Several cellular mobile network operators are considering deployment of 5G New Radio (NR) services in the millimeter wave (mmWave) bands. One specific 5G NR architecture that will facilitate easier adoption and minimize capital expenditures for the Mobile Network Operator (MNO) is called Integrated Access and Backhaul (IAB). IAB is a multi-hop, self-backhauling topology that enables wireless backhauling of Gbps of data rate over ultra-wide operational bandwidths thus avoiding the need for wired, Fiber connectivity to each base station. While IAB networks significantly reduce deployment barriers of 5G solution in mmWave bands, meeting Quality of Service (QoS) requirements for different packet flows in a wireless multi-hop network have significant constraints that do not manifest in a single-hop network. In this research work, we develop a novel Long Availability Indicator (LAI) Packet scheduling algorithm at each node of a 4-hop IAB mesh network and adapt the algorithm at each node as the packet traverses the 4-hop mesh network. The LAI Packet scheduler periodically determines, for each node at each hop level, the dynamic ratio of time slots per unit time that are to be used for packet forwarding to next hop node and for scheduling mobiles in current hop. We analyze mean data rates and mean latencies at each hop level for different time slot allocation ratios, termed Availability Indicator (AI) Weight Vector, of the LAI Packet scheduling algorithm. We compare the LAI Packet scheduler’s performance against a round-robin (RR) scheduler. We present via extensive modeling of the IAB network, that the choice of AI Weight Vector at the very first hop considerably influences the efficiency of the IAB network. We show that there exists a sweet spot for the initial weight of the AI Weight Vector for the call model we have tested with. Further, we demonstrate that the AI Weight Vector at all intermediate hops must be adapted dynamically based on the choice of initial AI Weight Vector selected at first hop. We also show that traditional paradigms such as RR not only degrade IAB network performance, but they are also not viable at all within the IAB framework.