'c Policy' Batch Service Queueing System under Bernoulli Scheduled Vacation and Manual Service

’c Policy’ Batch Service Queueing System

In this paper, we introduce a new generalization of univariate and bivariate modified discrete Weibull distribution. Various properties of the univariate generalized modified discrete Weibull distribution, such as survival function, probability mass function, hazard rate function, probability generating function, and moment generating function, are derived. The joint distribution function, joint probability mass function, marginal distributions, moment generating function, and conditional distribution of the proposed bivariate distribution are derived. Parameters of the distributions are estimated using maximum likelihood estimation. The use of these distributions is illustrated using real-life datasets.

This paper describes discrete-time single arrival and single-batch service queue with reneging and vacation interruption, under policy 'c'.The system activates when the queue size reaches a predetermined point 'c' and serves all the units in a batch. if there is a queue size less than 'c', either server switches to manual service with the probability 'p', or the server takes a vacation with probability '(1-p)'. Once it starts manual service or takes a vacation, the same continues up to the queue size reaches 'c'. The inter-arrival and service time are considered to be independent and geometrically distributed.