End-to-End Delay Analysis for Fixed Priority Scheduling in WirelessHART Networks Abusayeed Saifullah, You Xu, Chenyang Lu, Yixin Chen

2 Motivation  Challenges in process control  Harsh environment  Real-time and reliability requirements  WirelessHART  Open standard for process industries  Fixed-priority transmission scheduling for real-time flows in WirelessHART networks  Fast schedulability analysis is required for acceptance test, admission control, and adaptation Process control Controller Wireless Sensor- Actuator Network

3 WirelessHART Network Model  Components  A gateway, field devices (sensors and actuators)  A network manager: creates and distributes the schedule  Time Division Multiple Access  Spectrum diversity  Multi-channel (defined in IEEE )  No spatial reuse of the same channel in a time slot  Route diversity 3

Real-Time Flows  Sensor-controller-actuator flow through multiple routes  Considered an individual flow through each route  A set of flows F={F 1, F 2, …, F N } ordered by priorities  Each flow F i is characterized by  A source (a sensor node), a destination (an actuator), route through the gateway (where controllers are located)  A period P i  A deadline D i ( ≤ P i )  Total number of transmissions C i along the route 4 highest lowest priority

Scheduling Problem  Fixed priority scheduling  Transmissions happen based on the priorities of their flows  Flows are schedulable if R i ≤ D i F i F  Goal: efficient end-to-end delay analysis  Establish an upper bound of end-to-end delay for each flow  Sufficient schedulability analysis: any set of flows deemed schedulable by the analysis is indeed schedulable 5 end-to-end delay of F i deadline of F i

End-to-End Delay Analysis  A lower priority flow is delayed due to  Channel contention: when all channels are assigned to higher priority flows in a slot  Conflict: its transmission and a transmission of a higher flow involve the same node and 5 are conflicting 4 and 5 are conflicting and 4 are conflict-free  Each delay is analyzed separately  Consider both types of delays in the analysis to establish an upper bound of end-to-end delay of each flow

Delay due to Channel Contention  Observation: WirelessHART transmission scheduling vs. global multiprocessor scheduling  Similarity: channel contention  Difference: transmission conflicts  Channel contention: map to multiprocessor scheduling  Each channel  a processor  Each flow F i  a task with period P i, deadline D i, execution time C i  Built on state-of-the-art response time analysis for global multiprocessor scheduling 7

 When 2 transmissions, one from lower priority flow F l and one from higher priority flow F h, conflict, F l is delayed  Q(I,h): total transmissions of F h sharing nodes with F l  In worst case, an instance of F h can delay F l by Q(l,h) slots  In the figure, Q(l,h) = 5, and F h can delay F l by 5 slots Delay due to Conflict 8 F l delayed by 2 slots F l delayed by 2 slots F l delayed by 1 slot

Precise Bound on Conflict Delay 9 Total number of MCP of length at least 4 Length of an MCP  Q(I,h) often overestimates the delay  Δ(I,h): more precise bound of delay an instance of F h can cause on F l  Maximal common path (MCP) between two flows  Maximal overlap on their routes  On an MCP, F l can be delayed by F h at most by 3 slots Q(I,h)=8 but Δ(I,h)=3

Total Delay due to Conflict  In a time interval of t slots the delay caused by F h on F l is upper bounded by  The total delay of F l due to transmission conflicts with higher priority flows is upper bounded by 10 P h is period of F h hp(F l ) is the set of higher priority flows of F l

Complete Analysis  R k ch : upper bound of end-to-end delay of F k considering that it is delayed only due to channel contention  R k ch,con : upper bound of end-to-end delay of F k considering that it is delayed due to both channel contention and transmission conflict  For every flow in decreasing order of priority  Step 1: derive an upper bound assuming it does not conflict with any higher priority flow.  Step 2: incorporate the conflict delay into the bound of Step 1 11 conflict channel contention

Step 1 for Flow F k  Ω k ( x ): total delay that the higher priority flows can cause on F k due to channel contention in an interval of x slots  Determined considering the end-to-end delay R i ch,con of every higher priority flow F i  Analyzed based on the response time analysis for multiprocessor (Guan et al. RTSS 2009)  R k ch is the minimum value of x determined by a fixed-point algorithm in equation 12 m : total number of channels Number of transmissions along the route of F k

Step 2 for Flow F k  R k ch,con is the minimum value of y that solves the following equation using a fixed-point algorithm 13 End-to-end delay of F k assuming it does not conflict with any higher priority flow Total delay of F k due to conflict with higher priority flows  If x (in Step 1) or y (in Step 2) exceeds D k (deadline), the algorithm terminates and reports the case as unschedulable The analysis runs in pseudo polynomial time.

Simulations  Real network topologies  Testbed of 48 TelosB motes  Random topologies  Priority assignment policies  Deadline monotonic (DM)  Proportional Deadline monotonic  Metrics  Acceptance ratio  Pessimism ratio 14 Testbed topology

Acceptance Ratio (Testbed Topology) 15  Number of channels=12  Priority assignment policy: DM

Pessimism Ratio (Random Topology) 16

Conclusion  WirelessHART is an important standard for process monitoring and control  Efficient end-to-end delay analysis is required for  Acceptance test  Online admission control  Adaptation to network and workload dynamics  Contribution: The first efficient delay analysis for fixed- priority scheduling in WirelessHART networks  Evaluation on testbed topology and random topologies  Estimated bounds are safe and reasonably tight  Effective under various priority assignment policies 17