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This paper studies the machine repair
problem consisting of M operating machines with S spare
machines, and R servers (repairmen) who leave for a vacation of
random length when there are no failed machines queuing up for
repair in the repair facility. At the end of the vacation the
servers return to the repair facility and operate one of three
vacation policies: single vacation, multiple vacation, and hybrid
single/multiple vacation. The Markov process and the
matrix-geometric approach are used...
This paper considers an M/M/R/N queue with heterogeneous servers in which customers balk (do not enter) with a constant probability . We develop the maximum likelihood estimates of the parameters for the M/M/R/N queue with balking and heterogeneous servers. This is a generalization of the M/M/2 queue with heterogeneous servers (without balking), and the M/M/2/N queue with balking and heterogeneous servers in the literature. We also develop the confidence interval formula for the parameter , the...
This paper considers an M/M/R/N queue with heterogeneous
servers in which customers balk (do not enter) with a constant
probability (1 - b). We develop the maximum likelihood
estimates of the parameters for the M/M/R/N queue with balking and
heterogeneous servers. This is a generalization of the M/M/2
queue with heterogeneous servers (without balking), and the
M/M/2/N queue with balking and heterogeneous servers in the
literature. We also develop the confidence interval formula for
the parameter...
Consider an M/M/1 retrial queue with collisions and working vacation interruption under N-policy. We use a quasi birth and death process to describe the considered system and derive a condition for the stability of the model. Using the matrix-analytic method, we obtain the stationary probability distribution and some performance measures. Furthermore, we prove the conditional stochastic decomposition for the queue length in the orbit. Finally, some numerical examples are presented.
In the Hammersley–Aldous–Diaconis process, infinitely many particles sit in ℝ and at most one particle is allowed at each position. A particle at x, whose nearest neighbor to the right is at y, jumps at rate y−x to a position uniformly distributed in the interval (x, y). The basic coupling between trajectories with different initial configuration induces a process with different classes of particles. We show that the invariant measures for the two-class process can be obtained as follows. First,...
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