Geodesic
The problem of two periodic tasks
Diskretnaya Matematika, Tome 3 (1991) no. 4, pp. 16-23 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study existence conditions for an admissible schedule with interruptions on one processor for a system of two tasks $(p_1,d_1,c_1)$ and $(p_2,d_2,c_2)$, in which each of the tasks $i\in\{1,2\}$ becomes ready for the $k$th execution at time $(k-1)p_i$, must be completed before $d_i+(k-1)p_i$ and requires for its execution $c_i$ units of processor time. We present two methods for testing the existence of an admissible schedule, including a polynomial method for the number of binary digits necessary for coding input data, and an algorithm of Euclidean type. 
@article{DM_1991_3_4_a2,
     author = {D. S. Gershuni},
     title = {The problem of two periodic tasks},
     journal = {Diskretnaya Matematika},
     pages = {16--23},
     year = {1991},
     volume = {3},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1991_3_4_a2/}
}
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D. S. Gershuni. The problem of two periodic tasks. Diskretnaya Matematika, Tome 3 (1991) no. 4, pp. 16-23. http://geodesic.mathdoc.fr/item/DM_1991_3_4_a2/