Analysis of an $M^{[X]}/ G_{1}(a,b),G_{2}(a,b)/1$ unreliable G-queue with optional re-service, Bernoulli vacation, delay time to two phase of repair
Authors :
G. Ayyappan 1 and R. Supraja 2 *
Author Address :
1,2 Department of Mathematics, Pondicherry Engineering College, Pillaichavady, Puducherry - 605 014, India.
*Corresponding author.
Abstract :
In this paper, we consider the queueing system where the batch of customers arrive at the system according to the compound Poisson process and two types of service, each of which has an optional reservice is provided to the server under Bernoulli vacation. After completion of each type of service, the customer may go for reservice of the same type of service without joining the tail of the queue or they may depart the system. An unpredictable breakdown may occur at any moment during the functioning of the server with any type of service or re-service and at that situation, the service channel will breakoff for a short period of time. A breakdown in a busy server is represented by the arrival of a negative customer which consequently leads to the loss of the customer who is in service. Delay time is referred to as the waiting time of the server for the two phase of repair to start. By considering elapsed service time as the supplementary variable, the PGF of the number of customers in the queue at a random epoch is derived and this PGF is further used to establish explicitly some of the following performance measures namely various states of the system, the mean queue length, and the mean waiting time in the queue. At last, some particular cases are discussed and the numerical illustrations are provided.
Keywords :
Two types of service, Re-service, Bernoulli vacation, G-queue, Delay time to repair, Two phase of repair time.
DOI :
Article Info :
Received : July 24, 2018; Accepted : September 15, 2018.
