Modeling Wireless Sensor Networks Using Finite-Source Retrial Queues with Unreliable Orbit

Abstract. Motivated by the need for performance models suitable for modeling and evaluation of wireless sensor networks, we introduce a retrial queueing system with a finite number of homogeneous sources, unreliable servers, orbital search, and unreliable orbit. All random variables involved in model construction are assumed to be independent and exponentially distributed. Providing a generalized stochastic Petri net model of the system, steady-state analysis of the underlying continuous-time Markov chain is performed and steady-state performance measures are computed by the help of the MOSEL-2 tool. The main novelty of this investigation is the introduction of an unreliable orbit and its application to wireless sensor networks. Numerical examples are derived to show the influence of sleep/awake time ratio, message dropping, and message blocking on the senor nodes' performance

Asymptotic waiting time analysis of finite source M/GI/1 retrial queueing systems with conflicts and unreliable server

The goal of the present paper is to analyze the steady-state distribution of the waiting time in a finite source M/G/1 retrial queueing system where conflicts may happen and the server is unreliable. An asymptotic method is used when the number of source N tends to infinity, the arrival intensity from the sources, the intensity of repeated calls tend to zero, while service intensity, breakdown intensity, recovery intensity are fixed. It is proved that the limiting steady-state probability distribution of the number of transitions/retrials of a customer into the orbit is geometric, and the waiting time of a customer is generalized exponentially distributed. The average total service time of a customer is also determined. Our new contribution to this topic is the inclusion of breakdown and recovery of the server. Prelimit distributions obtained by means of stochastic simulation are compared to the asymptotic ones and several numerical examples illustrate the power of the proposed asymptotic approach

Numerical Analysis of Finite Source Markov Retrial System with Non-Reliable Server, Collision, and Impatient Customers

A retrial queuing system with a single server is investigated in this paper. The server is subject to random breakdowns. The number of customers is finite and collision may take place. A collision occurs when a customer arrives to the busy server. In case of a collision both customers involved in the collision are sent back to the orbit. From the orbit the customers retry their requests after a random waiting time. The server can be down due to a failure. During the failed period the arriving customers are sent to the orbit, as well. The novelty of this analysis is the impatient behaviour of the customers. A customer waiting in the orbit may leave it after a random waiting time. The requests of these customers will not be served. All the random variables included in the model construction are assumed to be exponentially distributed and independent from each other. The impatient property makes the model more complex, so the derivation of a direct algorithmic solution (which was provided for the non-impatient case) is difficult. For numerical calculations the MOSEL-2 tool can be used. This tool solves the Kolmogorov system equations, and from the resulting steady-state probabilities various system characteristics and performance measures can be calculated, i.e. mean response time, mean waiting time in the orbit, utilization of the server, probability of the unserved impatient requests. Principally the effect of the impatient property is investigated in these results, which are presented graphically, as well

Energieeffiziente und rechtzeitige Ereignismeldung mittels drahtloser Sensornetze

This thesis investigates the suitability of state-of-the-art protocols for large-scale and long-term environmental event monitoring using wireless sensor networks based on the application scenario of early forest fire detection. By suitable combination of energy-efficient protocol mechanisms a novel communication protocol, referred to as cross-layer message-merging protocol (XLMMP), is developed. Qualitative and quantitative protocol analyses are carried out to confirm that XLMMP is particularly suitable for this application area. The quantitative analysis is mainly based on finite-source retrial queues with multiple unreliable servers. While this queueing model is widely applicable in various research areas even beyond communication networks, this thesis is the first to determine the distribution of the response time in this model. The model evaluation is mainly carried out using Markovian analysis and the method of phases. The obtained quantitative results show that XLMMP is a feasible basis to design scalable wireless sensor networks that (1) may comprise hundreds of thousands of tiny sensor nodes with reduced node complexity, (2) are suitable to monitor an area of tens of square kilometers, (3) achieve a lifetime of several years. The deduced quantifiable relationships between key network parameters — e.g., node size, node density, size of the monitored area, aspired lifetime, and the maximum end-to-end communication delay — enable application-specific optimization of the protocol

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

Performance Modeling of Finite-Source Cognitive Radio Networks

This paper deals with performance modeling aspects of radio frequency licensing. The utilization of mobile cellular networks can be increased by the idea of the cognitive radio. Licensed users (Primary Users - PUs) and normál users (Secondary Users - SUs) are considered. The main idea is, that the SUs are able to access to the available non-licensed radio frequencies. A finite-source retrial queueing model with two non independent frequency bands (considered as service units) is proposed for the performance evaluation of the system. A service unit with a priority queue and another service unit with an orbit are assigned to the PUs and SUs, respectively. The users are classified into two classes: the PUs have got a licensed frequency, while the SUs have got a frequency band, too but it suffers from the overloading. We assume that during the service of the non-overloaded band the PUs have preemptive priority over SUs. The involved inter-event times are supposed to be independent and exponentially distributed random variables. The novelty of this work lies in the fact that we consider the effect of retrial phenomenon of SUs in performance modeling of radio frequency licensing by using a finite-source queueing model which takes the unreliability of radio transmission into account for the first time. In the literature, most work studied the performance of cognitive radio networks under a mixed spectrum environment of licensed and unlicensed bands where the blocked SUs and the preempted SUs are forced to leave the system forever when there are no idle channels in the system. But in practical situation, the blocked SUs and the preempted SUs may do not leave the system forever and try to continue their services after random amount of time. By the help of an appropriate continuous time Markov chain using MOSEL (MOdeling Specification and Evaluation Language) tool several numerical examples are provided showing the effects of different input parameters on the main performance measures of the cognitive radio networks. Our primary focus is to determine an optimal number of SUs, where at the secondary band the gained utilization, that is when switching to the cognitive radio, has a maximum value

Numerical analysis of finite source Markov retrial system with non-reliable server, collision, and impatient customers

A retrial queuing system with a single server is investigated in this pa- per. The server is subject to random breakdowns. The number of customers is finite and collision may take place. A collision occurs when a customer arrives to the busy server. In case of a collision both customers involved in the collision are sent back to the orbit. From the orbit the customers retry their requests after a random waiting time. The server can be down due to a failure. During the failed period the arriving customers are sent to the orbit, as well. The novelty of this analysis is the impatient behaviour of the customers. A customer waiting in the orbit may leave it after a random waiting time. The requests of these customers will not be served. All the random variables included in the model construction are assumed to be exponentially distributed and independent from each other. The impatient property makes the model more complex, so the derivation of a direct algorithmic solution (which was provided for the non-impatient case) is difficult. For numerical calculations the MOSEL-2 tool can be used. This tool solves the Kolmogorov system equations, and from the resulting steady-state probabilities various system characteristics and performance measures can be calculated, i.e. mean response time, mean waiting time in the orbit, utilization of the server, probability of the unserved impatient requests. Principally the effect of the impatient property is investigated in these results, which are presented graphically, as well