Analysis of single-server queue with phase-type service and energy harvesting

Abstract

We propose a queueing model suitable, for example, for modelling operation of nodes of sensor networks. The sensor node senses a random field and generates packets to be transmitted to the central node. The sensor node has a battery of a finite capacity and harvests energy during its operation from outside (using solar cells, wind turbines, piezoelectric cells, etc.). We assume that, generally speaking, service (transmission) of a packet consists of a random number of phases and implementation of each phase requires a unit of energy. If the battery becomes empty, transmission is failed. To reduce the probability of forced transmission termination, we suggest that the packet can be accepted for transmission only when the number of energy units is greater than or equal to some threshold. Under quite general assumptions about the pattern of the arrival processes of packets and energy, we compute the stationary distributions of the system states and the waiting time of a packet in the system and numerically analyze performance measures of the system as functions of the threshold. Validity of Little's formula and its counterpart is verified.