Foundations — Real-time constraints — hard and soft deadlines

5.5.12 · D1 · Coding › Embedded Systems & Real-Time Software › Real-time constraints — hard and soft deadlines

Yeh Real-time constraints — hard and soft deadlines ka "toolbox unpack karo" wala page hai. Parent note tumhare saamnay bahut saare letters phenkta hai — $r_i$, $D_i$, $R_i$, $C_i$, $T_i$, $n$, $U$, $\lceil \cdot \rceil$, $\sum$. Yahan hum har ek ko, order mein, earn karte hain, pehle se kisi formula mein use hone se pehle.

Step 0 — "Task" aur "job" kya hota hai?

Kisi bhi symbol se pehle, humein woh cheez chahiye jo symbols describe karti hai.

Ek factory worker (task) ki picture socho jo din mein kaafi baar wahi kaam karta hai (har kaam ek job hai). Hum tasks ko subscript $i$ se label karte hain: task 1, task 2, task 3 — likha jata hai ${\text{task}}_i$. Subscript sirf ek name tag hai taaki hum "$i$-wey task" ke baare mein baat kar sakein bina har ek ki picture banaaye.

Step 1 — Timeline: cheezein kab hoti hain

Real-time ki har cheez ek single horizontal time axis par rehti hai, seconds daayein taraf badhte hain. Ek job ke liye teen moments matter karte hain.

Teen alag ideas kyun? Kyunki "kaam kab arrive karta hai", "kab due hai", aur "actually kitna time laga" genuinely alag questions hain, aur deadline teeno ko relate karta hua ek statement hai.

Relative vs absolute deadline

Parent likhta hai $d_i=r_i+D_i$. Ise algebra ki jagah picture ki tarah padho:

Step 2 — Kaam kitna time leta hai? WCET $C_i$

Ek job ko finish karne ke liye kuch CPU time chahiye. Lekin woh amount run to run vary karti hai — cache miss, longer input, branch lena — toh ek akela number kaam nahi karega. Humein choose karna hoga ki kaun sa number.

Note karo $C_i$ ek duration hai (seconds of CPU), bilkul $R_i$ aur $D_i$ ki tarah. In teeno "seconds" quantities ko straight rakhna aadhi battle hai.

Step 3 — Repeating work: period $T_i$

Bahut saare real-time tasks periodic hote hain — yeh har fixed interval mein ek fresh job release karte hain. Yeh spacing period hai.

Periodic tasks aur event-triggered ones ke beech ka difference Periodic vs Aperiodic Tasks mein cover kiya gaya hai. Abhi ke liye picture hold karo: ek metronome jo har $T_i$ seconds mein tick karta hai, aur har tick par $C_i$ tak length ki ek job appear hoti hai.

Step 4 — CPU ka share: utilisation $U_i$ aur $\sum$

Ab hum woh money question pooch sakte hain: ek task processor ka kitna hissa khaata hai?

$T_i$ length ke ek period mein, task ko (worst case) $C_i$ seconds of CPU chahiye. Us period ka woh fraction jo task par spend hota hai:

Ratio kyun? Kyunki "2 ms of work" ka koi matlab nahi jab tak pata na ho yeh kitni baar repeat hoti hai. 2 ms har 10 ms mein light hai; 2 ms har 3 ms mein heavy hai. Ratio $C_i/T_i$ ongoing demand capture karta hai, jo exactly wahi hai jo shared CPU ko care karna chahiye.

Summation symbol $\sum$

Kai tasks combine karne ke liye hum unke shares add karte hain. Parent likhta hai $U={\sum }_{i=1}^n\frac{C_i}{T_i}$, jahan $n$ Step 0 se task count hai.

Step 5 — Ceiling symbol $\lceil x\rceil$

Parent ka exact test $\lceil \frac{R_i}{T_j}\rceil$ use karta hai. Woh funny bracket aakhri symbol hai jo unlock karna hai.

Poori preemption count logic RTOS scheduler design aur Rate-Monotonic Scheduling mein belong karti hai; yahan humein sirf symbol padhna tha.

Foundations topic ko kaise feed karte hain

Top to bottom padhna: raw ideas (task, WCET, period, symbols) combine hokar deadline test aur utilisation sum banate hain, jo saath milkar deadlines ki classification aur schedulability proofs ko power karte hain jo parent note build karta hai.

Equipment checklist

Daayein side cover karo aur reveal se pehle jawab do.