System State Distributions In One Finite Source Unreliable Retrial Queue

The object of this paper is to study joint and marginal distributions of the system states at any arbitrary time moment for a single server, finite source retrial queue, in which the server can sustain breakdowns during service times. The server life times as well as the intervals between repetitions are exponentially distributed, while the repair and the service times are generally distributed. Unlike the unreliable model studied by J. Wang et al. [23], in which the interrupted customer waits for the server back from repair, to accomplish the remaining service, in our model this customer goes to the orbit, losing the service time, elapsed before the breakdown occurs

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

Approximate Analysis of an Unreliable M/M/2 Retrial Queue

This thesis considers the performance evaluation of an M/M/2 retrial queue for which both servers are subject to active and idle breakdowns. Customers may abandon service requests if they are blocked from service upon arrival, or if their service is interrupted by a server failure. Customers choosing to remain in the system enter a retrial orbit for a random amount of time before attempting to re-access an available server. We assume that each server has its own dedicated repair person, and repairs begin immediately following a failure. Interfailure times, repair times and times between retrials are exponentially distributed, and all processes are assumed to be mutually independent. Modeling the number of customers in the orbit and status of the servers as a continuous-time Markov chain, we employ a phase-merging algorithm to approximately analyze the limiting behavior. Subsequently, we derive approximate expressions for several congestion and delay measures. Using a benchmark simulation model, we assess the accuracy of the approximations and show that, when the algorithm assumptions are met, the approximation procedure yields favorable results. However, as the rate of abandonment for blocked arrivals decreases, the performance declines while the results are insensitive to the rate of abandonment of customers preempted by a server failure

Non-Markovian Queueing System, Mx/G/1 with Server Breakdown and Repair Times

This paper deals with the steady state behavior of an MX/G/1 queue with breakdown. It assumed that customers arrive to the system in batches of variable size, but serve one by one. The main new assumption in this paper is that the repair process does not start immediately after a breakdown and there is a delay time waiting for repairs to start. We obtain steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, the average waiting time in the queue

A Note on an M/M/s Queueing System with two Reconnect and two Redial Orbits

A queueing system with two reconnect orbits, two redial (retrial) orbits, s servers and two independent Poisson streams of customers is considered. An arriving customer of type i, i = 1, 2 is handled by an available server, if there is any; otherwise, he waits in an infinite buffer queue. A waiting customer of type i who did not get connected to a server will lose his patience and abandon after an exponentially distributed amount of time, the abandoned one may leave the system (lost customer) or move into one of the redial orbits, from which he makes a new attempt to reach the primary queue, and when a customer finishes his conversation with a server, he may comeback to the system, to one of the reconnect orbits where he will wait for another service. In this paper, a fluid model is used to derive a first order approximation for the number of customers in the redial and reconnect orbits in the heavy traffic. The fluid limit of such a model is a unique solution to a system of three differential equations

Unreliable Retrial Queues in a Random Environment

This dissertation investigates stability conditions and approximate steady-state performance measures for unreliable, single-server retrial queues operating in a randomly evolving environment. In such systems, arriving customers that find the server busy or failed join a retrial queue from which they attempt to regain access to the server at random intervals. Such models are useful for the performance evaluation of communications and computer networks which are characterized by time-varying arrival, service and failure rates. To model this time-varying behavior, we study systems whose parameters are modulated by a finite Markov process. Two distinct cases are analyzed. The first considers systems with Markov-modulated arrival, service, retrial, failure and repair rates assuming all interevent and service times are exponentially distributed. The joint process of the orbit size, environment state, and server status is shown to be a tri-layered, level-dependent quasi-birth-and-death (LDQBD) process, and we provide a necessary and sufficient condition for the positive recurrence of LDQBDs using classical techniques. Moreover, we apply efficient numerical algorithms, designed to exploit the matrix-geometric structure of the model, to compute the approximate steady-state orbit size distribution and mean congestion and delay measures. The second case assumes that customers bring generally distributed service requirements while all other processes are identical to the first case. We show that the joint process of orbit size, environment state and server status is a level-dependent, M/G/1-type stochastic process. By employing regenerative theory, and exploiting the M/G/1-type structure, we derive a necessary and sufficient condition for stability of the system. Finally, for the exponential model, we illustrate how the main results may be used to simultaneously select mean time customers spend in orbit, subject to bound and stability constraints

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