On Queueing Delay in a Model of Wireless Network Node with Breakdowns

The paper is devoted to the transient analysis of the probability distribution of the queueing delay in the model of a network node with transmitter/receiver failures. The model assumes that the input stream of messages arriving at the node is described by a Poisson process, and the processing time of a single message and the time of a one-time failure-free operation have exponential probability distributions. The removal time of a single failure can have an arbitrary probability distribution. The representation for the conditional probability distribution of the queueing delay at any fixed time instant t in terms of the Laplace transform is obtained using the matrix-based approach. Numerical examples are also attached.