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The minimum RTT to Peshawar and to Islamabad (left hand graph) appears to have reduced dramatically after April 2010. This is partially due to bringing on new hosts that have lower RTT between them. In April there was a factor of 2 increase in the number of host pairs (this is seen in the middle and right hand graphs).
If we select the same host-pairs in both say Nov 2010 and April 2010 then the improvement ((ipdv(Apr)-ipdv(Nnov))/ipdv(Apr) in IPDV is about 47%. Thus things have improved with lower IPDVs for the selected host pairs, or in other words the improvement is not just that more recntly added hosts had lower IPDVs.
Throughput
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We derive the throughput from the loss and RTT measurements as _throughput = 1460*8\[bits\]/(RTT\[msec\]*sqrt(loss)) kbits/s. _ |
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The speed of light in fibre is roughly _0.66*c_ (where c is the speed of light in vacuum). Using 300,000km/s as c this yields Round Trip Distance = _RTD\[km\]=100\[km/msec\]*minimum_RTT\[msec\]_ as a way to derive the distance between the two hosts making the minimum RTT measurement. This assume the minimum RTT is only affected by the transmission of light in the fibre (i.e. no delays due to network devices such as routers) and that the fibre route is direct (a great circle route) between the two hosts. The use of minimum RTT is meant to eliminate most network device delays for reasonable fast circuits (e.g. at 100Mbits/s assuming no queingqueuing the router delays is ~ 0.12msec). To accomodate these extra delays one introduces a function alpha, so that _RTD\[km\]=alpha*100\[km/msec\]*minimum_RTT\[msec\]._ Large values of alpha close to one indicate a direct path, and small values usually indicate a very indirect path. This assumes no queuing and minimal network device delays. The chart below shows the alpha values between regions in Pakistan. It is based on the minimum RTTs seen between Dec 2009 and Nov 2010. |
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Average Alpha measured between regions of Pakistan with the standard deviations (as error bars) and the number of host pairs contributing to the measurement. Spreadsheet |
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It is seen that the links between Karachi and Lahore, Karachi and Islamabad, and Karachi and Peshawar are very direct (values of alpha close to one) and are also very consistent (low values of the standard deviations). Islamabad and Quetta apparently are connected very indirectly (low value of alpha). Looking at the map at the top this makes sense since the route goes via Karachi in the South and then back northwards to Quetta. The links between Islamabad and Lahore, Islamabad and Peshawar and Lahore and Peshawar all have lower vales of alpha and thus appear to be more indirect and have higher variability. A common element in the links between these three regions is that they all pass through Islamabad (see map at top).
Understanding the large variations Jan-Apr 2010
We were concerned about the large variations seen in January 210 through May 2010. Zafar suggested the problem might be to do with the congestion of the links. Jitter (Inter Packet Delay Variation - IPDV) tends to be a good indicator of queuing/congestion, so he suggested looking at this.
The IPDV shows similar behavior to the average RTT:
We then looked to see what portion of the larger IPDV early in the year was related to adding new monitoring and remote hosts. If we select the same host-pairs in both say Nov 2010 and April 2010 then the improvement ((ipdv(Apr)-ipdv(Nnov))/ipdv(Apr) in IPDV is about 47%. Thus things have improved with lower IPDVs for the selected host pairs.
Unfortunately we do not have traceroutes between all the sites to see if they have changed over time.
Comparing for Nov 2010 the average IPDV for all pairs with that for just the pairs in both April 2010 and November 2010 one gets 5.13ms verses 4.58. Thus some of the reduction appears to be due to the new hosts added.
, prior to this there are less than 100. It is suspected that this is partially the cause of the more stable values of IPDV following this date.
Returning to the average RTT graph, we believe it is less confusing to mainly focus on the data from May 2010 onwards, in order to remove the effects of small statistics. In this case, the average RTTs from Jun through November 2010 have been pretty flat.
Differences in RTTs for regions
Looking at the data for November 2010 it is seen that the average RTts to Karachi and Lahore are two to three times less than those to Quetta, Islamabad and Peshawar. This needs to be investigated.