Joint deterministic scheduling for multiple coexisting industrial wireless sensor networks via multi–dimensional conflict graphs

The increasing deployment of Industrial Wireless Sensor Networks (IWSNs) in smart manufacturing often results in multiple networks operating concurrently in the same area. Without coordination, inter-network interference and inefficient spectrum use can undermine deterministic communication and violate strict reliability and latency requirements. This paper proposes a joint deterministic scheduling scheme for multiple coexisting IWSNs that schedules all networks within a unified time–frequency solution space, enabling concurrent exploitation of time-domain and frequency-domain resources. Specifically, coexistence scheduling is modeled using a multi-dimensional conflict graph (MDCG) that explicitly captures both intra-network and cross-network conflict relationships among candidate link transmissions. Based on the MDCG, the joint scheduling task is formulated as an integer optimization problem and transformed into finding a maximal independent set (MIS) to minimize the overall weighted end-to-end delay across all networks. Since MIS search in MDCGs is NP-hard, we further decompose the global problem into a sequence of hop-level maximum weighted independent set (MWIS) subproblems and develop an iterative hop-wise scheduling algorithm for efficient solving. Extensive simulations under different traffic patterns and coexistence scales show that the proposed method can reduce superframe length and end-to-end delay while improving resource utilization and schedulability compared with representative time-domain and frequency-domain coexistence schedulers.