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Another, less likely possibility is dynamic routing such that sometimes the traffic takes one route and at others a different one. You might set up a cronjob to gather traceroutes every 10 mins for a few days and look if you can see anything that could cause large changes. On the other hand I would expect these to be step changes.

Traceroutes from NUST to UETTaxila and from PCTL to UETTaxila were taken. 

The traceroute from NUST to UETTaxila is shown below:

No Format

[16:38:09 pinger]$ /usr/sbin/traceroute pinger.uettaxila.edu.pk traceroute to pinger.uettaxila.edu.pk (121.52.150.164), 30 hops max, 40 byte packets
 1  115-186-131-65.nayatel.pk (115.186.131.65)  0.729 ms   0.546 ms   0.695 ms
 2  115-186-128-177.nayatel.pk (115.186.128.177)  0.835 ms   0.703 ms   0.707 ms
 3  static.khi77.pie.net.pk (221.120.202.13)  23.949 ms   23.940 ms   23.903 ms
 4  static-10GE-KHI275-P01-SwA.pie.net.pk (202.125.128.173)  23.655 ms   23.651 ms   23.899 ms
 5  rwp44.pie.net.pk (221.120.254.13)  23.714 ms   23.640 ms   23.440 ms
 6  rwp44.pie.net.pk (202.125.148.136)  23.825 ms   23.813 ms   23.720 ms
 7  rwp44.pie.net.pk (221.120.236.106)  56.231 ms rwp44.pie.net.pk (221.120.236.110)  56.437 ms rwp44.pie.net
 8  * * *

We verified that the routers labelled KHI or khi are located in Rawalpindi and not not in Karachi.
There is a long delay between hops 2 and 3 as one moves from Nayatel to PIE. Since we believe both of these routers are relatively close to one another (i.e. < 20km) the delay caused by link distances should be ~ 1ms (1ms ~ 100km is roughly the RTT time for light in fibre or electrons in copper). Thus the delay of ~ 24ms is likely caused by congestion on the link that in turn causes queuing/buffering. A queuing delay of say 20ms on a 100Mbits/s link corresponds to a buffer length of ~ 330* 1500 Byte packets or a buffer space of ~ 500KBytes. The fact that the router interfaces at hops 5,6,and 7 all have the same name even though they have different addresses does not give a lot of confidence in where they are located. If they are all colocated, then the delay between hops 6 and 7 of ~ 32ms must be due to queuing. Unfortunately the traceroute appears to terminate in Rawalpindi before it reaches UETTaxila.

The traceroute from PCTL to UETTaxila is shown below:

No Format

C:\Users\zafar>tracert pinger.uettaxila.edu.pk
Tracing route to pinger.uettaxila.edu.pk [121.52.150.164] over a maximum of 30 hops:
  1    <1 ms     1 ms     1 ms  ZXDSL831II.home [192.168.1.1]
  2    33 ms    29 ms    30 ms  119.153.31.1
  3    19 ms    20 ms    18 ms  203.99.170.26
  4    19 ms    22 ms    18 ms  rwp44.pie.net.pk [221.120.253.9]
  5    20 ms    19 ms    20 ms  rwp44.pie.net.pk [202.125.148.136]
  6    55 ms    53 ms    45 ms  rwp44.pie.net.pk [221.120.236.106]
  7    42 ms    27 ms    24 ms  121.52.150.164.pern.pk [121.52.150.164]
Trace complete.

Again the route goes through the 3 router interfaces with the name rwp44.pie.net.pk. There is also a long delay between hops 1 and 20 suggesting congestion on the link since PERN and Rawalpindi are within 20km of one another\, in fact they may even be colocated.

On the other hand looking at the smokeping plot above there is an obvious reduction in minimum RTT on or about November 10th. Prior to that date it is about 60ms, after that date it drops to about 35ms.