energy-efficient distributed dynamic bandwidth allocation algorithm for Passive Optical Access Networks

The rapid deployment of passive optical access networks (PONs) increases the global energy consumption of networking infrastructure. This paper focuses on the minimization of energy consumption in Ethernet PONs (EPONs). We present an energy-efficient, distributed dynamic bandwidth allocation (DBA) algorithm able to power off the transmitter and receiver of an optical network unit (ONU) when there is no upstream or downstream traffic. Our main contribution is combining the advantages of a distributed DBA (namely, a smaller packet delay compared to centralized DBAs, due to less time being needed to allocate the transmission slot) with energy saving features (that come at a price of longer delays due to the longer queue waiting times when transmitters are switched off). The proposed algorithm analyzes the queue size of the ONUs in order to switch them to doze/sleep mode when there is no upstream/downstream traffic in the network, respectively. Our results show that we minimized the ONU energy consumption across a wide range of network loads while keeping delay bounded.Postprint (published version

A Flow-aware MAC Protocol for a Passive Optical Metropolitan Area Network

The paper introduces an original MAC protocol for a passive optical metropolitan area network using time-domain wavelength interleaved networking (TWIN)% as proposed recently by Bell Labs . Optical channels are shared under the distributed control of destinations using a packet-based polling algorithm. This MAC is inspired more by EPON dynamic bandwidth allocation than the slotted, GPON-like access control generally envisaged for TWIN. Management of source-destination traffic streams is flow-aware with the size of allocated time slices being proportional to the number of active flows. This emulates a network-wide, distributed fair queuing scheduler, bringing the well-known implicit service differentiation and robustness advantages of this mechanism to the metro area network. The paper presents a comprehensive performance evaluation based on analytical modelling supported by simulations. The proposed MAC is shown to have excellent performance in terms of both traffic capacity and packet latency

Age Optimal Information Gathering and Dissemination on Graphs

We consider the problem of timely exchange of updates between a central station and a set of ground terminals $V$, via a mobile agent that traverses across the ground terminals along a mobility graph $G = (V, E)$. We design the trajectory of the mobile agent to minimize peak and average age of information (AoI), two newly proposed metrics for measuring timeliness of information. We consider randomized trajectories, in which the mobile agent travels from terminal $i$ to terminal $j$ with probability $P_{i,j}$. For the information gathering problem, we show that a randomized trajectory is peak age optimal and factor-$8\mathcal{H}$ average age optimal, where $\mathcal{H}$ is the mixing time of the randomized trajectory on the mobility graph $G$. We also show that the average age minimization problem is NP-hard. For the information dissemination problem, we prove that the same randomized trajectory is factor-$O(\mathcal{H})$ peak and average age optimal. Moreover, we propose an age-based trajectory, which utilizes information about current age at terminals, and show that it is factor-$2$ average age optimal in a symmetric setting

A Priority-based Fair Queuing (PFQ) Model for Wireless Healthcare System

Healthcare is a very active research area, primarily due to the increase in the elderly population that leads to increasing number of emergency situations that require urgent actions. In recent years some of wireless networked medical devices were equipped with different sensors to measure and report on vital signs of patient remotely. The most important sensors are Heart Beat Rate (ECG), Pressure and Glucose sensors. However, the strict requirements and real-time nature of medical applications dictate the extreme importance and need for appropriate Quality of Service (QoS), fast and accurate delivery of a patient’s measurements in reliable e-Health ecosystem. As the elderly age and older adult population is increasing (65 years and above) due to the advancement in medicine and medical care in the last two decades; high QoS and reliable e-health ecosystem has become a major challenge in Healthcare especially for patients who require continuous monitoring and attention. Nevertheless, predictions have indicated that elderly population will be approximately 2 billion in developing countries by 2050 where availability of medical staff shall be unable to cope with this growth and emergency cases that need immediate intervention. On the other side, limitations in communication networks capacity, congestions and the humongous increase of devices, applications and IOT using the available communication networks add extra layer of challenges on E-health ecosystem such as time constraints, quality of measurements and signals reaching healthcare centres. Hence this research has tackled the delay and jitter parameters in E-health M2M wireless communication and succeeded in reducing them in comparison to current available models. The novelty of this research has succeeded in developing a new Priority Queuing model ‘’Priority Based-Fair Queuing’’ (PFQ) where a new priority level and concept of ‘’Patient’s Health Record’’ (PHR) has been developed and integrated with the Priority Parameters (PP) values of each sensor to add a second level of priority. The results and data analysis performed on the PFQ model under different scenarios simulating real M2M E-health environment have revealed that the PFQ has outperformed the results obtained from simulating the widely used current models such as First in First Out (FIFO) and Weight Fair Queuing (WFQ). PFQ model has improved transmission of ECG sensor data by decreasing delay and jitter in emergency cases by 83.32% and 75.88% respectively in comparison to FIFO and 46.65% and 60.13% with respect to WFQ model. Similarly, in pressure sensor the improvements were 82.41% and 71.5% and 68.43% and 73.36% in comparison to FIFO and WFQ respectively. Data transmission were also improved in the Glucose sensor by 80.85% and 64.7% and 92.1% and 83.17% in comparison to FIFO and WFQ respectively. However, non-emergency cases data transmission using PFQ model was negatively impacted and scored higher rates than FIFO and WFQ since PFQ tends to give higher priority to emergency cases. Thus, a derivative from the PFQ model has been developed to create a new version namely “Priority Based-Fair Queuing-Tolerated Delay” (PFQ-TD) to balance the data transmission between emergency and non-emergency cases where tolerated delay in emergency cases has been considered. PFQ-TD has succeeded in balancing fairly this issue and reducing the total average delay and jitter of emergency and non-emergency cases in all sensors and keep them within the acceptable allowable standards. PFQ-TD has improved the overall average delay and jitter in emergency and non-emergency cases among all sensors by 41% and 84% respectively in comparison to PFQ model