### A bulk queueing system under $N$-policy with bilevel service delay discipline and start-up time.

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This paper concerns a discrete time Geo[X]/G/1 retrial queue with general retrial time in which all the arriving customers require first essential service with probability ${\alpha}_{0}$ while only some of them demand one of other optional services: type − r (r = 1, 2, 3,...M) service with probability ${\alpha}_{r}$. The system state distribution, the orbit size and the system size distributions are obtained in terms of generating functions. The stochastic decomposition law holds for the proposed model. Performance measures...

In this paper, application of an evolutionary strategy to positioning a GI/M/1/N-type finite-buffer queueing system with exhaustive service and a single vacation policy is presented. The examined object is modeled by a conditional joint transform of the first busy period, the first idle time and the number of packets completely served during the first busy period. A mathematical model is defined recursively by means of input distributions. In the paper, an analytical study and numerical experiments...

We consider the steady-state behavior of random walks in the quarter-plane, in particular, the expected value of performance measures that are component-wise linear over the state space. Since the stationary distribution of a random walk is in general not readily available we establish upper and lower bounds on performance in terms of another random walk with perturbed transition probabilities, for which the stationary distribution is a geometric product-form. The Markov reward approach as developed...

We identify the regions of parameters of the arriving stream in which the ergodic, critical, or supercritical properties of the branching chain are established.