In this work, we present a schematic configuration and devicemodel for a graphene-nanoribbon (GNR)-array-based nanolaser, whichconsists of a three-variable rate equations that takes into accountcarrier capture and Pauli blocking in semiconductor GNR-array lasersto analyze the steadystate properties and dynamics in terms of therole of the capture rate and the gain coefficient in GNR array nanolasers.Furthermore, our GNR-array nanolaser device model can be determinedas two distinct two-variable reductions of the rate equations in thelimit of large capture rates, depending on their relative values.The first case leads to the rate equations for quantum well lasers,exhibiting relaxation oscillations dynamics. The second case correspondsto GNRs nearly saturated by the carriers and is characterized by theabsence of relaxation oscillations. Our results here demonstratedthat GNR-array as gain material embedded into a high finesse microcavitycan serve as an ultralow lasing threshold nanolaser with promisingapplications ranging widely from optical fiber communication withincreasing data processing speed to digital optical recording andbiology spectroscopy.