Priority queue with batch arrival, balking, threshold recovery, unreliable server and optimal service

Abstract

The threshold policy for the restoration of an unreliable server in a service system with bulk input and balking is investigated. The arriving customers in the queueing system are classified into two categories i.e. priority and ordinary customers. The priority customers are assumed to join the system in groups according to Poisson process. The ordinary customers join the system singly and require the essential service as well as optional service on demand and only a limited number of customers can wait in the queue when the server is busy. The service times of both types of customers and life time as well as repair time of the server are governed by the exponential distribution. When the server fails during the service of the ordinary customer, the repair is done following a threshold recovery rule according to which the repair of the failed server is started only when at least q ordinary customers are accumulated in the system. In case of failure while rendering the service to the priority customers, the server is immediately sent for the repair. The matrix geometric method (MGM) has been used to establish the queue size distribution and other performance indices. To validate the suggested MGM approach, numerical simulation is carried out by taking an illustration.

Maximum Entropy Solution for M^X/G/1 Priority Reiterate G-queue Under Working Breakdown and Working Vacation

“…In these situations, service discipline is frequently implemented at networks that handle jobs based on their priority. An unreliable server with bulk arrival reiterate waiting framework which have two kinds of subscribers that possess non-preemptive priority had been investigated by Jain and Bhargava (2008). Non-preemptive services controlled by an exponential timer and repeated leisure had been looked by Katayama and Kobayashi (2007).…”

Transient analysis of N-policy queue with system disaster repair preventive maintenance re-service balking closedown and setup times

“…Introduction. Queueing models with disaster and repair have been studied by many researchers in the past few decades as they possess wide applications in modeling many practical situations related to computer networks, communication systems, etc (refer [3], [4], [7], [8], [13], [14], [15], [19], [20], [25]). Closedown the system when it becomes empty and setup the system before starting the service, play a key role in various real life situations as they support economically to minimize the expenses of an organization.…”

“…This is called the queueing model with N-policy (refer [7], [18], [20]). During this time, new arrivals are getting discouraged and may decide not to join (balk) the queue (refer [6], [8], [11], [24]). When a customer is dissatisfied with the quality of service what he received, the necessity of immediate re-service/feedback is unavoidable to the customer's point of view.…”

“…Kumar et al [11] derived the time-dependent system size probabilities of the M/M/1 queueing model. Jain [8] investigated a batch arrival queueing model with unreliable server and balking. She obtained the probability generating function of the queue size at an arbitrary epoch.…”