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The aim of this paper is to analyze the queuing model entitled to cost optimization in bulk arrival and a batch service retrial queuing system with threshold, server failure, non-disruptive service, and multiple vacations. When bulk arrival of customers find the server is busy, then all customers will join in the orbit. On the other hand, if the server is free, then batch service will be provided according to the general bulk service rule. Batch size varies from a minimum of one and a maximum of ‘b’ number of customers. Customers in the orbit seek service one by one through constant retrial policy whenever the server is in idle state. The server may encounter failure during service. If the server fails, then ‘renewal of service station’ will be considered with probability . If there is no server failure with probability in the service completion or after the renewal process and if the orbit is empty, the server then leaves for multiple vacations. The server stays on vacation until the orbit size reaches the value N. For this proposed queuing model, a probability generating function of the orbit size will be obtained by using the supplementary variable technique and various performance measures will be presented with suitable numerical illustrations. A real time application is also discussed for this system. Additionally, a cost effective model is developed for this queuing model.

In this paper, we analyze a priority queueing system with a regular queue and an orbit. Customers in the regular queue have priority over the customers in the orbit. Only the first customer in the orbit (if any) retries to get access to the server, if the queue and server are empty (constant retrial policy). In contrast with existing literature, we assume different service time distributions for the high- and low-priority customers. Closed-form expressions are obtained for the probability generating functions of the number of customers in the queue and orbit, in steady-state. Another contribution is the extensive singularity analysis of these probability generating functions to obtain the stationary (asymptotic) probability mass functions of the queue and orbit lengths. Influences of the service times and the retrial policy are illustrated by means of some numerical examples. [ABSTRACT FROM AUTHOR]

The aim of this paper is to analyze the queuing model entitled to cost optimization in bulk arrival and a batch service retrial queuing system with threshold, server failure, non-disruptive service, and multiple vacations. When bulk arrival of customers find the server is busy, then all customers will join in the orbit. On the other hand, if the server is free, then batch service will be provided according to the general bulk service rule. Batch size varies from a minimum of one and a maximum of ‘b’ number of customers. Customers in the orbit seek service one by one through constant retrial policy whenever the server is in idle state. The server may encounter failure during service. If the server fails, then ‘renewal of service station’ will be considered with probability δ. If there is no server failure with probability 1 – δ in the service completion or after the renewal process and if the orbit is empty, the server then leaves for multiple vacations. The server stays on vacation until the orbit size reaches the value N. For this proposed queuing model, a probability generating function of the orbit size will be obtained by using the supplementary variable technique and various performance measures will be presented with suitable numerical illustrations. A real time application is also discussed for this system. Additionally, a cost effective model is developed for this queuing model. [ABSTRACT FROM AUTHOR]

We mathematically investigate a single server system accepting two types of retrial customers and paired service. If upon arrival a customer finds the server busy, it is routed to an infinite capacity orbit queue according to each type. Upon a service completion epoch, if at least one orbit queue is non-empty, the server seeks to find customers from the orbits. If both orbit queues are non-empty, the seeking process will bring to the service area a pair of customers, one from each orbit. If there is only one non-empty, then a single customer from this orbit queue will be brought to the service area. However, if a primary customer arrives during the seeking process it will occupy the server immediately. It is shown that the joint stationary orbit queue length distribution at service completion epochs is determined by solving a Riemann boundary value problem. Stability condition is investigated, while generalizations of the main model are also discussed. A simple numerical example is obtained and yields insight into the behavior of the system. [ABSTRACT FROM AUTHOR]

This paper analyses an M/G/1 retrial queue with working vacation and constant retrial policy. As soon as the system becomes empty, the server begins a working vacation. The server works with different service rates rather than completely stopping service during a vacation. We construct the mathematical model and derive the steady-state queue distribution of number of customer in the retrial group. The effects of various performance measures are derived. [ABSTRACT FROM PUBLISHER]

In the recent paper Phung-Duc (Oper Res Int, doi:, ) considered a tandem queue with retrials and losses and obtained the joint stationary distribution of the servers states and the number of customers in the retrial group for the constant retrial policy, the classical retrial policy and the linear retrial policy. We suggest an alternative method for analysis of the models which allows to find this distribution for a general retrial policy. For any specific retrial policy our approach gives a solution in much simpler terms as compared with Phung-Duc (Oper Res Int, doi:, ). [ABSTRACT FROM AUTHOR]

We analyze the non-preemptive assignment of a single server to two infinite-capacity retrial queues. Customers arrive at both queues according to Poisson processes. They are served on first-come-first-served basis following a cost-optimal routing policy. The customer at the head of a queue generates a Poisson stream of repeated requests for service, that is, we have a constant retrial policy. All service times are exponential, with rates depending on the queues. The costs to be minimized consist of costs per unit time that a customer spends in the system. In case of a scheduling problem that arise when no new customers arrive an explicit condition for server allocation to the first or the second queue is given. The condition presented covers all possible parameter choices. For scheduling that also considers new arrivals, we present the conditions under which server assignment to either queue 1 or queue 2 is cost-optimal. [ABSTRACT FROM AUTHOR]