A Discrete Time (a, c, d) Policy Bulk Service Queue with Accessible and Non-accessible Batches

A Discrete Time (a, c, d) Policy Bulk Service Queue

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.

In this paper we consider a discrete time (a, c, d) policy bulk service queue
with accessible and non-accessible batches. Here the server begins service only if the number of units in the queue (n) is at least c and serves a maximum of d units in a batch, with or without accessibility to the batches of ongoing service according as the on going service batch size is less than b or not. The server continue to serve even when the system size is less than c but not less than a secondary limit a(a c b d), after a service completion epoch. The analysis of the model is considered and the steady state probabilities, expected queue length, expected cost function and optimality problem are obtained.