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Discussion on the transient behavior of single server Markovian multiple variant vacation queues

100%

VADIVUKARASI M. , KALIDASS K.

tom 31

nr 1

123-146

We consider an M/M/1 queue where beneficiary visits occur singly. Once the beneficiary level in the system becomes zero, the server takes a vacation at once. If the server finds no beneficiaries in the system, then the server can take another vacation after the return from the vacation. This process continues until the server has exhaustively taken all the J vacations. The closed form transient solution of the considered model and some important time-dependent performance measures are obtained. Further, the steady state system size distribution is obtained from the time-dependent solution. A stochastic decomposition structure of waiting time distribution and expression for the additional waiting time due to the presence of server vacations are studied. Numerical assessments are presented.

A discussion on the optimality of bulk entry queue with differentiated hiatuses

100%

VADIVUKARASI M. , KALIDASS K.

nr 2

137-150

We consider Markovian differentiated hiatuses queues with bulk entries. With the help of the matrix geometric method, we discuss the stability condition for the existence of the steady-state solution of our model and we obtain the stationary system size by using a probability generating function. The stochastic decomposition form of stationary system size and the waiting time distribution of an arbitrary beneficiary are also analysed. Furthermore, we perform the expense analysis using the particle swarm optimization technique and we obtain the optimality of service rate and hiatus rate. Finally, we study the effects of changes in the parameters on some important performance measures of the system through numerical observations.

Survival probabilities for HIV infected patients through semi-Markov processes

75%

Masala G. , Cannas G. , Micocci M.

nr 1

13-36

In this paper we apply a parametric semi-Markov process to model the dynamic evolution of HIV-1 infected patients. The seriousness of the infection is rendered by the CD4+ T-lymphocyte counts. For this purpose we introduce the main features of nonhomogeneous semi-Markov models. After determining the transition probabilities and the waiting time distributions in each state of the disease, we solve the evolution equations of the process in order to estimate the interval transition probabilities. These quantities appear to be of fundamental importance for clinical predictions. We also estimate the survival probabilities for HIV infected patients and compare them with respect to certain categories, such as gender, age group or type of antiretroviral therapy. Finally we attach a reward structure to the aforementioned semi-Markov processes in order to estimate clinical costs. For this purpose we generate random trajectories from the semi-Markov processes through Monte Carlo simulation. The proposed model is then applied to a large database provided by ISS (Istituto Superiore di Sanità, Rome, Italy), and all the quantities of interest are computed.