looping over observations - retaining the values from previous observations

Hello all
I am trying to find out the length of wait for each individual for a service given we know the average length of wait in a queue. I hope the example data will make it clear what I am trying to find out.

Code:

. version
version 13.1

Code:

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(start_time los_in_queue end_time)
4 2 .
. 5 .
. 6 .
. 7 .
. 8 .
end

I want the data to look like:

obs.	start_time	los_in_queue	end_time
1	4	2	6
2	6	5	11
3	11	6	17
4	17	7	24
5	24	8	32

Basically, I want to retain the end_time of the first observation as a start_time for the second observation an so on.

My attempt overrides all previous values by the last value. Thanks in advance for pointing out where I went wrong.

Code:

. local N = _N
. local counter=1
. forvalues i = 1/`N' {
  2.      replace end_time = start_time[`i']+los_in_queue[`i']
  3.                 list start_time-end_time
  4.                 local i=`i'+1
  5.                 replace start_time = end_time[`i'-`counter']
  6.                 }
(5 real changes made)

. clist

          start_time     los_in_queue         end_time
  1.              32                2               32
  2.              32                5               32
  3.              32                6               32
  4.              32                7               32
  5.              32                8               32