Retrial queue

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

Analysis of Dynamic and Adaptive Retrial Queue System with the Incoming MAP-Flow of Requests

Abstract: In the paper, the dynamic and adaptive RQ-systems with incoming MAP-flow of requests are investigated with the method of asymptotic analysis. It is shown that the dynamic and the adaptive RQ-systems are asymptotically equivalent. The results obtained by investigating the dynamic RQ-systems can be used to determine the probability distribution of customers in the orbit of the adaptive RQ-systems.

Equilibrium customer and socially optimal balking strategies in a constant retrial queue with multiple vacations and $N$-policy

Abstract: In this paper, equilibrium strategies and optimal balking strategies of customers in a constant retrial queue with multiple vacations and the N-policy under two information levels, respectively, are investigated. We assume that there is no waiting area in front of the server and an arriving customer is served immediately if the server is idle; otherwise (the server is either busy or on a vacation) it has to leave the system to join a virtual retrial orbit waiting for retrials according to the FCFS rules. After a service completion, if the system is not empty, the server becomes idle, available for serving the next customer, either a new arrival or a retried customer from the virtual retrial orbit; otherwise (if the system is empty), the server starts a vacation. Upon the completion of a vacation, the server is reactivated only if it finds at least N customers in the virtual orbit; otherwise, the server continues another vacation. We study this model at two levels of information, respectively. For each level of information, we obtain both equilibrium and optimal balking strategies of customers, and make corresponding numerical comparisons. Through Particle Swarm Optimization (PSO) algorithm, we explore the impact of parameters on the equilibrium and social optimal thresholds, and obtain the trend in changes, as a function of system parameters, for the optimal social welfare, which provides guiding significance for social planners. Finally, by comparing the social welfare under two information levels, we find that whether the system information should be disclosed to customers depends on how to maintain the growth of social welfare.

Idle time utilization through service to customers in a retrial queue maintaining high system reliability

Abstract: We consider a k-out-of-n system in which life times of components are exponentially distributed with parameter λ/i, when there are i operational components. There is a single server who repairs the failed components. In addition, service is rendered to external customers also when there are no failed components (main customers). The external customers arrive according to a BM AP. If the arriving batch of external customers finds a free server, one among them gets into service and others, if any, move to an orbit of infinite capacity. If an arriving batch sees a busy server, the whole batch moves to the orbit. The inter-retrial times are exponentially distributed with parameter αi when there are i customers in the orbit. The external customer gets service only when the server is idle and its service is assumed to be nonpreemptive. The service times of main and external customers follow arbitrary distributions B1(· )a ndB2(·), respectively. The stability condition and steady-state distribution are obtained. Some performance measures are computed and numerical illustrations provided. In this paper we discuss the reliability of a k-out-of-n system subject to repair of failed components by a server in a retrial queue. A k-out-of-n system is characterized by the fact that the system operates as long as there are at least k operational components. We assume that the k-out-of-n system is cold. The system is cold in the sense that operational components do not fail while the system is in a down state (number of failed components at that instant is n − k + 1). Using the same analysis as employed in this paper, one can study the warm and hot systems also (a k-out-of- n system is called a hot system if operational components continue to deteriorate at the same rate while the system is down as when it is up. The system is warm if the deterioration rate while the system is up differs from that when it is down). A repair facility, consisting of a single server, repairs the failed components one at a time. The life-times of components are independent and exponentially distributed random variables with parameter λ/i when i components are operational. Thus on average, λ failures take place in unit time when the system operates with i components. The failed components are sent to the repair facility and are repaired one at a time. The waiting space has capacity to accommodate a maximum of n − k + 1 units in addition to the unit undergoing service. Service times of main customers (components of the k-out-of-n system) are independent identically distributed random variables with distribution function B1(t). In addition to repairing failed components of the system, the repair facility provides service to external customers. However these customers are entertained only when the server is idle (no component of the main system is in repair nor even waiting). These customers are not allowed to use the waiting space at the repair facility. So when external customers arrive for service (arrival process is BM AP) while the server is busy serving a component of the system or an external customer, they are directed to an orbit and try their luck after a random length of time, exponentially distributed with parameter αi when there are i customers in orbit. For a brief description of BM AP we refer to [12] and for an extensive literature survey to [3]. We stress the fact that at the instant when an external customer undergoes service if a component of the system fails, the latter’s repair starts only on completion of service of the external customer. That is, external customers are provided nonpreemptive service. The service times of external customers are independent identically distributed random variables with distribution function B2(t). Since external arrivals form a BM AP, either all in an arriving batch will proceed to an orbit on encountering a busy server or else one among the customers in the batch proceeds for service and the rest are directed to the orbit if the server is idle at that arrival epoch.

Performance Analysis of M/G/1 Retrial Queue with Finite Source Population Using Markov Regenerative Stochastic Petri Nets.

Abstract: This paper aims to present an approach for modeling and analyzing an M/G/1//2 retrial queue, using the MRSPN ( Markov Regenerative Stochastic Petri Nets ) tool. The consideration of the retrials and finite source population introduce analytical di culties. The expressive power of the MRSPN formalism provides us with a detailed modeling of retrial systems. In addition to this modeling, this formalism gives us a qualitative and a quantitative analysis which allow us to obtain the steady state performance indices. Indeed, some illustrative numerical results will be given by using the software package Time Net.

Modified Bernoulli vacation batch arrival and retrial clients in a single server queuing model with server utilization

Abstract: This paper investigates a batch arrival feedback retrial queue with two types of service under modified Bernoulli vacation where each type consists of an optional re-service where the busy server is subjected to starting failures In Poisson form, the consumer comes to the system in batches but can also baulk at certain specific times. Customers may re-service the same type without joining the orbit after the completion of each type of service or may leave the system. The server either goes on vacation at the completion stage of each service or can wait for the next client to serve. The model is analysed during the supplementary variable technique and the probability generating function of system size, the server utilization and the probability that the system is empty are found. Stochastic decomposition law is shown to hold good for this model also when there is no bulking permitted along with other performance measures to predict the behaviour of the system are derived. Further, we carry out some special cases for the proposed model.