Departure counting process in a wireless network node with sleep mode modelled via repeated vacations

Abstract

A finite-capacity queueing model with Poisson packet arrivals and generally-distributed processing times is investigated. The system operates under the multiple vacation policy, i.e. every time when the server becomes idle a number of independent vacation times is initialized until at least one packet is accumulated in the buffer. Using the analytical approach based on the concept of embedded Markov chain and total probability law, the explicit representation for the mixed double transform of the probability distribution of the number of packets completely processed until the given time t is found. Hence the mean number of departures in a fixed-length time period can be obtained easily. The considered queueing system can be efficiently used in modelling the nodes in wireless telecommunication networks, where the multiple vacation policy is a kind of energy saving mechanism. An illustrating numerical example is attached.