## 3 System Model
### Packet Transmission  
Any sector at any network node can have associated UEs. The IAB network transfers packets between the UEs and the core network, to which the IAB-donor is fiber-backhauled. Because mmWave NR is capable of extremely high data rates and this work is specifically focused on the TDM-induced delay, we assumed that the radio transmission of a packet between nodes or between a node and a UE occurs instantaneously. However, since not all the links can be active at the same time due to TDM, packets have to be buffered and wait for the link to be activated.  
As is shown in Figure 4, we let each sector of each node have one backhaul (BH) and two access buffers, one outbound (or downlink, \(AC_{DL}\)) and one inbound (or uplink, \(AC_{UL}\)). The inbound access buffer is an abstraction representing the packets waiting for uplink transmission at all UEs associated with the sector. The outbound access buffer contains the packets destined to the UEs associated with the sector. The backhaul buffer contains the packets waiting for transmission via the backhaul link supported by the sector antenna. It can correspond to either the downlink or uplink direction depending on whether the connected node is, respectively, farther from or closer to Node 1.  
Consider a packet traveling from a UE (uplink) associated with sector \(i\) of node \(n\) (denoted as \((n,i)\)). Let node \(n\) belong to tier \(k\). First, the packet arrives at the inbound (uplink) access buffer of sector \((n,i)\). Then, upon activation of the uplink access link in sector \((n,i)\), the packet reaches the node. If \(n=1\) (the node is the IAB-donor), then the packet leaves the system right away. If \(n>1\), then the packet instantaneously moves to the backhaul buffer of a sector \((n,j)\) facing tier \(k-1\), i.e., of a sector linking node \(n\) to a node belonging to tier \(k-1\) (it is possible that \(j=i\)). For the packet to move the next hop towards the IAB-donor, the link between node \(n\) and node \(m\) such that \(M_{n,m}=j\) must be activated. As soon as this happens, the packet arrives at node \(m\). Then again, if \(m=1\), the  
Figure 3: Example of an IAB RAN.  
packet leaves the system, and if \(m>1\), then the packet joins the backhaul buffer in the sector facing tier \(k-2\). The process continues until the packet reaches Node 1 and leaves the system. By the total packet delay in the uplink, we understand the time from the instant the packet joins the inbound access buffer in its sector to the instant it leaves the system.  
Next, consider a packet traveling downlink, from the core network to a UE in sector \((n,i)\), with node \(n\) belonging to tier \(k\). If \(n=1\), then the packet enters the system by joining the outbound access buffer in sector \((1,i)\) and leaves as soon as the corresponding access link is activated. If \(n>1\), then the packet first joins the backhaul buffer in a sector \((1,j)\) linked to node \(n\) if \(k=2\) or to a Tier 2 node through which node \(n\) can be reached. Once the backhaul link is activated, the packet arrives at node \(m\) such that \(M_{1,m}=j\). If \(m=n\), then the packet joins the outbound access buffer in the destination sector \((n,i)\) and waits for the outbound access link to be activated, upon which it leaves the system. If \(m\
eq n\), the packet is put into the backhaul buffer in a sector linking node \(m\) with node \(n\) or a Tier 3 node through which node \(n\) can be reached, etc. The process continues until the packet leaves the outbound access buffer in node \(n\). By the total packet delay in the downlink, we understand the time from the instant the packet joins a buffer in Node 1 to the instant it leaves the system via an access link.