36 lines
1.2 KiB
Typst
36 lines
1.2 KiB
Typst
#import "@preview/acrostiche:0.3.2": *
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#init-acronyms((
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"EBS": ("Equation-Based Scheduling",),
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))
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#align(center)[#text(size:2em)[Equation-Based Scheduling]]
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The principle of #acr("EBS") is to use a function to determine which task is allowed to communicate at anypoint in time.
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This principle provide a mathematically proovable way for each task to determine when to communicate.
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*Problem Statement:*
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#grid(
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columns: (1fr,15fr,1fr),
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[],[
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Given $n$ tasks $t_i, i in [0,n-1]$,
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and an array of $m$ time periods $A = [x_0, dots.h.c, x_(m-1)]$
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where each element $x_i in [t_0,dots.h.c, t_(n-1)]$ is the task allowed to communicate at time $tau_i$,
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provide a set of $n$ scheduling functions $S=(s_0,dots.h.c,s_(n-1))$ such that,
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for each time period $tau_i$, only $s_i(tau_i)$ associated with the task $t_i$ defined at by $A[i]$
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validates a pre-defined _enable_ condition.
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],
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[]
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)
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The _enable_ condition is any condition defined on the value of a scheduling function evaluated at a regular time.
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For example, a simple _enable_ condition can be the positivity of the value.
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In this case, the definition of the scheduling functions set is
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$
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S = cases(
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&s_i(tau_i) > 0 "if" A[tau_i] = t_i,
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&s_(j eq.not i) < 0 "else",
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)
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$
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