Retrial queue

About: Retrial queue is a research topic. Over the lifetime, 784 publications have been published within this topic receiving 12354 citations.

A discrete-time retrial queue with multiplicative repeated attempts

Abstract: The repeated attempts have been always made individually by each unsatisfied customer in discrete-time retrial queues. However, the time between two consecutive repeated requests can be independent of the number of customers applying for service. This paper considers a new retrial discipline, that we call multiplicative, which extends both types of repeated attempts.

A priority retrial queue with second multi optional service and m immediate Bernoulli feedbacks

Abstract: We consider an M/G/1 retrial queueing system with two phases of heterogeneous service and a finite number of immediate Bernoulli feedbacks. If an arriving customer finds an idle server, service commences immediately. Otherwise, the blocked customer either joins the infinite waiting room with probability p or leaves the service area and enters the retrial group with complementary probability q. All arriving customers are provided with the same type of service in the first phase. In the second phase, the customer has to choose from one of the several optional services which are available in the system. After having completed both phases of service, the customer is allowed to make an immediate feedback. The feedback service also consists of two phases. In the feedback, the first phase of service is of the same type as in the previous service. However, in the second phase the customer may be permitted to choose an optional service different from one chosen earlier. In this way, the customer is permitted to make a finite number feedbacks. We employ the embedded Markov chain technique to obtain a sufficient condition for the system to attain the steady state. We obtain the probability generating function of the system size and the marginal probability generating functions of the queue size and orbit size. We also obtain the distribution of the server state and some useful performance measures. We also obtain the stochastic decomposition law. We study the asymptotic behaviour under high rate of retrials. Finally, numerical calculations are used to observe system performance.

An infinite-source M/M/S retrial queuing network model with balking and impatient customers

Abstract: This paper discusses a multi-server retrial queuing system, where the customers may leave the system due to balking and impatience. Deviated from the classical retrial queue, we use a novel model that reflects the queue state, the ambition of queuing and the urgency of requests. In particular, when customers find that a certain amount of requests were in the service area, they will enter in orbit or service area. We study the interrelation of the parameters in the model, and effect of balking, retrial, and buffer size on performance measurements in the steady-state conditions. We also study the performance of the model of the queuing transaction in the computer networks under the specific parameter settings. Simulation results are presented by using OPNET Modeler tool.

A study on M/G/1 retrial queueing system with three different types of customers under working vacation policy

Abstract: This paper deals with a single server retrial queueing system with working vacations and vacation interruption. There are three different types of customers are considered, which are priority customers, ordinary customers and negative customers. The priority customers do not form any queue and have an exclusive preemptive priority to receive their services over ordinary customers. The negative customer is arriving during the service time of any positive customer, will remove the positive customer from the service. If the interrupted customer is an ordinary customer, he will leave the system. As soon as the orbit becomes empty at the time of service completion, the server goes for a working vacation. The server works at a lower speed during a working vacation period. Using the supplementary variable technique, the steady-state probability generating a function of the system and its orbit are found. Some numerical examples are presented.

Cost analysis of a bulk service retrial queue

Abstract: This paper studies a batch arrival general bulk service retrial queueing model with constant retrial rate. The primary customers arrive in bulk according to Poisson process and they get service under general bulk service rule with minimum of one customer and maximum of ‘b’ customers. If the arriving batch of customers, of size ‘ζ ’, 1≤ζ ≤ b , finds the server free, then all of them get service immediately; while, if the size of the arriving batch is more than ‘b’, then, ‘b’ customers enter the service station and the remaining ζ - b customers join the orbit. However, if an arriving batch of customers finds the server busy, then the entire batch joins the orbit in order to seek service again. The customers in the orbit will try for service one by one with a constant retrial rate ‘v’ when the server is idle. For the proposed model, the probability generating function of the steady-state queue size distribution at an arbitrary time, expected number of customers in the orbit, expected waiting time, expected length of busy period and expected length of busy cycle are obtained. The cost analysis of the queueing system is discussed. The effects of several parameters on the system are analysed numerically.