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

Performance modeling tools with applications

This paper deals with the role of performance modeling tools. It introduces 3 major tool development centers and shows how a given tool can be applied to investigate the performance of a finite-source retrial queueing system

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

An integrated approach to solving retrial queue complexity

Retrial queues have been proposed in literature as a means of managing lost traffic in wireless cellular networks. However, the retrial queue system has led to a more complex Markovic process in network analysis. This complexity is further worsened by the addition of handover prioritization. In this paper, a solution that can minimize this complexity has been studied. The solution involves an integration of computational and analytical modeling techniques. The work was simulated and tested in Matlab/Simulink with guard channels as a handover prioritization scheme. Further evaluations were carried out on the effect of blocking probability (PB) as a quality of service (QoS) parameter. Numerical results obtained from the integrated approach show that the retrial queue reduces the PB for all requests (new and handover). The result obtained from this paper simplifies the solution to the complexity found in retrial queue systems. Furthermore, it was also deduced that reduced retrial rate with corresponding increase in the retrial queue size improves the network quality without an increase in system complexity.Keywords: Markov, retrial, probability, network, traffi

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