r of the control system with transmission time delay included in Sm,d when the data packet fails. Furthermore, when there is no transmission time delay, i.e. dm.n =0, the expression (14.5) can be written as (14.9) Then, the expression (14.8) can be written as (14.10) where the parameter of the control system without transmis- sion time delay when the data packet is successfully transmitted, and = is the 14 Optimizing Resource Allocation in URLLC for Real-Time Wireless Control Systems parameter of the control system without transmission time delay when the data packet transmission fails. The above discussion indicates that the proposed presented model in this section can be used regardless of transmission time delay. 14.2.2 Wireless Communication Model In the rest of this chapter, we focus on the uplink from the sensor to the BS, but the deriva- tions can be extended into the downlink transmission in a straightforward manner. For the convenience of discussion, we assume that the uplink is imperfect, which experiences trans- mission time delay and packet loss, and the downlink is perfect. The scenario with both uplink and downlink experiencing imperfect channel will be considered as future work. Specifically, M plants are randomly distributed in the coverage of the BS with radius R. In addition, each plant is sampled by a corresponding sensor. To avoid interference, we consider orthogonal frequency division multiple access (OFDMA), where each sensor is allocated multiple subcarriers within a given continuous bandwidth, each subcarrier can be allocated to at most one sensor, and the given bandwidths for different sensors are not overlapping. Furthermore, we consider flat fading channel, where the channel gains over different subcarriers for one sensor are approximately identical and perfectly known for the sensor. We assume that the number of allocated bandwidth and transmission duration for the m-th sensor at time index n are Nm,n and Tm.n' respectively. Then, for the m-th sensor at time index n, the received signa