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Consider a uniprocessor system executing three tasks T1,T2 and T3 each of which is composed of an infinite sequence of jobs which arrive periodically at intervals of 3, 7 and 20 milliseconds, respectively.

What does the which in the above sentence refer to ?

My approach

T1 comprises of infinite jobs (say J1 ,J2,J3) etc . Similarly T2(J1,J2,J3..) and T3(J1,J2,J3...) Then

  • When which refer to each job instances of T1 then it should be T1(0,3,7,20,23) T2(0,3,7,20,23) T3(0,3,7,20,23) etc
  • When which refer to each job instances of 3 tasks then T1 should be T1(0,3,6,9,12...) T2(0,7,14,21,28...) T3(0,20,40,60,80) etc.

PS: I need to know what does which referring to as well as the value of T1 according to your interpretation of which

  • The important word here isn't "which" or "jobs", but "respectively". Task T1 has jobs which arrive at intervals of 3 ms. T2 has jobs arrive at intervals of 7. T3, 20. "Respectively" indicates that each task has its own interval, and that the order of both lists is consistant. – Gary Botnovcan Jan 10 '17 at 9:53
  • There is a grammatical error in your example which is confusing. The expression each of which is composed of an infinite sequence of jobs is a non-defining (non-restrictive) relative clause, and as such must be set off with commas. That makes it a supplement, a non-essential piece of information, so the noun phrase it contains, an infinite sequence of jobs, cannot be the antecedent of "which". So, finally, I'd say that "which" refers to the noun phrase three tasks T1,T2 and T3 – BillJ Jan 11 '17 at 14:19
  • Thanks @BillJ . Now, one added question to the discussions. How can we modify the above sentence so that "which" will be refering to " each of which is composed of an infinite sequence of jobs" – Akhil Nadh PC Jan 12 '17 at 7:19
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Your question (nor the original at geeksforgeeks.org for that matter, the whole thing being quite cryptic and ambiguous as far as I can make out), is not sufficient to answer with numbers in the way you are asking. For example, where are you getting 3,6,9,12 from? Remember this is an English language forum, not a computer architecture one! :-)

Nevertheless, regardless of the computer scheduling specifics, the second "which" (i.e. the one you have bolded and are asking about) can be taken to refer only to the word "jobs" in "infinite sequence of jobs". Compare your sentence with the following I've constructed to have the same syntactic structure:

Consider a room containing three boxes each of which contains a different number of kittens which jump out of and then back into their respective boxes at random intervals.

The first "which" refers to the boxes, and the second "which" refers to the kittens.

  • Comments are not for extended discussion; this conversation has been moved to chat. – snailcar Jan 11 '17 at 17:05
  • Well I think we were nearing the end of a pretty focused discussion aimed at coming up with a good final answer for the OP. I wouldn't class that exactly as "extended", but fair enough. However, unfortunately neither I nor some SE gods have ever been able to get chat working from my SE account. So this move means I'm out. But I think @Akhil had plenty of good advice anyway, so I'm sure he'll get his question resolved regardless. – tkp Jan 12 '17 at 4:52
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The grammar of the word "which" will not help you answer your question. The definition of the word "respectively" will.

Even the simplest of searches reveals that the two lists can be mapped in a direct one-to-one correspondence, in exactly the orders presented.

In this context, the jobs of task T1 arrive in intervals of 3 milliseconds, the jobs of task T2 arrive in intervals of 7 milliseconds, and the jobs of task T3 arrive in intervals of 20 milliseconds.

The sentence that you've cited says nothing about when each countdown clock starts. I assume that you're looking at GATE2015-1_46 on GATE Overflow. The rest of that question states that all tasks initially arrive at the beginning of the first millisecond. From this, we know that the jobs of T1 arrive at: 1st ms, 4th ms, 7th ms, 10th ms and so on. Jobs of T2 arrive at: 1st ms, 8th ms, 15th ms, 22nd ms and so on. Jobs of T3 arrive at 1st ms, 21st ms, 41st ms, 61st ms and so on.

I repeat, the clocks start at the first millisecond, not the "zeroth". If you don't keep your terms consistent, you can easily run into what programmers call "a fencepost error".

There is one more instance of the word "respectively" in this question. Unless you understand the word "respectively", you will not know how long each task takes to complete an instanced job.

The grammatical ambiguity that I cannot easily resolve is related to the priority of the tasks. Priority and frequency are inversely proportional given the text of the question. But, does a high frequency universally imply a low period, or does the author of the question mistake period and frequency as synonyms? In the business world, I'd ask for clarification. In academia, I'd simply assume that frequency and period are inverse. The inverse of an inverse brings you back to where you started. So, period 20 is the highest priority (lowest frequency), period 7 is a middling priority, and period 3 is the low priority (and the highest frequency).

Any pending job for task T3 is done before any pending job for task T2. Any pending job for task T2 is done before any pending job for task T1. If you don't understand why, I should (at least in theory) suggest you also research the term preemptive. If your search engine is as bad as mine, you might miss the intended implication: that the preemptive thing happens before another, without the other's consent. The highest-priority item, regardless of the order in which it is received, is handled first.

That's as complete a description of the English as you could wish for. Anything beyond this is clearly in non-ELL realms, such as mathematics and programming.

  • 1
    Thanks for confirming " respectively " . But answer given above is emphasizing on "which" . Actually I dont want to bring the technical terms to English forum . If I get the proper interval of Tasks i could myself solve the problem. And YES if you consider the lines before what I have stated from GATE OVERFLOW . One will have to start from milli second 1. Like I told ,, I dont want to bring such technical terms into picture . I simply wanted to know the meaning of the sentence :) – Akhil Nadh PC Jan 11 '17 at 7:35

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