Analysis of MAP/G/1 queue with inventory as the model of the node of wireless sensor network with energy harvesting

Queueing systems where certain inventory items are required to provide service to a customer have become popular in the literature from early 1990th. Such systems are similar to those models analysed in the literature models with paired customers, assembly-like queues, passenger–taxi models, etc. During the last few years they are considered in the context of modelling operation of the nodes of a wireless sensor network with energy harvesting. Distinguishing feature of the model considered in this paper, besides the suggestion that arrival flow of customers is described by the Markovian arrival process, is the assumption about a general distribution of the service time while only exponential or phase-type distribution was previously assumed in the existing literature. We apply the well-known technique of M / G /1 type Markov chains and semi-regenerative processes to obtain the ergodicity criterion in a transparent form, stationary distribution of the system under study and the Laplace–Stieltjes transform of the sojourn time distribution. This creates an opportunity to formulate and solve various optimization problems. A number of numerical examples illustrate the computational tractability of the theoretical results and illustrate the behavior of the system performance measures depending on its parameters.