End-to-End Delay Analysis for Fixed Priority Scheduling in WirelessHART Networks

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

2. Motivation Process control • 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 analysisis required for acceptance test, admission control, and adaptation Wireless Sensor-Actuator Network Controller

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 802.15.4) • No spatial reuse of the same channel in a time slot • Route diversity 3

4. Real-Time Flows • Sensor-controller-actuator flow through multiple routes • Considered an individual flow through each route • A set of flowsF={F1, F2, …, FN} ordered by priorities • Each flow Fi is characterized by • A source (a sensor node), a destination (an actuator), route through the gateway (where controllers are located) • Aperiod Pi • A deadline Di ( ≤ Pi) • Total number of transmissionsCi along the route highest lowest priority

5. Scheduling Problem • Fixed priority scheduling • Transmissions happen based on the priorities of their flows • Flows are schedulable if Ri ≤ DiFi 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 end-to-end delay of Fi deadline of Fi

6. 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 2 1 3 4 5 1 and 5 are conflicting 4 and 5 are conflicting • Each delay is analyzed separately 3 and 4 are conflict-free • Consider both types of delays in the analysis to establish • an upper bound of end-to-end delayof each flow

7. 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 flowFi a task with period Pi, deadline Di, execution time Ci • Built on state-of-the-art response time analysis for global multiprocessor scheduling

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

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

10. Total Delay due to Conflict • In a time interval of t slots the delay caused by Fh on Flis upper bounded by • The total delay of Fl due to transmission conflicts with higher priority flows is upper bounded by Ph is period of Fh hp(Fl) is the set of higher priority flows of Fl

11. Complete Analysis • Rkch : upper bound of end-to-end delay of Fk considering that it is delayed only due to channel contention • Rkch,con : upper bound of end-to-end delay of Fk 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 channel contention conflict

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

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

14. 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 Testbed topology

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

16. Pessimism Ratio (Random Topology)

17. 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