Analysis of Multiprogramming-Multiprocessor Retrial Queueing Systems with Bernoulli Vacation Schedule
Keywords:
Busy period, first-step principle, number of retrials, retrial queue, steady-state distribution, vacation, waiting time.Abstract
We study a Markovian finite orbit capacity retrial queue of a multiprogramming-multiprocessor computer network system in which the service channels avail vacation under Bernoulli schedule. For this system, the steady-state probabilities of the number of programs in the system and the mean number of programs in the orbit along with other descriptors of the system are obtained by adopting the matrix analytic methods. Moreover, the expressions for the Laplace-Stieltjes transforms of the busy period of the system and the waiting time of a program in the orbit are determined. The probability generating function for the number of retrials made by a program is also derived. Some key performance measures of the system and various moments of quantities of interest are discussed. Finally, extensive numerical results are carried out to reveal the influence of the system parameters on the system performance measures.
