## 1 Introduction  
The bandwidth and delay requirements in the Fifth-Generation (5G) cellular networks are an order of magnitude stricter than in the currently deployed systems [1, 2, 3]. Furthermore, the microwave frequency bands utilized for mobile communications today are close to exhaustion and become less efficient with respect to increasing quality of service (QoS) needs [4]. As a result, the 3 rd Generation Partnership Project (3 GPP) standards organization has recently specified millimeter wave communication (mmWave) New Radio (NR) technology capable of operating in the band from 24 to 100 GHz. Although the mmWave band allows for much higher transmission rates, its use is challenging due to a short propagation range and a strong susceptibility to blockage [5, 6]. For this reason, 5G mmWave NR base stations (BS) must be located more densely, leading to high network deployment costs. To alleviate this problem, self-backhauled networks have been proposed as a solution to this problem. 3 GPP calls the corresponding technology Integrated Access and Backhaul (IAB) and specifies it in TR 38.874 [7] and TS 38.401 [8]. The key feature of IAB is multi-hop wireless backhauling. In an IAB deployment, only some BSs (called IAB-donors) have a wired backhaul to the core network, whereas others (IAB-nodes) are wirelessly backhauled to IAB-donors, directly or hop-by-hop via multiple IAB-nodes. In such a setup, the end-to-end packet delay may greatly increase due to multi-hop transmission and the related queuing [9]. The problem is made even more difficult by the half-duplex communication requirements for the current wireless systems [10]. Accordingly, the IAB-nodes and IAB-donor cannot simultaneously transmit and receive information over multiple antennas they are associated with. The IAB-donor must carefully plan and schedule the uplink and downlink, as well as access and backhaul transmissions in the whole network. Separation of uplink and downlink transmission (half-duplex IAB) can be performed via time, frequency, or spatial division multiplexing (TDM [11], FDM [12], SDM [13]). According to 3 GPP TR 38.874 [7], TDM should be considered as the preferred option. The use of TDM means that each IAB-node, at each time instant, must either receive traffic or transmit. Moreover, in accordance with 3 GPP TS 38.174 [14], each antenna, at each time instant, can work either for access or for backhaul. 3 GPP IAB is the first architecture for commercial cellular networks to use multi-hop radio transmission. It must satisfy the quality of service requirements set by the ITU-R and 3 GPP standards, one of which is the end-to-end delay. In multi-hop systems, the end-to-end delay requirement presents the main design challenge, especially given the constraints of half-duplex transmission. The arising time allocation problem between access and backhaul was tackled, for instance, via convex programming [15; 16] and heuristics [17]; however, these solutions are suitable for special cases only. In [18], the authors conducted demo end-to-end simulations using ns-3, concentrating on the upper layers of the protocol stack. The performance measures such as the average delay to retrieve an HTTP web page and network bandwidth were compared for deployments consisting of only IAB-donors, of only IAB-donors fully connected by a wired connection, and for typical IAB. The study demonstrated a significant reduction in latency when IAB-nodes are present in the network, close to the values that are collected from a fully meshed wired network consisting of IAB-donors. The authors noted the influence of the network topology and route selection schemes on its performance indicators, but did not take this into account when modeling and using abstract deployments. The work in [19] was devoted to the cross-layer modeling of routing and resource allocation. When solving these problems, the authors addressed the transmission delay, taking it into account when formulating the optimization problem.