Abstract
As embedded time-triggered applications have widely replaced mechanical systems in modern automobiles, holistic scheduling of tasks and messages of such applications on in-vehicle networks has become a critical issue. For offering QoS (Quality of Service) guarantees, the holistic schedule must satisfy numerous constraints such as protocol specifications, delay constraints and precedence constraints between tasks schedules and messages transmissions. Existing approaches to this problem search through a vast design space of all possible joint task and message schedules. This leads to a high complexity and limits the scalability of such approaches for scheduling the large scale systems. To cope with this problem, we propose an approach that divides the holistic scheduling problem to two sub-problems: the sub-problem of message scheduling and the sub-problem of task scheduling, while precedence relations and end-to-end information passing between task instances and messages are preserved and the end-to-end deadlines are guaranteed. This helps to reduce the workload on the problem solvers and improves efficiency and scalability. In the first sub-problem, our approach optimizes scheduling the set of messages and allocates time windows for scheduling each task with respect to precedence constraints, end-to-end deadlines and FlexRay protocol specifications. The length of each time window helps to preserve the respective tasks schedulability and to provide flexibility for both task and message scheduling. The objective is defined with respect to extensibility issues. In the second sub-problem, our approach optimizes schedule of the set of tasks with respect to their allocated time windows and timing constraints. The objective is defined with respect to latency issues. We optimize the solution to each sub-problem using Mixed Integer Linear Programming optimization framework. Performance evaluations show that, compared with existing holistic scheduling approaches, our approach is more scalable and obtains better solutions in a reasonable amount of time.
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Abbreviations
- L :
-
length of FlexRay cycle
- H :
-
number of communication cycles in a FlexRay cycle
- l slot :
-
length of static slot
- n slot :
-
number of static slots in static segment
- l CC :
-
length of communication cycle
- G :
-
application DAG
- V :
-
set of tasks
- E :
-
set of messages
- τ i :
-
i-th task in a given application
- ECU(τ i):
-
ECU that hosts τ i
- HP i :
-
set of tasks with higher priority than τ i running in ECU(τ i)
- T i :
-
period of invocations of τ i
- C i :
-
execution time of τ i
- D i :
-
relative deadline of τ i
- WCRT(τ i):
-
worst case response time of τ i
- τ i,p :
-
p-th job of the task τ i
- M :
-
set of messages communicating on the bus
- m i,p :
-
generated message by τ i,p
- r i. :
-
repetition rate of m i
- w i :
-
size of message m i in bits
- G=(V,E):
-
DAG of application g
- Instance-Graph(g):
-
instance graph of application g
- SC i,p :
-
set of successors of τ i,p running in ECU(τi)
- PD i,p :
-
set of predecessors of τ i,p running in ECU(τi)
- V i,p j,q :
-
set of jobs in the path between m i,p and m j,q
- Reduced-Graph(g):
-
reduced DAG of Instance-Graph(g)
- tw i,p j,q :
-
time window assigned to jobs in V i,p j,q
- ltw i,p j,q :
-
length of time window tw i,p j,q
- D(m i,p,m j,q)max:
-
maximum required length for tw i,p j,q
- R i,j :
-
a lower bound for the length of tw i,p j,q
- u i :
-
assigned FID to m i
- b i :
-
assigned base cycle to m i
- X i,p k,n :
-
mapping of m i,p to a slot; true if m i,p is assigned to the k-th slot of the n-th CC
- \({A_{k,n,EC{U_e}}}\) :
-
ownership of a slot by an ECU; true if ECU e is assigned to the k-th slot of the n-th CC
- Φ i :
-
initial phase of task τ i
- a i,p :
-
arrival time of task instance τ i,p
- s i,p :
-
start time of task instance τ i,p
- f i,p :
-
finish time of task instance τ i,p
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Darbandi, A., Yoon, S. & Kim, M.K. Schedule construction under precedence constraints in flexray in-vehicle networks. Int.J Automot. Technol. 18, 671–683 (2017). https://doi.org/10.1007/s12239-017-0067-8
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DOI: https://doi.org/10.1007/s12239-017-0067-8