Load Balancing: Can't understand the summation term

[zak100]

TL;DR

Hi,
I am trying to understand a summation term related to load balancing

I can’t understand the term Summation of (j tj). Are we multiplying j and tj. But the text is not talking about multiplying, it says”Total processing time

Somebody please guide me.

Zulfi.

 

[jedishrfu]

the summation just sums the terms.

$\sum_{n=0}^{10}{(2n+1)} = 1 + 3 + 5 + 7 + ... + 21$

in your case:

$\sum_{j=1}^{m}{(t_j)} = t_1 + t_2 + t_3 + ...$

but they left out the limits of j=1 to m.

 

[zak100]

Hi,
Thanks for your response.

You mean its not multiplying j with $t_j$
$\sum_j t_j$

Thanks.

God bless you.

Zulfi.

 

[jedishrfu]

The j is saying that is the index the summation indexes over rather like a “for”loop in programming j is the “for” loop index.