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

Vadivukarasi Manickam, Kalidass Kaliappan

Operations Research and Decisions

2022

Vol. 32, No. 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.

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

Vadivukarasi Manickam, Kalidass Kaliappan

Operations Research and Decisions

2021

Vol. 31, No. 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.

Fitting and goodness-of-fit test of non-truncated and truncated power-law distributions

Deluca A., Corrales A.

Acta Geophysica

2013

Vol. 61, no. 6

1351--1394

Recently, Clauset, Shalizi, and Newman have proposed a systematic method to find over which range (if any) a certain distribution behaves as a power law. However, their method has been found to fail, in the sense that true (simulated) power-law tails are not recognized as such in some instances, and then the power-law hypothesis is rejected. Moreover, the method does not work well when extended to power-law distributions with an upper truncation. We explain in detail a similar but alternative proce dure, valid for truncated as well as for non-truncated power-law distributions, based in maximum likelihood estimation, the Kolmogorov–Smirnov goodness-of-fit test, and Monte Carlo simulations. An overview of the main concepts as well as a recipe for their practical implementation is provided. The performance of our method is put to test on several empirical data which were previously analyzed with less systematic approaches. We find the functioning of the method very satisfactory.