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Response-time Calculation and Priority Assignment with Integer Programming Methods



Björn Lisper, Peter Mellgren

Publication Type:

Conference/Workshop Paper


Proc. Work-in-progress and Industrial Sessions, 13th Euromicro Conference on Real-Time Systems


Exact response-time calculation for cyclical tasks with fixed priorities requires that equations involving ceilings are solved. These equations are usually solved iteratively. For simple response-time problems with fixed priorities the iterations are guaranteed to converge if there is a solution. For more complex cases, however, like scheduling of real-time tasks in distributed systems, the iterative method does not always provide the best solution, in particular if the combined response-time/optimal priority assignment problem is considered. We show how to reformulate equations with ceilings into integer linear programming problems, which can be solved with known optimization methods. This reformulation is directly applicable to classical exact response-time calculation. We also show how optimal assignment of priorities can be incorporated in the model, which turns the optimization problem into a bilinear integer programming problem. A possible application is holistic scheduling with optimal priority assignments in distributed real-time systems.


author = {Bj{\"o}rn Lisper and Peter Mellgren},
title = {Response-time Calculation and Priority Assignment with Integer Programming Methods},
editor = {Eduardo Tovar and Christer Norstr{\"o}m},
pages = {13--16},
month = {June},
year = {2001},
booktitle = {Proc. Work-in-progress and Industrial Sessions, 13th Euromicro Conference on Real-Time Systems},
url = {}