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This note introduces reliability issues to the analysis of queueing systems. We consider an M/G/1 queue with Bernoulli vacations and server breakdowns. The server uptimes are assumed to be exponential, and the server repair times are arbitrarily distributed. Using a supplementary variable method we obtain a transient solution for both queueing and reliability measures of interest. These results provide insight into the effect of server breakdowns and repairs on system performance.

In this paper, we study the two-dimensional tri-diagonal quasi-birth-and-death (QBD) process with infinite blocks and the blocks are infinite double sides tri-diagonal matrices, which has an important application in queue theory such as joining the shortest queue problem. Our objective is to develop an accurate and easily implementable algorithmic approach to compute the stationary probabilities of the process. We also give the computational complexity for the algorithm and some numerical examples.

This paper discusses continuous fractal traffic queueing models by combining the density evolution method with fractal-chaos function theory. We use fractal-chaos functions to control the input process of queueing models. By setting up and carrying out the density evolution equations, we obtain the limiting probability of the number of packets in the system with invariant measures. Simulation results are obtained to show a heavy tailed property. We believe that this model will benefit engineering applications, where the engineer just needs to adjust the parameters of S/sub (x)/ to present the appropriate models in a mobile communication process.

The paper discusses continuous fractal M/M/1 traffic models by combining the density evolution method with fractal-chaos function theory. We use fractal-chaos functions to control the input process of queueing models. By setting up and carrying out density evolution equations, we obtain the limiting probability of the number of packets in the system with invariant measures. Simulation results are obtained showing a heavy tailed property.