650 research outputs found

    Performance Evaluation of Finite-Source Cognitive Radio Networks with Impatient Customers

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    The current paper takes into consideration a cognitive radio network with impatient customers, by the help of finite-source retrial queueing system. We consider two different types of customers (Primary and Secondary) assigned to two interconnected frequency bands. A first frequency band with a priority queue and a second one with an orbit, both are respectively dedicated for the Primary Users (PUs) and Secondary Users (SUs). In case the servers are busy, both customers (Licensed and Unlicensed) join either the queue or the orbit. Before joining the orbit, secondary customers receive a random retrial time according to exponential distribution, which is the holding time before the next retry. Unlicensed users (impatient) are obliged to leave the system once their total waiting time exceeds a given maximum waiting time. The novelty of this work is the investigation of the abandonment and its impact on several performance measures of the system such as the mean response time and waiting time of users, probability of abandonment of SU, etc. Several figures illustrate the problem in question by the help of simulation

    Single server retrial queueing models.

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    Most retrial queueing research assumes that each retrial customer has its own orbit, and the retrial customers retry to enter service independently of each other. A small selection of papers assume that the retrial customers themselves form a queue, and only one customer from the retrial queue can attempt to enter at any given time. Retrial queues with exponential retrial times have been extensively studied, but little attention has been paid to retrial queues with general retrial times. In this thesis, we consider four retrial queueing models of the type in which the retrial customers form their own queue. Model I is a type of M/G/1 retrial queue with general retrial times and server subject to breakdowns and repairs. In addition, we allow the customer in service to leave the service position and keep retrying for service until the server has been repaired. After repair, the server is not allowed to begin service on other customers until the current customer (in service) returns from its temporary absence. We say that the server is in reserved mode, when the current customer is absent and the server has already been repaired. We define the server to be blocked if the server is busy, under repair or in reserved mode. In Model II, we consider a single unreliable server retrial queue with general retrial times and balking customers. If an arriving primary customer finds the server blocked, the customer either enters a retrial queue with probability p or leaves the system with probability 1 - p. An unsuccessful arriving customer from the retrial queue either returns to its position at the head of the retrial queue with probability q or leaves the system with the probability 1 - q. If the server fails, the customer in service either remains in service with probability r or enters a retrial service orbit with probability 1 - r and keeps returning until the server is repaired. We give a formal description for these two retrial queueing models, with examples. The stability of the system is analyzed by using an embedded Markov chain. We get a necessary and sufficient condition for the ergodicity of the embedded Markov chain. By employing the method of supplementary variables, we describe the state of the system at each point in time. A system of partial differential equations related to the models is derived from a stochastic analysis of the model. The steady state distribution of the system is obtained by means of probability generating functions. In steady state, some performance measures of the system are reported, the distribution of some important performance characteristics in the waiting process are investigated, and the busy period is discussed. In addition, some numerical results are given. Model III consists of a single-server retrial queue with two primary sources and both a retrial queue and retrial orbits. Some results are obtained using matrix analytic methods. Also simulation results are obtained. Model IV consists of a single server system in which the retrial customers form a queue. The service times are discrete. A stability condition and performance measures are presented.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2005 .W87. Source: Dissertation Abstracts International, Volume: 67-07, Section: B, page: 3883. Thesis (Ph.D.)--University of Windsor (Canada), 2006

    An M/G/1 Retrial Queue with Single Working Vacation

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    We consider an M=G=1 retrial queue with general retrial times and single working vacation. During the working vacation period, customers can be served at a lower rate. Both service times in a vacation period and in a service period are generally distributed random variables. Using supplementary variable method we obtain the probability generating function for the number of customers and the average number of customers in the orbit. Furthermore, we carry out the waiting time distribution and some special cases of interest are discussed. Finally, some numerical results are presented

    The busy period and the waiting time analysis of a MAP/M/c queue with finite retrial group

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    We concentrate on the analysis of the busy period and the waiting time distribution of a multi-server retrial queue in which primary arrivals occur according to a Markovian arrival process (MAP). Since the study of a model with an infinite retrial group seems intractable, we deal with a system having a finite buffer for the retrial group. The system is analyzed in steady state by deriving expressions for (a) the Laplace–Stieltjes transforms of the busy period and the waiting time; (b) the probabiliy generating functions for the number of customers served during a busy period and the number of retrials made by a customer; and (c) various moments of quantites of interest. Some illustrative numerical examples are discussed

    Performance evaluation of finite-source Cognitive Radio Networks with impatient customers

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    The current paper takes into consideration a cognitive radio network with impatient customers, by the help of finite-source retrial queueing system. We consider two different types of customers (Primary and Secondary) assigned to two interconnected frequency bands. A first frequency band with a priority queue and a second one with an orbit, both are respectively dedicated for the Primary Users (PUs) and Secondary Users (SUs). In case the servers are busy, both customers (Licensed and Unlicensed) join either the queue or the orbit. Before joining the orbit, secondary customers receive a random retrial time according to Exponential distribution, which is the holding time before the next retry. Unlicensed users (impatient) are obliged to leave the system once their total waiting time exceeds a given maximum waiting time. The novelty of this work is the investigation of the abandonment and its impact on several performance measures of the system such as the mean response time and waiting time of users, probability of abandonment of SU, etc. Several figures illustrate the problem in question by the help of simulation

    Stability Analysis of GI/G/c/K Retrial Queue with Constant Retrial Rate

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    We consider a GI/G/c/K-type retrial queueing system with constant retrial rate. The system consists of a primary queue and an orbit queue. The primary queue has cc identical servers and can accommodate the maximal number of KK jobs. If a newly arriving job finds the full primary queue, it joins the orbit. The original primary jobs arrive to the system according to a renewal process. The jobs have general i.i.d. service times. A job in front of the orbit queue retries to enter the primary queue after an exponentially distributed time independent of the orbit queue length. Telephone exchange systems, Medium Access Protocols and short TCP transfers are just some applications of the proposed queueing system. For this system we establish minimal sufficient stability conditions. Our model is very general. In addition, to the known particular cases (e.g., M/G/1/1 or M/M/c/c systems), the proposed model covers as particular cases the deterministic service model and the Erlang model with constant retrial rate. The latter particular cases have not been considered in the past. The obtained stability conditions have clear probabilistic interpretation
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